An Observational Study of the Dynamic Martian Upper Atmosphere

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Aeronomy of Mars: An Observational Study of the Dynamic Martian Upper Atmosphere

Alexander Siddle

Department of Physics, Imperial College London

Submitted in partial fulﬁlment of the requirements for the degree of Doctor of Philosophy

December 2020 Declarations

I declare that all work presented in this thesis is my own, unless explicitly stated and referenced.

The copyright of this thesis rests with the author. Unless otherwise indicated, its contents are licensed under a Creative Commons Attribution-Non Commercial 4.0 International Licence (CC BY-NC). Under this licence, you may copy and redistribute the material in any medium or format. You may also create and distribute modiﬁed versions of the work. This is on the condition that: you credit the author and do not use it, or any derivative works, for a commercial purpose. When reusing or sharing this work, ensure you make the licence terms clear to others by naming the licence and linking to the licence text. Where a work has been adapted, you should indicate that the work has been changed and describe those changes. Please seek permission from the copyright holder for uses of this work that are not included in this licence or permitted under UK Copyright Law.

Alex Siddle - December 2020

The work presented in this thesis has contributed to two peer-reviewed published papers:

• Chapter 5 - A. G. Siddle et al. (2019). ‘Global characteristics of gravity waves in the upper atmosphere of Mars as measured by MAVEN/NGIMS’. in: Icarus 333, pp. 12–21

• Chapter 7 - A. G. Siddle et al. (2020). ‘Density structures in the Martian lower thermosphere as inferred by Trace Gas Orbiter accelerometer measurements’. In: Icarus, p. 114109

2 Abstract

The Martian upper atmosphere is highly dynamic over both short and long temporal and spatial scales. Our understanding of this region primarily stems from a wealth of data gathered both in-situ and remotely from spacecraft orbiting the Red Planet. In 2014 NASA’s Mars Atmosphere and Volatile Evol- ution (MAVEN) spacecraft began orbiting Mars with the primary objective to probe and characterise the upper atmosphere using composition data. Data from the Neutral Gas and Ion Mass Spectrometer (NGIMS) on board MAVEN has been utilised throughout this thesis.

Daily, monthly and seasonal density and temperature variations have been explored. An apparent day-night asymmetry is observed in temperature with the dayside typically 50-100 K warmer due to solar-EUV heating. Seasonal analysis has found densities to be signiﬁcantly enhanced around perihelion compared to other times throughout a Martian year. Perturbations in density and temperature proﬁles have been interpreted as vertically propagating gravity waves. Diurnal and seasonal variations of gravity wave characteristics have been examined with enhanced activity on the nightside. Fully understanding these features is required if the complexities of the upper atmosphere are to be fully grasped.

The Martian science community was fortunate to have a plethora of spacecraft at Mars during the June 2018 global dust storm. This thesis has examined the response of the upper atmosphere to such an important and rare event. A notable expansion of the atmosphere is observed whereby the upper atmosphere is raised by several kilometres, due to heating in the lower atmosphere. It is hoped that results can inform efforts made to model and predict the effects of a dust storm. For the first time, gravity waves at Mars during a global dust storm have been studied. Atmospheric perturbations are found to be significantly enhanced during the dust storm event.

During 2017/2018, ESA’s Trace Gas Orbiter (TGO) undertook its aerobraking phase to circularise itself into its science orbit. During this period, density data were able to be retrieved in the lower thermosphere from accelerometer measurements. The retrieval process was not part of this thesis; however, these data are used for the ﬁrst time. Standalone analyses are performed with these data but are also combined with results from MAVEN owing to the two spacecraft sampling similar regions concurrently. This overlapping period is exploited, and densities are hydrostatically connected to understand the entire thermosphere structure. By combining wave data, it has been inferred that shorter wavelengths are

3 saturated within the thermosphere, whereas larger wavelengths continue to grow with height.

4 Acknowledgements

First and foremost, to Ingo. You taught me so much over the years from trivial things like atmospheric physics to the more essential skills in life, such as how to think like a scientist, and more importantly how to have a laugh whilst you’re doing it. I could not have asked for a more friendly, knowledgeable and humourous supervisor. The pleasure is all mine.

Thanks must go to my original office mates – David, Ewen and Lars - who took me under their wing and provided much joy and humour throughout the many years we shared an office together. The arrival of the next cohort – Joe, Emma, Harry, Maks and Ned - saw us kicked out of our office. Truly unforgivable. Despite that, you’ve all added something unique to the research group, from the revival of SPAT walks to the introduction of MarsBallTM. A special mention must go to Joe, who followed my path from Lancaster to Imperial. As such, the patent profession awaits your imminent arrival. Next up are Earn, Pete and Sadie. You three were always up for a drink, whether it be coffee or alcohol. Both of which were crucial during the final months of my PhD. And finally my newest office mates Adrian, Ronan and Tom. I may have only spent half my time in the office, but it’s been a pleasure (and please keep the office plants alive!)

I want to thank Roger Yelle and Shane Stone for their guidance with everything and anything MAVEN/NGIMS related. It was a pleasure to meet you, and thank you for your support on my ﬁrst paper. Thanks must go to Sean Bruinsma and J-C Marty for undertaking the unenviable task of retrieving data from Trace Gas Orbiter. Such meticulous work often goes underappreciated. This wonderous dataset was the basis of my second paper, so for that and your support, I am incredibly grateful.

Thank you to Adam and Apostolos for assessing me throughout the years and thereby ensuring I had a chance of achieving a PhD. Thank you to Adam, Bob and Stephen for taking the time to read this thesis and asking me all the wrong questions. Joking aside, your pertinent comments have made this thesis a much stronger piece of work.

Thank you to all my family for the endless support over the past few years. It really does mean the world. There’s undoubtedly an art to asking about a PhD and then always remembering something needs doing within seconds of me opening my mouth.

5 Finally, thanks to Southeastern for rarely sticking to their timetable, allowing me more time to work on the train. Those extra few minutes certainly added up over the years - as did the price hikes.

6 Contents

List of Figures 11

List of Tables 14

Abbreviations 15

1 Introduction 17 1.1 Introduction...... 17 1.2 Motivation for Studying Mars...... 18 1.3 Previous Observations of Mars...... 18 1.3.1 Pre-Spacecraft Observations...... 18 1.3.2 Previous Spacecraft Observations...... 19 1.4 Mars Planetary Properties...... 21 1.5 Atmospheric Structure...... 24 1.5.1 Density Structure...... 24 1.5.2 Temperature Structure...... 26 1.6 Martian General Circulation Models...... 33 1.6.1 Laboratoire de Météorologie Dynamique Mars Climate Database...... 33 1.6.2 Other Martian General Circulation Models...... 34 1.7 Gravity Waves...... 36 1.7.1 Gravity Wave Generation...... 36 1.7.2 Gravity Wave Evolution...... 37 1.7.3 Gravity Wave Observations...... 39 1.7.4 Modelling Gravity Waves...... 40 1.8 Dust Storms...... 41

7 CONTENTS

1.8.1 Dust Storm Observations...... 41 1.8.2 Dust Storm Theory...... 44 1.9 Response of Upper Atmosphere to Dust Storms...... 46 1.10 Open Questions...... 48 1.11 Summary...... 49

2 Instrumentation and Data 50 2.1 Introduction...... 50 2.2 The Mars Atmosphere and Volatile Evolution Mission...... 50 2.2.1 Spatial and Temporal Coverage...... 52 2.2.2 The Neutral Gas and Ion Mass Spectrometer...... 52 2.2.3 Accelerometer...... 56 2.2.4 Comparison Between NGIMS and ACC Data...... 58 2.3 The ExoMars Mission...... 61 2.3.1 Trace Gas Orbiter...... 62 2.3.2 Rosalind Franklin Rover...... 64 2.4 Concurrent MAVEN and ExoMars Data...... 64 2.5 Summary...... 66

3 Data Analysis and Model Comparison 67 3.1 Introduction...... 67 3.2 Deriving Temperature Profiles From Density Data...... 67 3.3 Drawbacks of Current Temperature Derivation Technique...... 70 3.4 Comparison Between Derived and Extracted MCD Temperature Profiles...... 71 3.5 Comparison Between MCD and In-Situ Density Data...... 74 3.5.1 Comparison with Viking Landers’ Densities...... 74 3.5.2 Comparison with NGIMS Densities...... 75 3.6 Peak Offset in TGO Profiles...... 79 3.7 Summary...... 82

4 Background Density and Temperature Analysis 83 4.1 Introduction...... 83 4.2 Averaging Temperature Proﬁles...... 84

8 CONTENTS

4.3 Investigating Diurnal Temperature Variations...... 85 4.4 Investigating Diurnal Horizontal Temperature Gradients...... 90 4.5 Investigating the Eﬀects of the 27-Day Solar Cycle on Atmospheric Density...... 92 4.6 Investigating Seasonal Density and Temperature Variations...... 97 4.6.1 Identifying Regions Sampled Multiple Times by MAVEN...... 97 4.6.2 Density Variability with Season...... 101 4.6.3 Temperature Variability with Season...... 103 4.6.4 Southern Polar Warming...... 106 4.7 Summary...... 109

5 Gravity Waves in the Martian Upper Atmosphere 111 5.1 Introduction...... 111 5.2 Atmosphere Perturbations...... 112 5.3 Effects of Spacecraft Trajectory on Inferred Gravity Wave Wavelengths...... 114 5.4 Comparing Temperature and Density Perturbations...... 117 5.5 Altitudinal Effects on Gravity Waves...... 121 5.6 Global Characteristics of Gravity Waves...... 124 5.7 Effect of Topography on Gravity Waves...... 128 5.8 Comparing Wave Activity Over Successive Orbits...... 130 5.9 Wave Characteristic Comparison with Other Planets...... 135 5.10 Summary...... 138

6 Eﬀects of June 2018 Dust Storm on the Martian Upper Atmosphere 140 6.1 Introduction...... 140 6.2 Dust Storm Growth and Atmospheric Expansion...... 141 6.3 Dust Storm Decay...... 149 6.4 Dust Storm Eﬀects on Gravity Waves...... 155 6.5 Summary...... 158

7 Results from Trace Gas Orbiter Aerobraking Campaign 160 7.1 Introduction...... 160 7.2 Separation of Background and Wave Proﬁles...... 161 7.3 Background Density Structures...... 164

9 CONTENTS

7.3.1 TGO and MAVEN Densities...... 164 7.3.2 Comparison with Laboratoire de Météorologie Dynamique Mars Climate Database 167 7.4 TGO Temperatures...... 170 7.4.1 Deriving TGO Temperatures...... 170 7.4.2 Background TGO Temperatures...... 171 7.5 Waves...... 174 7.6 Combining MAVEN and TGO Data for Continuous Vertical Proﬁles...... 178 7.6.1 Comparing TGO and MAVEN Densities...... 179 7.6.2 Hydrostatically Connecting TGO and MAVEN Density Proﬁles...... 180 7.7 Summary...... 183

8 Conclusions and Future Work 185 8.1 Summary and Conclusions...... 185 8.2 Future Work...... 189

Appendices 193

A Visualisation of Regions Sampled Multiple Times by MAVEN 194

B Deriving Lower Atmosphere Heating Caused by a Dust Storm 195

C Software Used 197

D Data Used 198

Bibliography 199

10 List of Figures

1.3.1 Infographic of previous missions to Mars...... 20 1.5.1 Nine density profiles using MAVEN/NGIMS data for orbit 1064...... 27 1.5.2 Schematic diagram showing monochromatic radiation penetrating a plane and horizontally stratified atmosphere...... 28 1.5.3 Atmospheric temperature profile from entry phase of Mars Pathfinder...... 29 1.5.4 Energy balance terms for noon and midnight conditions from 1-D model...... 31 1.8.1 Early-storm and mid-storm photos taken during the June 2018 dust storm...... 43

2.2.1 MAVEN’s coverage in altitude, local time and latitude...... 53 2.2.2 Neutral Gas and Ion Mass Spectrometer schematic...... 54 2.2.3 Comparison of NGIMS and ACC density proﬁles...... 59 2.2.4 Boxplots of the ratio between NGIMS and ACC densities during the Deep Dip campaigns 60 2.3.1 TGO to MG05 density ratios for a proﬁle in January 2018...... 63 2.4.1 TGO and MAVEN’s coverage in altitude, local time and latitude...... 65

3.2.1 Diagram showing convergence of temperature profiles after applied offsets...... 69 3.3.1 Binned periapsis temperature difference between inbound and outbound profiles as a function of solar zenith angle...... 71 3.4.1 Comparison between derived and extracted MCD temperatures...... 73

3.5.1 Comparison between MCD and Viking CO2 and N2 densities...... 75

3.5.2 Ratio of CO2, Ar and N2 densities between NGIMS and MCD data...... 76

3.5.3 Ar/CO2 and N2/CO2 ratios derived from MCD and NGIMS data in solar zenith angle.. 78 3.6.1 TGO density proﬁle examples as function of time from closest approach and altitude.. 80 3.6.2 Time oﬀset as a function of ratio of latitude to longitude traversed during pass..... 81

11 LIST OF FIGURES

4.2.1 First Deep-Dip derived temperature profiles...... 85 4.3.1 Temperatures interpolated onto the 160 km, 170 km, 180 km, 190 km and 200 km altitude levels and shown against solar zenith angle...... 87 4.3.2 Average temperature profiles for solar zenith angles less than 30° and greater than 150° . 88 4.4.1 DD1 derived temperature gradient profiles...... 91 4.4.2 Horizontal temperature gradients in solar zenith angle binned by solar zenith angle and altitude...... 92 4.5.1 27-day rolling average density data interpolated at 190 km...... 94 4.6.1 Seasonal density variations shown in solar longitude...... 102 4.6.2 Seasonal temperature variations shown in solar longitude...... 104 4.6.3 Temperature ratios during overlapping sampling periods...... 107 4.6.4 Average temperatures on the dayside and nightside near perihelion and aphelion interpolated at 150 km, 160 km, 170 km and 180 km as a function of latitude...... 108

5.2.1 Example extraction of perturbations from temperature and density waves...... 115 5.3.1 Estimated wavelengths along spacecraft trajectory shown as a function of angle of trajectory to the normal...... 117 5.4.1 Histograms of wave amplitudes from all studied MAVEN orbits...... 120 5.4.2 Histograms of wave wavelengths from all studied MAVEN orbits...... 121 5.5.1 Average gravity wave amplitude as a function of altitude...... 122 5.6.1 Gravity wave amplitudes as a function of solar zenith angle and Mars-Sun distance... 126 5.7.1 Averaged gravity wave amplitudes superimposed over Martian topography...... 129 5.8.1 Wave propagation between orbits 4092 and 4093 waves, and orbits 6833 and 6834... 131 5.8.2 Comparison between waves from orbit 3811 and 3812 with the former shifted by 5 km, 1 km and 15 km...... 133 5.8.3 Waves extracted from inbound pass of orbit 6107 and 6108 with corresponding temperature proﬁles...... 134

6.2.1 Binned CO2,N2 and Ar densities as a function of solar longitude during the onset of the June 2018 global dust storm...... 143

6.2.2 Averaged inbound CO2, Ar and N2 density proﬁles and ratios for pre-storm and storm orbits...... 144

12 LIST OF FIGURES

6.2.3 Averaged outbound CO2, Ar and N2 density proﬁles and ratios for pre-storm and storm orbits...... 145 6.2.4 Post-onset to pre-onset density ratios taken at 170 km as a function of molecular mass. 146 6.2.5 Post-onset altitude as a function of pre-onset altitude for inbound and outbound legs.. 147 6.3.1 Inbound densities throughout June 2018 dust storm...... 151 6.3.2 Outbound densities throughout June 2018 dust storm...... 152 6.3.3 Corrected storm decay rates for June 2018 and Noachis dust storms...... 155 6.4.1 Pre- and post-onset density perturbations during the 2018 global dust storm...... 157

7.2.1 Example TGO density proﬁles...... 162 7.2.2 TGO wave extraction example with wave spectra...... 163 7.3.1 Interpolated TGO and MAVEN densities at 110 km, 150 km and 190 km...... 165 7.3.2 Comparison between TGO and MCD densities at 110 km in SZA, longitude, LST and latitude...... 168 7.3.3 Ratio of TGO to MCD densities at 110 km in SZA, longitude, LST and latitude at 105 km, 110 km, 115 km and 120 km...... 169 7.4.1 Derived TGO temperatures at periapsis...... 173 7.5.1 Binned TGO and MAVEN wave spectra normalised with scale height...... 175 7.5.2 Example of concurrent MAVEN and TGO gravity waves...... 178 7.6.1 Ratio between TGO and MAVEN densities at 125 km altitude as a function of solar zenith angle...... 179 7.6.2 Hydrostatically connecting TGO and MAVEN density and temperature proﬁles..... 183

A.0.1Latitude-local time overlap period...... 194

13 List of Tables

1.4.1 Comparison of Mars and Earth’s planetary properties...... 22 1.4.2 Mars’s seasons in Ls and sol range...... 23 1.8.1 Global-scale dust storms on Mars...... 42

2.2.1 MAVEN Deep Dip Ephemeris...... 54

4.5.1 Extracted periods observed in density due to solar rotation eﬀects...... 96 4.6.1 Inbound-inbound latitude-local time overlap...... 98 4.6.2 Outbound-outbound latitude-local time overlap...... 99 4.6.3 Inbound-outbound latitude-local time overlap...... 100

5.2.1 Characteristics of extracted example waves...... 116

6.3.1 Dust storm decay timescales for Noachis dust storm...... 153 6.3.2 Dust storm decay timescales determined for June 2018 dust storm...... 154

7.2.1 Periapsis locations for proﬁles shown in Figures 7.2.1a-c...... 161

14 Abbreviations

ACC Accelerometer. amu Atomic Mass Unit = 1.66×10−27 kg.

AU Astronomical Unit = 1.496×108 km.

CME Coronal Mass Ejection.

DD Deep-Dip.

EDM Entry, Descent and Landing Demonstrator Module.

ESA European Space Agency.

EUV Extreme Ultraviolet.

GCM General (Global) Circulation Model.

IMU Inertial Mass Unit.

IUVS Imaging Ultraviolet Spectrograph.

LMD-MCD Laboratoire de Météorologie Dynamique Mars Climate Database.

LST Local Solar Time.

M-GITM Mars Global Ionosphere-Thermosphere Model.

M-S Distance Mars-Sun Distance.

MARSIS Mars Advanced Radar for Subsurface and Ionosphere Sounding.

MAVEN Mars Atmosphere and Volatile Evolution Mission.

15 Abbreviations

MEX Mars Express.

MGS Mars Global Surveyor.

MRAMS Mars Regional Atmospheric Modeling System.

MRO Mars Reconnaissance Orbiter.

MY Martian Year.

NASA National Aeronautics and Space Administration.

NGIMS Neutral Gas and Ion Mass Spectrometer.

ODY Mars Odyssey.

ROSCOSMOS Roscosmos State Corporation for Space Activities.

TGO Trace Gas Orbiter.

UAMS Upper Atmospheric Mass Spectrometer.

VL Viking Lander.

16 Chapter 1

Introduction

1.1 Introduction

Mars’ atmosphere is highly variable over short and long temporal and spatial scales. This thesis aims to present an exposition on the dynamic nature of the Martian upper atmosphere (above 100 km), which has been achieved by using observational data from multiple spacecraft currently orbiting Mars. This chapter introduces the concepts used throughout the study from a history of observations to basic dust storm theory. Chapter 2 introduces the spacecraft, instrumentation and subsequent datasets used for analysis throughout this study. Chapter 3 presents data analysis techniques that are utilised throughout this study, such as an example derivation of temperature from density data. Additionally, comparisons between observational and model results are presented. Chapter 4 discusses background trends in temperature and density with particular emphasis placed on daily and seasonal trends achieved by analysing data taken during periods of near-identical local time and latitude. Chapter 5 examines wave activity within the upper atmosphere, and their relationships with solar zenith angle and topography are investigated. Spatially, these are the smallest variations studied. Chapter 6 investigates the effects of the 2018 global dust storm on the upper atmosphere. Density increases during the event are quantified, and decay timescales are derived. The impact of the dust storm on waves is also investigated. Results are compared to previous dust storm investigations. Chapter 7 uses density data from Trace Gas Orbiter (TGO) to probe deeper in the upper atmosphere. Results from this are compared to those earlier in the thesis. Moreover, where possible, datasets are ’combined’ with the Mars Atmosphere and Volatile Evolution (MAVEN) data to construct profiles spanning the upper atmosphere. As evident by the summary of chapters’ topics above, this thesis covers a diverse range of subjects. As such, the Introduction endeavours to present the basic knowledge required to understand each chapter more or

17 1.2. MOTIVATION FOR STUDYING MARS less in the order each topic appears.

1.2 Motivation for Studying Mars

Mars provides an excellent arena to study both geological and atmospheric physics as it shares similarities with Earth but can also be strikingly different in other aspects. Water is necessary for forming and sustaining life as we know it, with water being known to have flowed on the Martian surface; so, was there life on Mars at some part in its past? If not, what other conditions need to be met to sustain life on the Red Planet? These questions can only be answered by sending spacecraft to Mars, performing experiments and collecting invaluable data. Mars is untouched and provides a laboratory to study geological processes by examining surface and below-surface soil. Mars is believed to have had a similar natural landscape to Earth, given the large quantity of water thought to have been present there based on geological data. By studying Mars, it may be possible to understand why two potentially once similar planets have diverged into their current states. Will the natural evolution of Earth tend towards a Mars- like world? Mars once had a thick CO2 atmosphere which is slowly being lost to space. To what extent and at which point did the loss of the atmosphere lead to the severely altered landscape that we observe today? Looking further afield and to the future, newly discovered planets could fall into the Mars-like category. Therefore, understanding our closet neighbours aid future analyses of distant places. Finally, an exciting thought is human space travel and the colonisation of Mars. Understanding the extent and nature of the variability of the Martian atmosphere in addition to its scientific significance is of practical importance for space mission planning. What effects do dust storms have on orbiting spacecraft? How do gravity waves impact the expected trajectory of satellites? Although these topics are not explicitly investigated here, such effects on the atmosphere are assessed for future studies.

1.3 Previous Observations of Mars

1.3.1 Pre-Spacecraft Observations

Observations of Mars are not restricted to modern times. Humans have been fascinated by Mars for thousands of years. The below information is summarised from https://marsmobile.jpl.nasa.gov/ allaboutmars/mystique/history/. Around 400 BC the Babylonians used celestial bodies to predict astronomical events and observed Mars, though they saw it as a mysterious red spot in the sky. With the advancement of telescopes over the next 1000 years, Galileo Galilei was the ﬁrst person to observe

18 1.3. PREVIOUS OBSERVATIONS OF MARS

Mars using such a device. Our knowledge of Mars strengthens during the 17th century. By using fixed land features on Mars, a solar day of the Red Planet was refined from 24 hours by Christiaan Huygens to 24 hours 40 minutes by Giovanni Cassini. It is now taken to be 24 hours 39 minutes and 35.244 seconds (Allison and Schmunk, 2018). In 1877, Schiaparelli produced a map showing what are thought to be large canals on Mars. By the start of the 20th century, many features of Mars had been discovered. Yellow clouds had been spotted, which were taken to be dust clouds. The ice caps and their seasonal expansion and reduction had been noted. The moons of Mars are discovered during this century. Mars’ main features have been identified and contemplated from tens to thousands of years, and it is exciting to live during a time of great space exploration to understand these distant features further.

1.3.2 Previous Spacecraft Observations

Figure 1.3.1 shows an infographic displaying all successful (and less successful) missions to Mars up to NASA’s Mars 2020 rover mission (due for launch in July 2020). The first successful flybys of Mars were in 1964 by Mariner 3 and 4, followed five years later by Mariner 6 and 7. Images from Mariner 4 inferred that a dense atmosphere had not been present since the formation of the cratered surface (Leighton et al., 1965). Further images from Mariner 6 and 7 agree with this. The Viking 1 and Viking 2 missions in 1975 were the first successful landers and allowed in situ measurements of the atmosphere to be made for the first time as they descended through the atmosphere. The Upper Atmospheric Mass Spectrometers (UAMS) on board Viking 1 and 2 gave the first measurements of atmospheric composition between 100 km and 200 km. CO2 was found to be the dominant species along with N2, CO, O2, NO and other trace constituents (Nier and McElroy, 1977). Like the Viking spacecraft, Pathfinder used accelerometer data to determine atmospheric density, pressure and temperature profiles (Seiff and Kirk, 1977; Magalhães et al., 1999). NASA’s Pathfinder consisted of a lander and rover, Sojourner, which was the first successful rover to land on the Red Planet. Further, Sojourner was the first rover to roam outside of the Earth-Moon system. Pathfinder was a trailblazer for future rover missions.

Twenty-one years after the successful Viking landings, Mars Global Surveyor (MGS) graced the atmosphere with its presence. Through its aerobraking campaign, MGS was the first spacecraft to measure atmospheric density extensively (Lyons et al., 1999). The physics of aerobraking is discussed in Section 2.2. MGS made significant discoveries including, but not limited to, information about Mars’ 10 km layered crust (Malin et al., 1998), ancient lava flows (Hartmann et al., 1999) and evidence of the presence of sources of liquid water at shallow depths beneath the Martian surface (Malin and Edgett,

19 1.3. PREVIOUS OBSERVATIONS OF MARS

Figure 1.3.1: An infographic from @TheMarsSociety depicting both successful and unsuccessful missions to Mars (@TheMarsSociety, 2016).

2000). Following on from Pathfinder’s success, NASA’s Mars Exploration Rover mission consisted of Spirit and Opportunity. Their objective was to study the surface and geology of Mars. Arriving in January 2004, both rovers explored Mars for over five years, with Opportunity finally succumbing to the harsh conditions found at Mars. Opportunity discovered signs of water in the first rocks it studied (Squyres et al., 2004). NASA’s Mars Science Laboratory (MSL) consisted of another Rover, Curiosity. The objectives of this rover are to study the climate and geology of Mars, leading to conclusions about the habitability of Mars. As of December 2020, Curiosity is still operational. NASA’s Mars Atmosphere and Volatile Evolution (MAVEN) arrived at Mars in 2014 and is the first spacecraft to fully characterise the composition of the thermosphere (above 100 km). Data from this mission are used throughout this thesis; as such, it is detailed further in Chapter 2. The first of the two-part joint ESA/ROSCOSMOS

20 1.4. MARS PLANETARY PROPERTIES mission, ExoMars, arrived in 2016. The primary purpose is to gain a better understanding of the trace gases present in the atmosphere. Acceleration data are used from this spacecraft throughout this thesis; thus, the mission is discussed further in Chapter 2. The most recent mission to Mars is NASA’s InSight; a lander tasked with measuring seismic activity within Mars’ interior. InSight successfully landed at Elysium Planitia in November 2018.

There are many future missions planned for Mars in 2020 alone: UAE’s Hope Mars Mission (climate and weather - e.g. dust storms), NASA’s Mars 2020 Rover (ancient environment and geological processes), ESA/ROSCOSMOS’s ExoMars Rosalind Franklin (search for biomolecules or biosignatures from past life), and China’s Mars Global Remote Sensing Orbiter, Lander, and Small Rover (search for current and past life). Each dataset will add a new and unique perspective of the Red Planet.

1.4 Mars Planetary Properties

Mars is the furthest terrestrial planet from the Sun and shares similarities with Earth. Table 1.4.1 shows a comparison between these two planets’ properties. Mars has a radius of 3394 km, which is nearly a factor of two smaller than Earth’s at 6378 km. Mars’ significantly smaller mass leads to a gravitational acceleration of ∼3.72 ms−2 at the surface, compared to 9.81 ms−2 at Earth. This smaller acceleration reduces the velocity needed for particles to escape Mars’ gravitational field, which has implications when investigating the atmospheric loss of lighter species. The behaviour of species’ densities has a dependence on gravitational acceleration, thus has implications on the density distribution. A Martian year is equivalent to ∼1.88 Earth years. The length of a solar day (sol) on Mars is slightly longer than a day on Earth, measuring 24h 39m 35s. This small difference lends itself to the formation of similar tides, as governed by the rotation period. Waves are produced with harmonics being an integer multiple of the rotation period. The equilibrium surface temperature is lower on Mars (210 K) than Earth (256 K). This is primarily due to differences in their respective planet-Sun distance. For Mars, this is 1.38-1.67 AU (1 AU is equal to 1.496×108 km) and 0.98-1.02 AU for Earth. The difference in albedo between the two planets plays a role too. Earth and Mars have respective values of 0.250 and 0.306, respectively (McDunn, 2012). The difference in planet-Sun distance causes the solar flux at Mars to be about 35-50% of that at Earth. The planetary inclinations are comparable also; Mars has a tilt of 25° to its orbital plane and Earth’s tilt is 23.5°.

21 1.4. MARS PLANETARY PROPERTIES

Property Mars Earth

Equatorial radius (km) 3394 6378 Mass (kg) 6.42×1023 5.97×1024 Gravitational acceleration at surface (ms−2) 3.72 9.81 Equilibrium temperature (K) 210 256 Mean scale height (km) 10.8 7.5 Mean density (kgm−3) 3933 5515 Solar day, sol (h) 24.66 24 Solar year (sol) 668.6 365.24 Planet-Sun distance (AU) 1.38-1.67 0.98-1.02 Axial inclination (°) 25 23.5 Longitude of perihelion (°) 251 281 Longitude of aphelion (°) 71 103

Table 1.4.1: Comparison of Mars and Earth’s planetary properties. Adapted from Zurek et al., 1992 and McDunn, 2012

Assuming solar flux at Mars to be proportional to the Mars-Sun distance squared, then solar flux varies by ∼38% over a Martian year. The solar longitude, Ls, describe seasons. Solar longitude is the Mars-Sun angle, measured from the Northern Hemisphere spring equinox where Ls=0°. Ls varies from 0-360° over a Martian year. Table 1.4.2 describes the Martian seasons in detail. The year begins at Northern spring equinox (Ls=0° ), followed by Northern summer solstice (Ls=90° ), then Northern autumn equinox (Ls=180° ), and finally Northern winter solstice (Ls=270° ). Lewis et al., 1999 introduced ’Martian months’, however, these are not universally used within the community. Each Martian month covers 30° solar longitude; therefore, the duration of each Martian month varies depending on the season due to its eccentric orbit. The longest month is between Ls=60 and 90° and has a duration of 66.7 sols. Aphelion occurs during this month at Ls=71° . The shortest month is between Ls=240 and 270° and has a duration of 46.1 sols. Perihelion occurs during this month at Ls=251° .

22 1.4. MARS PLANETARY PROPERTIES

Month No. Ls Range (◦) Sol range Duration (sol) Details

1 0-30 0.0-61.2 61.2 N. Spring Equinox at Ls=0◦ 2 30-60 61.2-126.6 65.4 3 60-90 126.6-193.3 66.7 Aphelion at Ls=71◦ 4 90-120 193.3-257.3 64.5 N. Summer Solstice Ls=90◦ 5 120-150 257.3-317.5 59.7 6 150-180 317.5-371.9 54.4 N. Autumn Equinox Ls=180◦ 7 180-210 371.9-421.6 49.7 Dust Storm Season begins 8 210-240 421.6-468.5 46.9 Dust Storm Season Perihelion at Ls=251◦ 9 240-270 468.5-514.6 46.1 Dust Storm Season N. Winter Solstice Ls=270◦ 10 270-300 514.6-562.0 47.4 Dust Storm Season 11 300-330 562.0-612.9 50.9 Dust Storm Season 12 330-360 612.9-668.6 55.7 Dust Storm Season ends

Table 1.4.2: Mars’s seasons in Ls and sol range. Notable events are shown in the far right column. Adapted from http://www-mars.lmd.jussieu.fr/mars/time/solar_longitude.html

23 1.5. ATMOSPHERIC STRUCTURE

1.5 Atmospheric Structure

1.5.1 Density Structure

An atmosphere is defined as the envelope of gases surrounding a planetary body. For a body to possess a permanent atmosphere the forces acting upon such an atmosphere must be balanced. Assuming the atmosphere can be approximated by spherical symmetry, the forces acting on a parcel of gas can be easily calculated. The three forces acting upon a parcel are a downward force caused by the pressure of the fluid above, an upward force from the fluid pushing upwards and the weight of the parcel causing a force downwards. For a mathematical explanation, a short cylinder of gas is considered. The cylinder has a cross-section area, A, and depth, dz, and density, ρ. This gives the cylinder a total volume of dV and total mass ρdV . The cylinder is located a distance z from the centre of the body. Given all forces act within the radial direction, vector notation has been omitted. The upward force exerted on the bottom of the cylinder, Fz, is given by Equation 1.1

Fz = PzA (1.1) where Pz is the atmospheric pressure at z. The downward force exerted on the top of the cylinder,

Fz+dz, is given by Equation 1.2

Fz+dz = −Pz+dzA = −(Pz + dP )A (1.2) where Pr+dz is the atmospheric pressure at z+dz. dP is the change in pressure over dz. The ﬁnal force acting on the cylinder is its weight, Fg, given by Equation 1.3.

Fg = −gdm = −gρdV = −gρAdz (1.3)

For the parcel to be in equilibrium, all three forces (Eqs.1.1-1.3) need to sum to zero (Equation 1.4).

Fz + Fz+dz + Fg = 0 (1.4)

By substituting Eqs.1.1-1.3 into Equation 1.4 leads to Equation 1.5

PzA − (Pz + dP )A − gρAdz = 0 (1.5)

And solving for dP leads to

dP = −gρdz (1.6)

24 1.5. ATMOSPHERIC STRUCTURE

As g and ρ are always positive, dP will be negative when dz is positive. Therefore, pressure decreases with altitude. The pressure gradient in altitude is given by Equation 1.7 dP = −gρ (1.7) dz

This is the equation of hydrostatic equilibrium.

The Ideal Gas Law can be used to determine atmospheric pressure as a function of altitude. The Ideal Gas Law, Equation 1.8, is given by

P = nkT (1.8) where n is number density, k is Boltzmann constant equal to 1.38×10−23 m2kgs−2K−1, and T is temperature . As number density is given by

n = ρ/m (1.9) where m is molecular mass of the gas. Then the Ideal Gas Law can be rewritten as

P = ρkT/m (1.10)

Equation 1.10 can be rearranged for ρ and substituted into Equation 1.7 leading to dP mgP = − (1.11) dz kT then dP mgdz = − (1.12) P kT

Integrating Equation 1.12 between r0 and r gives P mg ln = − (z − z0) (1.13) P0 kT where P0 and z0 are initial pressure and altitude levels. Then P mg = exp − (z − z0) P0 kT (1.14) (z − z ) = exp − 0 H where

H = kT/mg (1.15)

25 1.5. ATMOSPHERIC STRUCTURE is the scale height. H is a constant for thermal equilibrium. It represents the distance over which the number density decreases by a factor of e.

Using the Ideal Gas Law (Equation 1.10) and the description of pressure in an ideal atmosphere (Equation 1.16), the density distribution in altitude can be derived. This leads to

ρ mg = exp − (z − z0) ρ0 kT (1.16) (z − z ) = exp − 0 H In order to show density behaviour within the upper atmosphere, data from the MAVEN/NGIMS mission are shown. Figure 1.5.1 shows the variation of nine atomic and molecular species during the inbound leg of orbit 1064. Shown are the densities of CO2, Ar, N2, O, CO, O2, NO, N and He from 135 km to 350 km. CO2 is dominant below ∼250 km. The lightest elements (e.g., He, O) have the largest scale heights; therefore, their densities vary more slowly with altitude. The heavier elements such as

CO2 and Ar have smaller scale heights, shown by stronger gradients in Figure 1.5.1, as they are more aﬀected by gravity. Straight lines signify that data obey the behaviour of an isothermal atmosphere. A sharp increase in the gradient shows an increase in temperature.

1.5.2 Temperature Structure

In atmospheric physics, heating by radiation is prompted by the absorption and re-emission of electromagnetic energy; the main source of such energy is the Sun. With the Sun as a blackbody, it emits in the shorter wavelengths with a peak in the visible portion of the spectrum at ∼420 nm. Ultraviolet (UV) and infrared (IR) radiation are also emitted at lower intensities. UV, EUV and X-rays are absorbed in the upper atmosphere, causing dissociation and ionisation. The Sun’s radiation is absorbed at the surface and remitted at longer wavelengths. Additionally, solar radiation is absorbed and will lose energy due to ionisation. Absorption occurs when matter retains radiant energy. The intensity of radiation within an atmosphere is now discussed.

An infinitely long cylinder filled with a gas with number density n is considered. Each particle has an absorption cross section denoted by σ. The initial radiation at an initial distance, s0, is I(s0). After a distance s the photon flux is I(s). Likewise at s + ds, the photon flux is I(s + ds). Now,

I(s0) > I(s) > I(s + ds) (1.17)

26 1.5. ATMOSPHERIC STRUCTURE

Figure 1.5.1: An example of the variation with altitude of nine atomic and molecular species during a single deep dip pass on orbit 1064 (Ls=256, LST 11:50 A.M., and latitude 4.5°S at periapsis on this orbit) is shown. For the trace gas He, gas scattering in the instrument at the lowest altitudes may distort the proﬁle. N, O2, O, and NO are derived from open source measurements and the remaining gases from closed source data. Taken from Mahaﬀy et al., 2015a.

The change in photon ﬂux is proportional to the length of the considered cylinder, shown by Equation 1.18

dI ∝ Isds (1.18)

Equation 1.18 can be rewritten using −σn as a constant of proportionality, dI = −σnds (1.19) Is dI ds where Is is the relative change in photon ﬂux over a path length . For completeness, this can be integrated between zero and s to give

Is = I0 exp(−σns) (1.20)

27 1.5. ATMOSPHERIC STRUCTURE

This is known as Beer’s Law and relates the reduction in photon ﬂux to the initial photon ﬂux. The above is for monochromatic radiation only. The form is dependent on wavelength and composition. This formulation can be extended to derive intensity as a function of altitude (z) and solar zenith angle

(χν), can be determined using Beer’s Law. The solar zenith angle is the angle between the Sun and an observer’s zenith. Solar zenith angle is used throughout this study, consequently understanding its implications on the observed behaviour is important. Figure 1.5.2 shows a graphic of solar zenith angle.

Figure 1.5.2: Schematic diagram showing monochromatic radiation penetrating a plane and horizontally stratiﬁed atmosphere. Taken from Schunk and Nagy, 2009

In an atmosphere, the reduction in radiation intensity along an oblique ray path, dzcos χν, is given by, dz dI = σn I (1.21) cos χν Equation 1.21 is positive since altitude is increasing. As the angle becomes more oblique, the ray travels further through the atmosphere to cover the same altitude range. The radiation as a function of altitude is determined by integrating Equation 1.21 between inﬁnity and z. z z Z dI Z σn0 = exp (−z/H) dz (1.22) ∞ I ∞ cos χν then σn0H I(z) = I∞ exp exp(−z/H) (1.23) cos χν

28 1.5. ATMOSPHERIC STRUCTURE

Radiation, therefore, increases exponentially with height. Locations equidistant from the subsolar point should receive equal radiation. Radiation decreases further from the subsolar point as solar zenith angle increases.

Mars’ vertical temperature structure is similar to Earth due to similar physics occurring within the atmospheres. Figure 1.5.3 shows temperature profiles derived by Viking 1 and 2 and Pathfinder accelerometer data. The figure has been adapted from Magalhães et al., 1999 to show the three central regions outlined here - the troposphere, mesosphere, and thermosphere. Earth possesses these three regions as well as a stratosphere located above the troposphere. Mars does not have an ozone layer like Earth or equivalent. A gas is required that absorbs UV in that region, which leads to heating. The troposphere and mesosphere are not explored during this study; however, the physics of each region will be briefly discussed.

Figure 1.5.3: Atmospheric temperature profile from entry phase of Mars Pathfinder. Modified from Magalhães et al., 1999

29 1.5. ATMOSPHERIC STRUCTURE

The region above ∼100 km shown in Figure 1.5.3 is the thermosphere. This is the least well- understood region of the atmosphere due to a lack of measurements and the key focus of this thesis. Within this region, temperatures rapidly increase with altitude as absorption of far and extreme UV radiation becomes progressively more dominant than other heating sources. Considering Mars’ eccentricity (Table 1.4.1), the solar flux present at Mars varies by ∼40% over a Martian year. The effect of changes in EUV flux has been modelled by general circulation models (Bougher et al., 2015) and derived from spacecraft measurements (Thiemann et al., 2018). Bougher et al., 2015 found mid-afternoon temperatures near 200 km are predicted to vary from 210 to 350 K (equinox) and 190 to 390 k (aphelion to perihelion). Solar insolation and EUV-forcing heat the thermosphere from below and directly, respectively. (Thiemann et al., 2018). By using MAVEN EUV solar occultations (EUV-SOs), Thiemann et al., 2018 aimed to decouple these two heating sources. Data were available to allow this; long-term decreasing solar variability was dominant, leading to a 50% reduction in EUV between the second and

first perihelion. Like in the mesosphere, CO2 cooling acts as an atmospheric thermostat that regulates lower thermospheric temperatures, near peak EUV absorption altitudes (Bougher et al., 1994). When considering the overall thermosphere, CO2 cooling is a secondary coolant (Bougher et al., 1999). CO2 cooling arises from the collision of atomic oxygen with CO2 allowing energy exchange between kinetic and vibrational states of the latter molecules. Hence, cooling rates are proportional to the abundance of O (Medvedev et al., 2015). There is a depletion in oxygen due to Mars being farther from the Sun, which reduces CO2 photolysis. (Bougher and Roble, 1991; Bougher et al., 1999). Yelle et al., 2014 constructed a 1-D model of the Martian upper atmosphere; temperature and composition are calculated by solving the coupled, time-dependent energy balance, diffusion, and continuity equations. The model domain covers the 100–250 km altitude region at a resolution of 1 km. They used this model to study the effects of Comet C/2013 A1 (Siding Spring) on Mars’ atmosphere. Stone et al., 2018 repurposed this model to understand heating and cooling rates in the Martian thermosphere based on results from MAVEN’s mass spectrometer measurements. They find that near noon, solar UV heating is balanced primarily by thermal conduction at high altitudes and CO2 cooling at lower altitudes. They attribute a peak in CO2 cooling to a combination of a decreasing collision rate with altitude and an increasing O mole fraction. In summary, the temperature in the thermosphere is balanced by the following heating and cooling terms: absorption of solar EUV and UV radiation primarily by CO2 and atomic O (heating), molecular conduction (cooling), horizontal advection (heating and cooling), adiabatic motions (heating and cooling), and 15 µm IR emission by CO2 (cooling). Figure 1.5.4 shows heating and cooling rates for noon and midnight conditions, taken from Stone et al., 2018.

30 1.5. ATMOSPHERIC STRUCTURE

Figure 1.5.4: Energy balance terms for (top) noon and (bottom) midnight conditions from 1-D model. The legend in the bottom panel refers to both panels. Taken from Stone et al., 2018

The ﬁnal region, not shown in Figure 1.5.3, is the exosphere. The bottom of the exosphere, the exobase, is deﬁned as the altitude at which the atmospheric scale height, H, equals the gas molecular mean free path or, equivalently, the altitude at which an upward-moving atom has a 1/e chance of not undergoing a collision before escaping to space. Below the exobase, a particle is likely to lose its energy through collisions and behave thermodynamically, but above, in the exosphere, it will be on a ballistic

31 1.5. ATMOSPHERIC STRUCTURE trajectory. Jakosky et al., 2017 calculated the exobase location using both these criteria. Exobase altitudes vary from ∼140 km to 200 km and vary due to a combination of variations with latitude, local solar time, solar zenith angle, and season. It is, therefore, not entirely possible to decouple these factors. The calculated altitudes are lower than previously quoted. For example, Haberle, 2015 state altitudes above 220-230 km, with variation caused by solar activity. While the heavier molecules that begin to escape are typically captured by the planet’s gravitational potential and thus return to the atmosphere along parabolic trajectories, a proportion of lighter molecules (albeit a tiny proportion, currently) do indeed escape to space.

Above, the energy budget in each region has been outlined. Additionally, dynamics play an essential role in the redistribution of energy. Most impactful is convection, whereby winds transport energy from warmer regions, such as at lower solar zenith angles, to colder regions. This can lead to winter polar warming which is examined in Chapter 4.

The atmosphere can be ’split’ in another way by considering the dominant diffusion process at different altitudes. In the lower atmosphere (below ∼100 km) mixing by dynamical processes acts to keep relative chemical compositions constant with pressure. Species’ abundances are controlled by chemistry. Within this region there a common scale height for all species, given by H = kt/µg, where µ is the mean molecular weight of species. Turbulence, or eddy diffusion, is dominant and mixes the species to counteract the distribution caused by gravitational effects. Its dominance is due to a small mean free path owing to significant pressure and densities. The lower atmosphere is often referred to as the homosphere. Above this region is the upper atmosphere, also known as the heterosphere. In the heterosphere, gases will be distributed vertically according to their scale height due to molecular diffusion.

In Mars’ heterosphere, the more massive species such as CO2 will dominate the lower altitudes above the homosphere and lighter species such as O will be dominant at higher altitudes (Mueller-Wodarg et al., 2008). The separation region between the lower and upper atmosphere is called the homopause or turbopause. Strictly, the homopause is not constant for all species as the diffusion coefficients for lighter species are larger than those for more massive species, so the altitude of the homopause is lower for species such as H, H2 and He (Fox, 2004). Jakosky et al., 2017 investigated how the altitude of the homopause varies using a year’s worth of Neutral Gas and Ion Mass Spectrometer (NGIMS) data. By extrapolating the ratio of N2/Ar, they were able to find the altitude at which the ratio is equal to that found near the surface by Mahaffy et al., 2013. Homopause locations vary from 150 km down to as

32 1.6. MARTIAN GENERAL CIRCULATION MODELS low as 50 km. Average altitudes are between 80 and 120 km. The rising and falling of the homopause are likely in response to the behaviour of the lower atmosphere. Seasonal forcing is believed to have a more substantial eﬀect on the lower atmosphere. In this study, the upper atmosphere refers to altitudes above ∼100 km and is the main focus of this thesis.

1.6 Martian General Circulation Models

Much of our understanding of Martian atmospheric dynamics comes from the successful implementation of general circulation models (GCMs). The coupled Navier-Stokes equations of energy, momentum, and mass continuity are solved on a spherical surface calculate winds, temperatures and composition. The earliest GCMs were developed for Earth’s atmosphere, and their success lead to the adaption and employment of these models to other planets. The Laboratoire de Météorologie Dynamique Mars Climate Database (LMD-MCD) is used in this thesis. It is a database fed by the GCM of González-Galindo et al., 2015. This model has an online interface (http://www-mars.lmd.jussieu.fr/mcd_python/) which allows users to produce plots for myriad ﬁelds easily.

1.6.1 Laboratoire de Météorologie Dynamique Mars Climate Database

The Mars Climate Database (MCD) v5.3 is a database of atmospheric statistics compiled from state-of- the-art GCM simulations of the Martian atmosphere (Lewis et al., 1999; Forget et al., 1999; Millour et al., 2018; González-Galindo et al., 2015). The MCD follows a whole atmosphere approach from the surface up to ∼300 km in this most recent version. Simulated data are stored on a 5.625°×3.75° longitude- latitude grid and are interpolated between data points if necessary. Data are available for an entire Martian year. In essence, for each grid point, the database contains 12 "typical" days, one for each month. There are many drivers behind variability in Mars’ atmosphere. Two such factors are solar conditions and suspended dust within the atmosphere. The former is incorporated by simulating solar minimum, average or maximum conditions. In this present study, climatology scenarios are used; these are designed to represent a typical Martian year. Solar minimum is used throughout this thesis. The MCD allows for more infrequent scenarios. There are three dust storm scenarios where opacity, τ, is set to 5 for solar minimum, average and maximum. ’Warm’ and ’cold’ scenarios allow particularly dust- heavy periods to be captured outside of dust storms. Lastly, historical conditions from Martian years (MYs) 24-32 are reproduced using best guesses for actual dust and solar EUV conditions. The MCD

33 1.6. MARTIAN GENERAL CIRCULATION MODELS is validated using available measurements across a variety of missions. Atmospheric temperatures are compared to measurements from MGS/TES (Thermal Emission Spectrometer), MRO/MCS (Mars Re- connaissance Orbiter/Mars Mars Climate Sounder) and MGS and Mars Express (MEX) radio occultation experiments. Surface pressures and temperatures are compared to TES, Viking, Pathﬁnder, Phoenix, and Mars Science Laboratory (MSL) measurements (Millour et al., 2015). Chapter 3 demonstrates the successes and drawbacks of the MCD in the upper atmosphere.

The MCD interface is open and versatile, allowing users to extract data from 12 climatological averages and location. For example, the vertical coordinate may be given as an altitude above the surface or a pressure coordinate. Further positional arguments are local time, latitude, longitude and solar longitude. Mars’ season can also be determined from entering an Earth date. The MCD can output, amongst other variables, the following: atmospheric pressure (Pa), density (kg/m3), temperature (K), zonal and meridional components of wind (m/s). Hence, data can be extracted from the MCD along spacecraft trajectories, leading to comparisons between model and spacecraft data. Number densities are available from the mass spectrometers on board MAVEN. However, the MCD outputs total density and volume mixing ratios. Partial densities cannot be derived from these quantities directly. The volume mixing ratio of the ith species, Xi, is equal to ni/ntotal where ni is the number density of the ith species and ntotal is the total number density. This is equal to Pi/Ptotal where Pi is the partial pressure of the ith species and Ptotal is the total pressure. Lastly, the partial pressure is given by the Ideal Gas Law,

Pi = nikT . Combining the previous three equations leads to Equation 1.24,

XiPtotal ni = (1.24) kT

This derived number density is now comparable to mass spectrometer data.

1.6.2 Other Martian General Circulation Models

The success of Martian GCMs is owed to their Earth-based ancestors. Modelling work began after the launch of the early Mars missions, such as the ﬂyby Mariner 4 spacecraft. The ﬁrst simulation was performed by Leovy and Mintz, 1969. Within a couple of decades, GCMs had developed further in their capabilities. The National Center for Atmospheric Research (NCAR) Earth-based thermospheric general circulation model (TGCM), as described in Dickinson et al., 1984, is one such ancestor. This

34 1.6. MARTIAN GENERAL CIRCULATION MODELS model was successfully modified for Venus (VTCGM) by Bougher et al., 1988b. Specific processes such as wave drag and CO2 cooling were introduced. The VTCGM has been validated using Pioneer data. This was adapted by Bougher and Dickinson, 1988 and later Bougher et al., 1990 for Martian conditions; this is somewhat easier due to Mars and Venus sharing some thermal and radiative processes common to CO2 dominant atmospheres. The MTCGM is a finite difference primitive equation model that self-consistently solves for time-dependent neutral temperatures, neutral-ion densities, and three-component neutral winds over the Mars globe. Unlike the MCD, the MTGCM is not a whole atmosphere model; it stretches from 70-300 km. This model is driven from below by the NASA Ames Mars MGCM around the 60-70 km level (Haberle et al., 1999). The Mars Global Reference Atmospheric Model (MarsGRAM) is based on the coupling of MGCM and MTGCM. Bougher et al., 2015 introduced a new GCM, the Mars Global Ionosphere-Thermosphere Model (M-GITM). This model is born from the GITM, described in Ridley et al., 2006. The latter is non-hydrostatic. As for previous models, planetary parameters are adjusted for Mars. M-GITM extends from 0 to 250 km. González-Galindo et al., 2010 examined thermal and wind structures output by two models - LMD-MCD and MTGCM (coupled to a lower atmosphere model). Common input parameters are used and different dust scenarios are used at Ls=0°, Ls=90° and Ls=270°. González-Galindo et al., 2010 conclude that both models are in good overall agreement; however, local features are not necessarily observed in both models, but are globally similar. Local features are exacerbated during increased dust loading.

Only recently has an empirical model of Mars’ thermosphere begun to be developed. MAVEN’s vast dataset has allowed this type of model to become a reality. Girazian et al., 2017 outline how, for any given combination of solar zenith angle, latitude, season and solar activity, the model will provide vertical proﬁles of neutral densities and temperature in the range 150-300 km. Functions are created to ensure that density data are available across the planet. Where needed, data from the M-GITM are used to bridge any gaps. It is expected that one signiﬁcant advantage of this class of model outputs near physically sampled regions is likely to be more accurate than from a numerical model. No literature is currently available that compares these model densities to observations.

35 1.7. GRAVITY WAVES

1.7 Gravity Waves

1.7.1 Gravity Wave Generation

Gravity waves are generated from a variety of sources including ﬂow over topography, atmospheric instabilities, and volatile convection; however, any process which perturbs the atmosphere could generate gravity waves. A basic description of the generation of gravity waves is as follows. If a parcel of gas in the atmosphere is considered then when it encounters an obstacle, such as a mountain range, it will be displaced upwards. This is the direction of energy propagation. It may be displaced downwards and reﬂected upwards, so this explanation still holds. If the parcel has density ρ0, volume V and is displaced from its initial position (z, p) to (z + z0, p − p0) it will experience a force acting on it. Here, z and p are altitude and pressure; primed variables are perturbations. As the parcel is displaced upwards, its density will be greater than the surrounding atmosphere. Gravity acts as the restorative force attempts to reinstate the parcel to its original location, and it will overshoot. The parcel now has a density lower than its surroundings and will be restored by buoyancy, again overshooting upon its return. From Newton’s Second Law, the motion of the parcel is governed by Equation 1.25

d2z0 (ρ0V ) = g(ρV ) − g(ρ0V ) (1.25) dt2

By using the Ideal Gas Law, the above equation becomes,

d2z0 ρ − ρ0 = g (1.26) dt2 ρ0 1/T − 1/T 0 = g (1.27) 1/T 0 T 0 − T = g (1.28) T

0 0 If T is the unperturbed background temperature, the temperature of the parcel at z + z is T -Γdz 0 0 where Γd is the lapse rate equal to -dT/dz. The background temperature at z + z will be T − Γz , where Γ is the dry adiabatic lapse rate equal to gcp. cp is heat capacity at constant pressure. Now, 0 0 T − T = −(Γd − Γ)z . The motion of the air parcel can be written as

2 0 d z g 0 = − (Γd − Γ) z (1.29) dt2 T

g 1/2 If the oscillation frequency is deﬁned as N = T (Γd − Γ) , then the equation of motion becomes d2z0 + N 2z0 = 0 (1.30) dt2

36 1.7. GRAVITY WAVES

The oscillation frequency N is called the Brunt-Väisälä (B-V) frequency and its value is important in determining the behaviour of gravity waves. There are three regimes the parcel can be found in, determined by the value of N 2. For N 2 >0, the oscillation is stable and will continue to oscillate at its original frequency if no external forces act upon it. For the case N 2 = 0, the weight and buoyancy terms are equal, resulting in no net force on the parcel, therefore remaining stationary. The last case is N 2 < 0 where the parcel will continue to move in the direction it was originally displaced and is said to be unstable. The Brunt-Väisälä frequency is used to quantify the stability of the atmosphere and is used frequently to calculate gravity wave properties such as potential energy and wind perturbations. If required, the value is taken from the literature. The described oscillations are rarely found purely in the vertical direction; waves nearly always have a horizontal component. Hence, periods of gravity waves are dependent on the ratio between the vertical and horizontal wavelengths. The shortest period waves are nearly purely vertically propagating and are labelled ’acoustic-gravity’ waves. In contrast, an oscillation primarily in the horizontal directions takes longer to return to its original position, and as such have more prolonged periods. These types of waves are ‘inertial-gravity’ (Medvedev and Yiğit, 2019).

1.7.2 Gravity Wave Evolution

Gravity waves couple the lower and upper atmosphere at Mars. Understanding the propagation of gravity waves is crucial to understanding the dynamics of the atmosphere. In the following section, the theoretical behaviour of gravity waves is described. Like all waves, gravity waves have speeds associated with them. The most useful is the intrinsic phase speed (c − u) which is the phase speed (c) measured relative to the mean flow (u). It is this speed that determines whether waves will be absorbed by the mean flow. In a conservative atmosphere where dissipation and heating are neglected, the vertical flux of energy, p0w0 associated with a gravity wave is related to the vertical flux of net horizontal momentum, 0 0 (ρ0u w ) by

0 0 0 0 p w = (c − u¯)ρ0u w

0 0 0 where p , w , u are the perturbation pressure, vertical and eastward wind speeds and ρ0 is the background density. This is Eliassen-Palm’s ﬁrst theorem (Eliassen and Palm, 1961). An upward propagating wave (p0w0 > 0) carries eastward momentum if the phase speed is eastward with respect to the mean ﬂow or c > u¯. The ‘noninteraction theorem’ derived by Eliassen and Palm, 1961 states that for steady-state internal gravity waves (IGWs),

d 0 0 (ρ0u w ) = 0 for u¯ 6= c (1.31) dz

37 1.7. GRAVITY WAVES u0 and w0 must therefore increase with height as density falls exponentially. If u¯ = c, the mean flow absorbs the waves and acts as a barrier to propagation. The wave spends more time in the flow allowing dissipative processes to act for longer (Vallis, 2006). There is no distinction between the flow and wave, so the latter is absorbed and can no longer propagate. For cases where the noninteraction theorem is valid and u¯ 6= c, waves pass vertically through a sheared environment without extracting or depositing momentum. Momentum is only extracted from the layers where waves form and deposited where they d 0 0 are finally absorbed. In a real atmosphere where dz (ρ0u w ) 6= 0, the condition for u¯ = c is not necessary for momentum deposition into the atmosphere. The properties of the medium do not change in time, nor horizontally, therefore both the absolute frequency and horizontal wavelength are invariant with altitude. However, the vertical wavelength does vary due to the intrinsic frequency changing. If the flow speed increases, then the intrinsic frequency decreases. This occurs at the critical layer. At this layer, the vertical wavelength tends to zero. Waves can grow with altitude until acted on by other forms of dissipation (eddy and molecular diffusion). The former is due to mixing owing to eddy motion. The latter is the thermal motion within a mixture. Waves can also break analogously to ocean waves if their amplitudes grow too large. Understanding how much and where momentum is deposited into the atmosphere is crucial to understanding the energy and momentum budget and upper atmospheric dynamics (e.g. Medvedev and Yiğit, 2012). Momentum of the wave can be imparted on the general background flow, for example with topographically generated gravity waves slowing down the mean flow. A further threshold for waves to contend with is instability. As a parcel is displaced upwards, it cools. Whether a parcel continues to oscillate is dependent on the surrounding environment. If the dry adiabatic lapse rate that is the lapse rate of the parcel is greater than the ambient (or actual) lapse rate, the parcel is sufficiently cooler than the atmosphere, thus will sink to its original position. For the opposite scenario, the parcel is warmer than its surroundings and consequently will continue to rise.

Gravity waves carry substantial momentum as they propagate from the lower to the upper atmosphere, so constraining wave energy and momentum deposition is crucial in understanding the dynamics of the upper atmosphere. As waves dissipate or break, their mechanical energy is irreversibly transferred to the atmosphere as heat. Secondly, it transpires that as amplitudes decay, the vertical net flux of sensible heat is no longer zero, as is found for conservatively propagating gravity waves. This flux is directed downwards, and the divergence of such flux causes heating (cooling) below (above) the region of dissipation (Walterscheid, 1981). Cooling rates in the Earth’s atmosphere due to gravity waves were found to be ∼100 K/day. Specific cases can present cooling of 1000 K/day (Yiğit and Medvedev,

38 1.7. GRAVITY WAVES

2009). Gravity waves also dynamically impart their influence on the upper atmosphere. One process by which this is possible is gravity waves ‘drag’. The divergence of the wave momentum flux can lead to an acceleration or deceleration of the mean flux. As waves break turbulence and dissipation occur, leading to a zonal force on the zonal flow. Barnes, 1990 predicted gravity wave drag of ∼1000 ms−1sol−1. This is commensurate to drag found by Fritts et al., 2006 using MGS accelerometer data.

1.7.3 Gravity Wave Observations

Gravity waves have been observed in the Martian thermosphere by previous spacecraft, primarily during their aerobraking campaigns. MGS density data were initially used for studying larger-scale phenomena, such as planetary-scale waves (e.g. Keating et al., 1998). Withers, 2006 quantified oscillatory trends in density profiles and interpreted them as gravity waves based on work by Bougher et al., 1999 and Tolson et al., 1999. Typical amplitudes were found to be ∼10%. Creasey et al., 2006a followed up on this work by deriving characteristic along-track wavelengths to be several hundred kilometres. A seasonal trend was found with significantly larger amplitudes during northern autumn compared to northern spring. Fritts et al., 2006 further expanded our understanding of wave structures in the upper atmosphere by utilising MGS and Odyssey (ODY) data. Wave growth with altitude was observed, in some cases by a factor of five over a 25 km altitude range. Research and interest into upper atmosphere wave structures were revitalised with the arrival of MAVEN in 2014. Early on, Yiˇgit et al., 2015a investigated

CO2 density perturbations in the Martian thermosphere and interpreted them as gravity waves. They compare observations to outputs from a gravity wave scheme. Similarly, England et al., 2016 extracted perturbations from CO2, Ar and N2 density data. The larger dataset allowed monthly means and seasonal effects to be explored. Terada et al., 2017 similarly investigated Ar density perturbations; the global distribution of gravity wave amplitudes was examined so potential links with topography could be found. Wave activity is briefly discussed in Stone et al., 2018 during their derivations of temperature profiles. Observational studies have been able to estimate the momentum fluxes due to gravity waves. Barnes, 1990 estimated a drag of ∼1000 ms−1sol−1 around 50-100 km. By scaling down momentum fluxes according to the scaling of amplitudes, Fritts et al., 2006 calculated momentum flux at ∼70-80 km to be ∼1000 ms−1sol−1, increasing (decreasing) by a factor of five at 100 km (50 km) using MGS and ODY accelerometer data. Accelerations caused by such momentum deposition is ∼70 ms−2. Such momentum fluxes and accelerations are derived from limited data. Much of the following discussion is taken from the summary of gravity waves presented by Medvedev and Yiğit, 2019 and Yiğit and Medvedev, 2019. All the above studies and individual results are discussed further in Chapter 5.

39 1.7. GRAVITY WAVES

Additionally, observations of waves in diﬀerent solar system atmosphere are highlighted.

1.7.4 Modelling Gravity Waves

GCMs such as the LMD-MCD are developing methods in which the effects of gravity waves can be included in models (Forget et al., 1999). Gravity waves occur at sub-grid scales and as such need to be parameterised. Yiˇgit et al., 2008 outlines a gravity wave scheme which has been implemented into Martian GCMs. This example scheme accounts for wave dissipation in the upper atmosphere due to molecular viscosity, thermal conduction, ion friction, and radiative damping in the form of the Newtonian cooling. Breaking/saturation effects are also included. This is one scheme for which its model results are discussed. Medvedev et al., 2011 implemented the gravity wave scheme of Yiˇgit et al., 2008 into a GCM described by Hartogh et al., 2005 and Medvedev and Hartogh, 2007. They studied the effects in the 100-130 km region. Medvedev et al., 2011 found that gravity waves decelerate atmospheric zonal flows during all seasons. In some cases, zonal flows were reversed. Reversals are primarily driven by deposition of momentum from gravity waves with intrinsic phase speeds greater than zero. Effects of gravity waves on atmospheric temperature were briefly studied, and winter polar warming was found. Medvedev and Yiğit, 2012 studied the thermal effects of gravity waves on the Martian atmosphere. For perpetual Northern winter (Ls = 270°), they found that heating due to irreversible conversion of gravity wave mechanical energy into heat is comparable to near-IR CO2 heating. Cooling by wave-induced downward flux is similar to IR CO2 cooling, in agreement with Parish et al., 2009. Overall, the inclusion of thermal effects of gravity waves systematically produces a colder thermosphere. Results provided by the model are in agreement with SPICAM observations (Forget et al., 2009) and ODY aerobraking temperature retrievals (Bougher et al., 2006). Gravity waves have also been implemented into models to explain other features within the Martian atmosphere. Yiˇgit et al., 2015b looked at CO2 clouds and the possibility of gravity waves creating pockets in the atmosphere with temperatures below the condensation point of CO2. The temperatures and locations are in agreement with observations; however, the frequency of cloud production exceeds observations.

For gravity waves to be parameterised and evolved through a model atmosphere, initialisation conditions are needed. By comparing gravity wave characteristics at different altitudes, comparisons to model results at similar altitudes can be made to fully understand the evolution of gravity waves and their consequential effects on the upper atmosphere. This is possible with the addition of MAVEN observations as it is the first mission to study the upper atmosphere; thus a wealth of new data are

40 1.8. DUST STORMS available to quantify and characterise gravity waves in diﬀerent regions at diﬀerent times. This is a key motivation for this thesis. Models require validation; this is achievable by a comparison of amplitudes and wavelengths. This is expanded upon in Chapter 5. As shown above, much work has been undertaken to implement gravity wave parameterisation within GCMs; this, of course, develops our understanding of physical processes and impact within the upper atmosphere.

Nevertheless, one reason for studying gravity waves is of a practical nature. As future spacecraft arrives at the Red Planet, an understanding of wave variability is needed for managing orbiters and ensuring the safety of their on board instruments during aerobraking.

1.8 Dust Storms

Martian dust storms have fascinated scientists for years owing to their unpredictability, complexities, and rarity. Furthermore, for the ﬁrst time, the upper atmosphere is probed during such a global event. The June 2018 global dust storm provides an arena to study all aspects of this episode. The lower atmosphere houses many spacecraft capable of detecting and measuring elements of the storm, such as the opacity by Opportunity. Does the upper atmosphere react in a similar way to the lower portion? Moreover, if not, how does it respond? Many questions like these are answered in Chapter 6. Observations of previous storms from ground-based and spacecraft instruments are discussed. Next, the physics of dust storms is brieﬂy outlined.

1.8.1 Dust Storm Observations

Global dust storms are rare occurrences at Mars; Table 1.8.1 lists all known dust storms excluding the June 2018 dust storm (Shirley, 2015). There was a 15-year wait after the 1956 storm for another then a succession of 4 storms within ten years developed. MRO was, fortunately, able to study the 2007 dust storm. However, observational data for earlier storms becomes sparse (e.g. Bougher et al., 2001). Mariner 9 detected the electron density response of the 1971 dust storm. This is discussed and modelled in Wang and Nielsen, 2003. Zurek and Martin, 1993 studied the interannual variability of dust storms on Mars. By using Earth-based observations of Mars and spacecraft, they attempt to understand whether the observed rate of dust storm formation is representative of previous decades. Due to Mars’ elliptical orbit, Zurek and Martin, 1993 makes the point that dust storms have occurred without being detected from Earth evidenced by Viking data. They conclude by saying that the chance of observing

41 1.8. DUST STORMS

Year Mars Year Ls (°) Calendar Dates

1924-1925 -16 310 5 Dec-Jan 1956 1 249 19 Aug-Nov 1971-1972 9 260 22 Sep-Jan 1973 10 300 13 Oct-Dec 1977 12 204 15 Feb-Apr 1977 12 268 27 May-Oct 1982 15 208 Oct 1994 21 254 9 Apr-Jul 2001 25 185 26 Jun-Oct 2007 28 262 22 Jun

Table 1.8.1: Global-scale dust storms on Mars. Adapted from Shirley, 2015

a planetary dust storm in a given year is about one in three and are typically restricted to southern spring and summer. Further to the study mentioned above, Wang and Richardson, 2015 investigated the origin, evolution, and trajectory of large dust storms during MY 24-30. Although dust storms were most frequently observed during the traditional dust storm season, storms can be further seasonally characterised. Northern hemispheric originating storms occur during northern autumn Ls=180-250° and winter Ls=305-350°. Southern storms originate earlier in the year around Ls=135-245°.

There are many ways to detect dust storms on Mars. Observations using telescopes are one method of discovering dust storms onsets. This requires Mars to be the target object. As Zurek and Martin, 1993 noted, dust storms may have been missed due to a lack of images. One advantage of telescopic images is the ability to observe the global evolution of storms, from initialisation to trajectory to decay; the spread of the dust storm over the visible face can be very informative. Figure 1.8.1 shows two images of Mars using Chilescope. The left image is taken a week after Opportunity ﬁrst detected the storm on 30th May 2018. Here, south is upwards, so the large India-shaped region is Syrtis Major. The development of a global dust storm can take several days or weeks to fully mature. The right image was taken on 7th July 2018 and showed the full extent and severity of the global dust storm. Features

42 1.8. DUST STORMS of topography are no longer visible as dust is lofted into the atmosphere.

Figure 1.8.1: Early- and mid-storm photos of the same hemisphere of Mars. South is up. Courtesy of Damian Peach / Chilescope team and Christophe Pellier

A similar method is spacecraft imagery. Very high-resolution images can be attained over a much more local area. A short orbital period allows the evolution of a dust storm to be studied over a particular region. This is particularly successful for global dust storms. However, as for telescopic images, the spacecraft needs to be in a favourable location. Dust storms can be indirectly detected by measuring the increased opacity of the atmosphere using instruments on board rovers such as NASA’s Curiosity.

ESA’s Trace Gas Orbiter (TGO) began its science mission in late April 2018, a few months before the onset of the 2018 global dust storm event. Solar occultations enabled layers of dust to be identiﬁed and for their impact on atmospheric water vapour to be established. (Vandaele et al., 2019) found layers of dust were found at altitudes around 25-40 km, in agreement with Gurwell et al., 2005. TGO discovered an increase in water vapour around these altitudes. One proﬀered idea stems from the known warming of the atmosphere, causing more robust circulation. This warming slows or inhibits ice cloud formation,

43 1.8. DUST STORMS allowing for an increase in water vapour. This result is not unique; Stone et al., 2019 found an injection of H2O in the thermosphere by up to a factor of six compared to quiet periods. This highlights the synthesis between the lower and upper atmosphere.

1.8.2 Dust Storm Theory

Dust storms are not fully understood with much effort being put into modelling the dust storm cycle. Barnes, 1999 provides a concise exposition of three key dust storm mechanisms: the initial lifting of dust into the atmosphere, dust heating of the atmosphere, and dust lofting, suspension and horizontal transport at higher altitudes. One mechanism for lifting dust is saltation (Greeley, 2002). With sufficiently high velocities, forces become strong enough to lift particles from the surface. Upon hitting the surface again dust can ’splash’, dislodging further dust (Bagnold, 1941). This positive feedback acts as an injection mechanism. Another mechanism discussed by Barnes, 1999 is the continual suspension and transport of dust in the atmosphere. In the PBL (planetary boundary layer), turbulent mixing keeps dust aloft. Convective cells can lift dust high into the atmosphere, penetrating regions otherwise unreachable by dust. From the television experiment on board Mariner 9, Leovy et al., 1972 determined the vertical extent of the global dust storm; during the first ∼40 days dust is typically lofted to altitudes of ∼45-60 km (Gurwell et al., 2005). The next stage in the growth of dust storms is heating of suspended dust. Comparatively, dust is more efficient at absorbing solar radiation than dominant CO2 in the atmosphere. During a dust storm, dust particles absorb solar radiation and radiate this back at longer wavelengths, notably infrared. The increased dust shades the surface as it absorbs incoming solar radiation; however, the atmosphere is inefficient at absorbing its radiation. Thus approximately only one half of absorbed radiation by dust is reabsorbed by the surface. The play-off between shading the surface and absorbed re-radiated energy causes a net cooling effect (Davies, 1979). Although heating occurs in the lower atmosphere, the effects are profound in the upper atmosphere, as will be shown in Chapter 6. During the 1977 storm, around the 25 km altitude level temperatures are enhanced by up to 30 K over several days. Heating occurs within a couple of days from dust injection and is heated throughout the loading process (Martin, 1979, Jakosky and Martin, 1987). Combining a theoretical approach with observations from Mariner 9, Zurek, 1978 found that heating rates during the 1971 global dust storm may have reached 80 K/day for over- head sunlight. Further, 20% of direct insolation is absorbed by the dusty atmosphere. As suggested by Moriyama, 1975 and confirmed by Zurek, 1978, optically thin atmospheres can heat the atmosphere by

44 1.8. DUST STORMS a few degrees.

The boundary between the warm and cool region becomes unstable and warm air lifts dust into the atmosphere, typically no higher than 45-60 km (Gurwell et al., 2005). Dust storms are more prevalent during Southern summer as Mars is near perihelion, where radiative heat sources are most inﬂuential. This creates a more substantial temperature gradient, inducing large storms. Dust storms can last for days, weeks or months and cover the entire planet. By absorbing solar radiation, the lofted dust places the surface in a state of shade. In doing so, the storm is being starved of its energy source. This is coupled with less intense radiation as Mars increases its distance from the Sun. Mars is prone to severe and long-lasting dust storms due to the inherent arid nature of the planet. The lack of water (or liquid) means that dust particles do not coalesce as they would on Earth. Another reason global dust storms are not present at Earth is large bodies of water, such as great lakes or oceans. Dust passing over water will be removed via spray and necessary moisture within the atmosphere.

Feedback processes due to dust storms such as whether lifted dust results in further radiative forcing leading to additional dust lifting processes is discussed. Rafkin, 2009 found that the initial response to dust loading is a decrease in surface pressure as the centre of the dust region. They investigated ’optimal’ conditions for dust storm growth using the Mars Regional Atmospheric Modeling System (MRAMS) coupled with the Cloud Aerosol and Radiation Models for Atmospheres (CARMA) (Rafkin et al., 2001, Michaels et al., 2006). They found that location is a crucial factor behind strong dust storm formation. The optimal location is at subtropical latitudes; here, solar forcing is strong as to warm the system, and the Coriolis force is sufficient to create circulation. Consequently, higher latitudes produce a smaller system due to reduced solar input. One ’unknown’ about dust storm initialisations is the threshold for dust-lifting and subsequent dust-lifting efficiencies; not only is dust needed to be lifted, but a sufficient amount is needed. Strong feedback occurs for such optimal conditions. Conceivably counter-intuitive, but excessive dust produces negative feedback leading to the inhibition of the storm. With focused vorticity, dust can continue to be lifted at night and storms sustained across multiple sols. And vice versa, a more dispersed storm will dissipate after about one sol. Energy is dissipated via frictional spin and gravity waves. Gravity waves emanating from localised dust storms were also observed in Spiga et al., 2013. Another condition that determines the severity of a dust storm is the initial size of the perturbation; the most considerable perturbations produce the deepest, most intense circulation patterns.

45 1.9. RESPONSE OF UPPER ATMOSPHERE TO DUST STORMS

Rafkin, 2009 imply that dust storms are tough to predict, as in agreement with previously mentioned studies. One factor is the dust distribution. Distribution is meant here as both the size of dust particulates and geographical location. The former is discussed initially. Studies reviewed shortly present results outside of dust storm conditions. Using the infrared interferometric spectrometer (IRIS) on board Mariner 9, Toon et al., 1977 were able to determine dust particle size and composition during the 1971-1972 dust storm. They found average dust cross-sections between ∼3µm and 6µm, with no significant change during the storm abatement period. The composition was similar to terrestrial dust, comprising of SiO2 plus a mixture of other minerals. Pollack et al., 1995 analysed Viking 1 and 2 images to improve on previous dust size results (Pollack et al., 1977; Pollack et al., 1979). Their latest study found radii of 1.85±0.3µm at Viking 2 during northern summer when dust loading was low and 1.52±0.3 µm at Viking 1 during the first dust storm. They affirm and reassure that although there is a variety of dust particle sizes, and thus radiative properties, it does not lead to a substantial change in solar energy deposition in the atmosphere over the Pollack et al., 1977 and Pollack et al., 1979 estimates. Later studies have shown dust at Mars is predominantly composed of silicate particles with sizes of the order 1-2µm (Tomasko et al., 1999; Wolff et al., 2006). Rafkin, 2009 took a lognormal distribution with a mode dust radius of 1µm. Based on observational data, this is a realistic parameter.

1.9 Response of Upper Atmosphere to Dust Storms

During a dust storm, the lower atmosphere is heated, as described above. In turn, the upper atmosphere expands upwards. Given the unpredictable nature of dust storms, observational data are relatively sparse. Therefore, dust storms have been incorporated into GCMs in an attempt to reproduce and understanding atmospheric responses. Hitherto, models and their results have been discussed within the context of the upper atmosphere. However, dust storms develop in the lower atmosphere. The initialisation of dust storms in models is considered now. In Bougher et al., 1997 two circulation models are used: a lower atmosphere model (NASA Ames General Circulation Model - MGCM) where the storm is generated and an upper atmosphere model where the response is studied (NCAR Mars Thermosphere General Circulation Model - MTGCM). The MGCM had an upper boundary at ∼100 km, and the MTGCM had a lower boundary of ∼80 km, thereby providing an overlap of both models leading to coupling via an exchange of boundary conditions near 70-80 km. Dust storms are simulated by coupling the

46 1.9. RESPONSE OF UPPER ATMOSPHERE TO DUST STORMS

MGCM with an aerosol transport model. Dust is injected into the Southern Subtropics for ten sols and subsequently evolves self-consistently for another 20 sols. To sequentially couple the MGCM and MT- GCM codes, the MGCM 1.32 µbar surface heights are extracted and zonally averaged over three sols; subsequently, these mean heights are speciﬁed at the MTGCM lower boundary. At MGS aerobraking altitudes (∼110 km), densities can increase by a factor of 2 over one day, reaching factors of 5-10 over several days. Further, compared to a benchmark altitude of 112.5 km for the 1.2-nbar pressure level, the above-modelled scenario saw an altitude shift of 27.5 km. This is much larger than has been observed during any recorded dust storm. This result is expanded upon in Chapter 6, and results from previous observations are discussed.

Medvedev et al., 2013 used a GCM extending from the surface to about 160 km including a spectral parameterisation of subgrid-scale gravity waves to study the effects of two independent dust storms on the Martian upper atmosphere. This model is described in Medvedev and Yiğit, 2012. Medvedev et al., 2013 studied equinoctial and solstitial dust storms from MY25 and MY28. They used dust loading information from the MGS-TES and MEX-PFS. They ran their model with and without gravity waves. The equinoctial storm began in the Southern Hemisphere soon after the spring equinox (∼190 Ls), rapidly increased over a few days extending as far as ∼60°N, and decayed until about 250° Ls. Between 190° and 205° Ls, the amount of airborne aerosol increased more than tenfold over the full range of latitudes. Similar results are obtained for runs with and without gravity waves included. Direct heating is expected in regions where aerosols are present; this is observed in the model runs. Temperatures increase by 30 K in dust regions and decrease by 10-15 K close to the surface. This recent result shows an agreement with this study. This latter result stems from less solar energy passing through the now near-opaque lower atmosphere. The middle and upper atmosphere is cooled during this scenario by up to 30 K. Zonal winds are found to be intensified during dust storms. Haberle et al., 1982 studied the effects of global dust storms on the atmospheric circulation. Significant changes occur with moderate injection of dust within the atmosphere where the jet speed and depth of circulation doubled. Further injection leads to further intensification with polar regions warmed through all altitudes by ∼20-25 K. Estimated temperature increases in the lower and upper atmosphere.

47 1.10. OPEN QUESTIONS

1.10 Open Questions

As MAVEN is the ﬁrst dedicated mission to characterise the upper atmosphere using compositional measurements, much work is required to understand the global overview of the upper atmosphere of Mars. This thesis aims to answers the following questions.

Models, such as the MCD, allow estimations of atmospheric conditions to be made at a global level. However, these models need to be validated against observational data to ensure their accuracy. As the MCD has recently been extended into the thermosphere, this thesis hopes to constrain the model with recent MAVEN data. Currently, there is no documented validation using thermospheric data. Is there a systematic diﬀerence between NGIMS and MCD densities?

MAVEN’s significant mission length allows a vast dataset to be constructed from which a global survey of the thermosphere can be undertaken. With this in mind, this allows temporal variations to be studied in density and temperature. What are typical dayside and nightside temperatures at the Red Planet and how do they compare with modelling efforts? This has been in local time by Stone et al., 2018, but this is now generalised in zenith angle. Open questions that can be addressed with this dataset include how the neutral thermosphere responds to solar-rotation effects; are effects prevalent at all altitudes studied by MAVEN? This extends previous work by Forbes et al., 2006. Additionally, the substantial mission length allows seasonal variations to be studied rigorously using a single dataset, for the first time, by removing other factors, such as latitude and local time. It is expected that densities and temperatures increase near perihelion, however by how much has not been systematically quantified.

The importance of gravity waves and their eﬀects on the thermosphere, both thermally and dynamically cannot be overstated. As gravity wave schemes become complex, observational data are required to validate models. Schemes need to ensure they can reproduce observations, leading to accurate momentum and energy values. This thesis aims to present a global survey of gravity wave characteristics from which models can be constrained. This is the ﬁrst study of its kind to fully characterise such waves in this way. What are typical amplitudes and dominant wavelengths of thermospheric gravity waves? How do these vary with zenith angle and season? This will hopefully lead to the improve initialisation conditions and gravity wave inclusion in GCMs should lead to a more accurate representation of the atmosphere, which is currently lacking. A question born out of the idea of cloud formation is, how

48 1.11. SUMMARY long can perturbations survive? Is the same wave observable on consecutive orbits and what are the implications of this?

The 2018 global dust storm gives an opportunity to undertake a case study into how the upper atmosphere responds and how this compares to previous storms. Although the behaviour, such as atmospheric expansion, is expected, we hope to quantify and compare with other instruments and storms. This is the first observational study to thermospheric gravity waves during a dust storm. The main open question is, how are gravity waves affected by dust storms? Is there a significant change in the wave spectrum during a storm? How would this affect the thermal and dynamical structure of the thermosphere?

The ﬁnal chapter introduces a brand new density dataset derived from TGO accelerometer measurements, so the questions to answer include what are typical densities and temperatures in this previously unstudied region, and how do values compare to the MCD? We hope to study wave evolution by utilising both the TGO and MAVEN datasets. How do amplitudes behave with increasing height? As postulated, can we observationally show that larger wavelengths dominate with altitude?

1.11 Summary

This chapter has introduced topics that are explored further later in the thesis. The Red Planet’s physical and orbital properties have been outlined. Furthermore, comparisons have been drawn with Earth. Typical density and temperature structures have been shown alongside a description of background physics. The LMD-MCD has been introduced in preparation for validation with observational data in Chapter 3. The generation, evolution, and implications of gravity waves in the Martian atmosphere have been summarised. The enormity and rarity of global dust storms have been introduced with the physics of storm growth and decay highlighted.

49 Chapter 2

Instrumentation and Data

2.1 Introduction

In this chapter, NASA’s Mars Atmosphere and Volatile Evolution mission (MAVEN) and ESA/ROSCOS- MOS’s ExoMars Trace Gas Orbiter (TGO) missions are introduced. Their main aims are outlined, and recent results are presented. MAVEN possesses, amongst other instruments, a mass spectrometer and an accelerometer. TGO possesses just the latter, amongst other instruments. The operations of these two instruments are described, and data retrieval techniques are outlined. MAVEN has both instruments and as such densities from these devices are compared. Fortunately for the science community, MAVEN and TGO sampled the upper atmosphere concurrently and in some instances gathered data in similar regions. This overlap period is shown, and the related studies performed in this thesis are introduced.

2.2 The Mars Atmosphere and Volatile Evolution Mission

The Mars Atmosphere and Volatile Evolution (MAVEN) mission was designed to explore the planet’s upper atmosphere, ionosphere, and interactions with the Sun and solar wind. A further aim is to elucidate the loss of Mars’ upper atmosphere over its history and fully characterise its composition (Jakosky et al., 2015b). These measurements allow the history of Mars’ atmosphere and climate, liquid water, and planetary habitability to be explored. Launched in November 2013, MAVEN began orbiting Mars in September 2014. After one year in orbit, NASA announced an extended mission of one year. As of December 2020, MAVEN is still active. It is the ﬁrst dedicated spacecraft to gather in-situ data about the composition and structure of the upper atmosphere and ionosphere of Mars. It is the ﬁrst spacecraft to measure atomic oxygen in the upper atmosphere, a crucial measurement for understanding

50 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION

CO2 cooling Fox, 2004. Processes that control the atmosphere will be explored, allowing a look back at Mars under diﬀerent boundary conditions. Another high-level objective is to measure the loss rate of the atmosphere to space. And again, the processes that control such loss are to be investigated. Additionally to the previous goal, with loss rates, it will be possible to step back in time to understand the history and evolution of the atmosphere. The latter points are not directly investigated in this study, but seminal work on this topic can be found in Jakosky et al., 2015a and Jakosky et al., 2017.

There are two main techniques employed to lower spacecraft into their science orbits, the first is involves the sole use of thrusters, and the second is aerobraking. The first is quicker, as once a spacecraft has reached its target body, thrusters are fired to reduce the spacecraft’s speed. The reduction in speed allows the spacecraft to be captured by the body’s gravity. Further thruster firings will lower the spacecraft’s altitude into its science orbit. This technique is considerably more expensive than aerobraking owing to the substantial use of propellant. The Mars orbit insertion (MOI) manoeuvre began with six thruster engines firing briefly to damp out deviations in pointing. Then, the six main engines quickly ignited and burnt for 33 minutes to slow the craft, allowing it to be captured in an elliptical orbit around Mars with a period of 35 hours. Six smaller manoeuvres were performed later to bring the highest and lowest points of the orbit to the altitudes desired for the science orbit. The overall fuel usage, and thus expenditure, can be dramatically reduced by implementing a technique called aerobraking. Thrusters are initially used to place the spacecraft in an elliptical orbit. Aerobraking involves flying the spacecraft through the atmosphere near periapsis. During its pass through the atmosphere, appreciable drag is exerted on the spacecraft, causing the spacecraft to decelerate and reduces its apoapsis distance given a loss of energy. At apoapsis, small thruster firings may be used to ensure the spacecraft passes once again through the atmosphere in the required density corridor. The density corridor is a range of densities that are a large enough to induce sufficient drag on the spacecraft, but not so large as to cause significant heating and mechanical damage. Aerobraking is a slower process, but it is made up for in lower cost. Additionally, data can be derived from its employment. As spacecraft fly through the atmosphere, the density can be recovered using the accelerations felt by the spacecraft as measured by the on board accelerometers. This is described later in this chapter. This technique was first used by NASA on the Magellan mission at Venus in 1993. It was first used as an orbital adjustment technique at Mars for MGS, leading to many discoveries about the atmosphere of Mars including gravity waves (e.g. Fritts et al., 2006, Tolson et al., 2007) and longer-term variability (e.g. Keating et al., 1998, Tolson et al., 2008). Its success is not limited only to MGS, as aerobraking was also employed for Odyssey (ODY)

51 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION and Mars Reconnaissance Orbiter (MRO).

At periapsis, MAVEN is ∼150 km above Mars’ surface where it can make in situ measurements of the upper atmosphere and has an apoapsis around 6300 km above the surface allowing for solar wind conditions to be studied. The elliptical orbit has allowed atmospheric loss mechanisms to be studied; this has to lead to Jakosky et al., 2015a concluding that the atmosphere is currently losing gas to space via stripping by the solar wind at a rate of 100 g/s leading to signiﬁcant loss over long periods. They found that enhanced solar activity, such as coronal mass ejections, increased the loss rate, thereby conﬁrming the relationship between the Sun and atmospheric loss. This loss rate can be applied to understand previous states of the atmosphere. A further study by Jakosky et al., 2017 revealed that Mars has lost about 66% of its atmosphere into space since its formation.

2.2.1 Spatial and Temporal Coverage

Figures 2.2.1a, b and c show MAVEN’s periapsis location in altitude, local solar time and latitude, respectively. Panel a shows periapsis altitudes typically above 140 km, with variation throughout the mission up to 180 km during the latter months of 2017. MAVEN performed Deep-Dip (DD) campaigns (red) which are visible between 120 km and 140 km. DD campaigns comprise orbits that probe deeper into the atmosphere, down to ∼120 km. These dives allow data in the lower thermosphere to be studied, allowing connections between the lower and upper atmosphere to be investigated. Densities are approximately an order of magnitude larger in this region than at 150 km. Each campaign lasts around seven days; the ﬁrst two to three days are occupied with lowering periapsis altitude and the remaining ﬁve days are used to gather density data. DD campaigns are referenced throughout this thesis, and as such, their locations are detailed in Table 2.2.1. Solar longitude is well sampled. Average latitude, solar zenith angle (SZA), local solar time (LST) and solar longitude (Ls) values for each DD campaign are shown. Panel b shows periapsis local solar times which MAVEN cycles through approximately every six months. Panel c shows periapsis latitudes. MAVEN requires longer to sample all latitudes; hence MAVEN has sampled each latitude only six times.

2.2.2 The Neutral Gas and Ion Mass Spectrometer

The Neutral Gas and Ion Mass Spectrometer (NGIMS) instrument on board MAVEN is used to study the composition and structure of the upper atmosphere (Mahaﬀy et al., 2015b). NGIMS measures both surface reactive and inert neutral species and ambient ions along the spacecraft track at altitudes below

52 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION

Figure 2.2.1: MAVEN’s periapsis location shown in (a) altitude, (b) local solar time and (c) latitude. Red points represent Deep-Dip passes. Solar longitude is shown on the bottom axis.

500 km. There are two operating modes (open- or closed-source) which alternate between odd and even orbit numbers. Figure 2.2.2 shows a diagram of gas flow through the instrument. The closed source operation works by opening an aperture permitting a sample of the atmosphere to flow into the antechamber before closing shortly after. The gas will thermalise in the antechamber, thereby becoming dependent only on mass and charge. Once thermalised, the gas passes through to the ionisation region, which consists of an electron impact hot filament ion source and becomes ionised and feels the effect of electric and magnetic fields. Once ionised, the gas flows through the quadrupole deflector and from this point follows the same path as the open-source gas. A quadrupole deflector consists of a DC quadrupole electric field. For the closed source measurements, the rods can be grounded to prevent bending of the gas. The open-source is used to sample gas constituents that are destroyed or transformed by collisions in the closed ion source. Constituents such as O and N are sampled via the open-source as

53 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION

Deep Dip () Orbits () Latitude (°) SZA (°) LST (hr) Ls (°)

1 714-747 42.6°N 109.1 18.3 291.1 2 1059–1086 3.8°S 9.3 11.9 328.6 3 1501–1538 62.6°S 110.4 3.5 11.4 4 1802–1838 63.9°S 91.1 16.0 37.5 5 3285–3327 33.2°N 96.5 5.2 166.9 6 3551–3586 2.9°S 166.4 0.7 194.1 7 5574–5620 63.6°N 87.0 20.3 49.4 8 5909–5950 18.9°N 25.0 13.7 76.3

Table 2.2.1: MAVEN Deep Dip Ephemeris. Note. Values are means at periapsis over each Deep Dip campaign. Adapted from Stone et al., 2018

Figure 2.2.2: Schematic of gas through NGIMS. Taken from Mahaﬀy et al., 2015b

they are surface reactive and can be absorbed by the ion source surface. The gas is collimated and passes through a crossed electron beam leading to ionisation. Once ionised, the gas is deﬂected 90° by the quadrupole deﬂector. For the open-source scenario, opposite voltages are applied to opposite rods

54 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION allowing the path to bend by 90°. After the quadrupole deﬂector, the paths taken by gases from the closed and open sources are the same. The gas passes through the ion lens system, which focuses the beam to ensure as much gas progresses through the instrument as possible. The next stage of NGIMS is gas ﬂow through the quadrupole mass analyser.

The mass analyser aims to select constituents with certain mass/charge ratios (m/z) for detection and achieves this as follows. Four hyperbolic quadrupole rods are constructed with opposite voltages applied to each parallel pair. In order to achieve mass selection an AC current with frequency ω is superimposed with a DC current to give ﬁnal voltages running through the rods of VDC + VAC cos(ωt) and

-VDC +VAC cos(ωt). This results in a 2-D quadrupole ﬁeld. The ionised particles will gyrate through the analyser, and only particles with a certain m/z value will successfully pass through for a given voltage ratio. All other particles will have unstable paths and collide with the rods. In around 4 s the mass analyser will cycle through all voltage ratios needed to cover the 2-150 amu mass range, allowing the atmosphere to be sampled with a spatial resolution of ∼100 m. The gas is then passed through another lens to focus it before entering the detector. The detector consists of electron multipliers that saturate at several million counts per second with an average gain of ∼5x107. The electron multipliers allow the detection of low signals given a background noise of less than one count per minute. The detectors measure the number of counts of each particle and combining all this information an abundance for each constituent can be calculated for each sampling period. A reservoir of gas in equal parts of N2, CO2, Ar, Kr, and Xe is stored in the instrument to ensure the accuracy and sensitivity of the instrument is satisfactory to mission requirements. At intervals of several weeks, the gas is released slowly in a restricted manner at apoapsis into the closed source. Biases can then be applied should the calibration yield inaccurate results (Jakosky et al., 2015b). For Ar, the sensitivity is ∼10−3-10−2 (counts/s)/(part/cc).

Stone et al., 2018 provides an explanation of the reduction techniques used to derive density data from raw instrument counts. The previous paragraph explained an idealistic situation; however, there are other signals which can detrimentally contribute to counts. Two such signals are background due to the desorption of gases from the inner surfaces of the instrument and background signal due to collisions in the quadrupole mass ﬁlter. Desorption is the release of adsorbed particles from a surface, in this case from the walls of the instrument. The signal due to desorption is greater on the outbound pass; thus, many studies consider only the inbound pass to reduce uncertainty. Although the background signal is 3-4 orders of magnitude smaller than periapsis densities, the successful removal of the background

55 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION signal allows densities at higher altitudes to be retrieved. Like many discrete detectors, NGIMS suﬀers from dead time. This is the period after an event (count) that the detector cannot process another count. The following is taken from Stone et al., 2018. The dead time correction takes the form

m = r exp(rτ) (2.1) where m is the measured count rate in units of per second, r the true event rate in units of per second, and τ the dead time given by

τ = max{A log m + B, 0} (2.2)

The coefficients A and B are determined from the data by comparing signals between molecular fragments at different counting regimes (Benna and Elrod, 2018). Deadtime coefficients A = 9.49×10−9 s and B = 1.39×10−7 s are used. Correcting for the detector dead time allows us to use count rates up to 2×107 s−1. Densities calculated for orbits beyond 748 are divided by a factor of 1.5331 to account for an observed change in the sensitivity of the instrument following DD1 (Benna and Elrod, 2018). Corrections are also required to account for an artificial increase in measured density due to an increase in density caused by interactions between the fast-moving spacecraft (∼4 km/s) and atmosphere. Benna and Elrod, 2018 explain correction factors to account for spacecraft ram effects.

2.2.3 Accelerometer

Although not part of the science payload, the accelerometers (ACC) on board MAVEN provide a wealth of data which can be exploited to retrieve atmospheric density, much like observations made by the accelerometers on board MGS (e.g. Keating et al., 1998; Withers, 2006; Tolson et al., 2007; Tolson et al., 2008). Acceleration data comes from the inertial measurement units (IMU) which detect any accelerations, including those due to atmospheric drag. This drag force is related to the density of the atmosphere and is recoverable. Accelerometers can be constructed using different operating principles. The basic working principle behind an accelerometer can be thought of as a mass on a spring encased within a housing. By measuring the extension of the spring, one can derive the acceleration of the system. Three orthogonal springs can be used to determine accelerations in all directions. Modern techniques involve the motion of silicon components for a fixed frame that measures the change in capacitance which is proportional to acceleration. ACC utilises an electromagnetic field which is varied in time to keep an electronically floating mass stationary relative to the case when the spacecraft senses

56 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION an acceleration. The current needed to do this is proportional to the total acceleration (Zurek et al., 2015). The accelerometer cannot implicitly diﬀerentiate between accelerations (e.g. between drag and gravity). Therefore these sources of acceleration need to be removed before recovering density from drag measurements. Tolson et al., 2008 discuss several of these in-depth. The total acceleration, am, felt by the spacecraft is

am = ab + aa + ag + aACS + ω × (ω × r) +ω ˙ × r (2.3) where, from left to right, the terms are the acceleration due to instrument bias, aerodynamic forces, gravity gradient, attitude control system thruster, and angular motion of the accelerometer about the centre of mass (last two terms). The aerodynamic forces term arises due to the atmosphere inducing a drag on the spacecraft. It is this term from which density is recovered once all other accelerations have been removed. The gravity term arises due to the irregular mass distribution of Mars. The effect of thruster firings on the spacecraft is understood, so by knowing when these firings occurred, they can be removed from the data. The acceleration contributions from the angular motion of the accelerometer are removed using the gyro data, discussed below. Accelerometers are mounted as close as possible to the centre of mass of spacecraft; this theoretically reduces the angular accelerations felt. Angular rates for each axis of the accelerometer are calculated, and polynomials are fitted and differentiated to give the acceleration (Tolson et al., 2008). The effect of solar radiation as a source of acceleration is important Earth but is assumed to be negligible at Mars (Bruinsma et al., 2004). Once all other accelerations have been removed from the data, the density of the atmosphere, ρ, can be recovered from the drag term using

2M ρ = 2 az (2.4) V CzA where M is the mass of the spacecraft, V is the velocity of the spacecraft, Cz is the aerodynamic drag coeﬃcient along the z-axis (pointing along trajectory), A is the area of the spacecraft perpendicular to its velocity vector, and az is the acceleration of the spacecraft centre of mass due to aerodynamic forces along the z-axis. Cz is a dimensionless quantity that accounts for the shape of the spacecraft and friction between the atmosphere and spacecraft. Cz is a function of density; therefore, the previous equation is solved recursively. M decrease as fuel is used for propulsive manoeuvres.

At 160 km, density is recoverable to ∼0.1kg/km3 for MAVEN which is equivalent to ∼5% noise level (Zurek et al., 2015). The IMU has limited resolution for measuring accelerations, which introduces

57 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION uncertainties. Error is potentially introduced when fluid models are used to determine the drag coefficient. The model includes the interaction of the gas flow with the spacecraft due to small-scale surface roughness, surface temperature and composition, gas composition and perhaps chemistry. All these errors equate to ∼10% of the drag coefficient (Zurek et al., 2015). Within each IMU is a three-axis ring laser gyroscope (RLG); each RLG measures rotation in one axis. For ease of explanation, it is assumed that beams travel in a circular motion around the rotation axis. In practice, mirrors are used to redirect beams. An initial input laser beam is split, causing rays to travel in a clock- and anticlockwise direction. A detector is located equidistant from the beam source. Without rotation, both beams are detected at the same time. With a clockwise rotation, the clockwise (anticlockwise) beam takes a longer (shorter) time to reach the detector unit. By calculating the time difference, the phase difference can be determined. The output voltage is proportional to the rotation; therefore RLGs measures rotation rate about its sensitive axis (Zurek et al., 2015).

Like all instruments, and as explained for NGIMS, calibration and biasing need to be performed to convert raw instrument readings into physical quantities. Instrument bias may be caused by heating of the IMU throughout an aerobraking pass and is seen as a systematic increase or decrease in accelerometer readings about their actual values. Thus, there are several occasions during the mission that the accelerometer bias is determined. These calibrations are generally performed before any propulsive manoeuvre where the accelerometers are used to determine the manoeuvre. Additionally, the bias is re-determined by fitting a line to the data before and after periapsis when the spacecraft is little affected by atmospheric drag. This linear fit can be removed from the data, reducing the bias (Zurek et al., 2015).

2.2.4 Comparison Between NGIMS and ACC Data

Along-track densities are retrieved by both NGIMS and ACC along all orbits, and therefore densities can be directly compared for each orbit. However, only DD orbits are used here. As NGIMS is capable of measuring the densities of multiple species, the total density is calculated using densities for CO2,

Ar and N2. At altitudes studied here, CO2 the dominant species, thus adding other more species to the total density makes a scant difference. Figures 2.2.3a-d show density profiles from four MAVEN orbits: 1061, 1062, 1063 and 1065, respectively. These orbits occurred during DD2 and occurred near noon, around 5°S and Ls=256°. NGIMS and ACC profiles are shown by blue and red lines, respectively. Inbound and outbound profiles are shown by solid and dashed lines, respectively.

58 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION

Figure 2.2.3: NGIMS (blue) and ACC (red) density proﬁles for orbit (a) 1061, (b) 1062, (c) 1063 and (d) 1065. Inbound and outbound legs are shown by solid and dashed lines, respectively.

Figure 2.2.3a exhibits apparent wave-like behaviour in the NGIMS data for both inbound and outbound legs, especially below 150 km. However, this behaviour is not repeated in ACC data, as similar behaviour would be expected for both instruments. Panel b shows excellent agreement not only between the instruments but also the passes; this implies very weak or no horizontal density gradients. Some wave activity is still visible below 150 km in the inbound NGIMS profile. Panel c displays different profiles. Again, perturbations are observed in only the NGIMS data. Lastly, profiles in panel d show remarkable agreement, particularly on the outbound leg. Two main inferences can be made: densities retrieved from both instruments are in general agreement with each other, and wave activity is more prominent in the NGIMS dataset, implying the resolution of ACC data is not sufficient for wave analysis. Fitted background profiles would invariably improve agreement between the datasets. Third-order polynomials are fit to the logarithm of the densities, which act as background profiles by removing wave activity. Agreement between the datasets can be quantified by taking the ratio between NGIMS and

59 2.2. THE MARS ATMOSPHERE AND VOLATILE EVOLUTION MISSION

ACC densities at given altitudes, denoted as ρNGIMS/ρACC . Altitudes of 120, 125, 130 and 135 km are used. Therefore, for each orbit, there are eight ratios - an inbound and outbound ratio for each of the four altitudes. Figures 2.2.4a-d show boxplots of ratios for seven DD campaigns at the four ﬁxed altitudes, respectively. Shown also is a dashed horizontal line that shows the expected ratio of one. DD3 (1501–1538) has been omitted based on a substantially broader range of ratios (0.1-3) than found for other campaigns. This exclusion allows other campaigns to be compared more easily.

Figure 2.2.4: Boxplots of ratios using interpolated density data from NGIMS and ACC at (a) 120 km, (b) 125 km, (c) 130 km and (d) 135 km for DD1-8, excluding DD3. A ratio of one is shown by a dashed horizontal line.

Figure 2.2.4a shows boxplots displaying ratios at 120 km. Only DD5 and DD6 dipped down to 120 km. For each campaign, median NGIMS and ACC densities are within 10% of each other. Furthermore, 50% of densities are within 20% of each other. Panel b shows ratios at 125 km. DD4 and DD8 probed down to this altitude. DD5 and DD6 stray away from their original behaviour at 120 km; the former has a median of around 0.8 while the latter ratio improves to near one. The range of values also diminishes,

60 2.3. THE EXOMARS MISSION suggestive that ACC and NGIMS densities are comparable. Both DD4 and DD6 show NGIMS and ACC densities are within 10% of each other; this is in excellent agreement. All DD campaigns probed down to at least 130 km, as visible in panel c. Here, all median ratios are within 25% of one with ranges stretching from ∼0.4 to 1.4. A general shift to lower ratios is evident for all DD campaigns indicating ACC densities are increasing more rapidly than NGIMS densities. Panel d shows ratios at 135 km and repeats the findings found at 130 km (panel c). Ratios continue to decrease, again suggestive of ACC densities becoming larger than NGIMS. One finding that has been implied in the above discussion is that ratios are distinctly different; there is no systematic difference between NGIMS and ACC densities, as may have been expected, shown by the large range of ratios. This suggests that a more complicated explanation that goes beyond a simple and predictable offset is required. It is known that both instruments perform most effectively at lower altitudes (higher densities); thus, uncertainties become fractionally smaller for higher densities. This is largely evident here. It is worth noting that, henceforth, ACC data are not used in this study for MAVEN. NGIMS are data preferred owing to the nature of studies undertaken; the first of two main reasons is the ability to differentiate between species, allowing to study the composition change, e.g. during dust storms. Secondly, ACC data exhibits significant noise (where uncertainties are greater than 5% of measured values) above ∼160 km, whereas NGIMS CO2 data remain noise-free well above 200 km. This allows a greater range of altitude variations to be studied.

2.3 The ExoMars Mission

ExoMars is a joint ESA-ROSCOSMOS two-part mission to search for signs of past life, variations in water, and investigate atmospheric trace gases and their sources (Vago et al., 2017). The ﬁrst part of this mission, launched in 2016, was Trace Gas Orbiter (TGO). TGO is tasked with identifying sources of methane and other trace gases that may evince biological or geological processes. Given its short lifetime of the order a few hundred years, when exposed to solar radiation any detection of methane implies it has been released recently. Thus far, TGO has detected no methane (Korablev et al., 2019). TGO’s science orbit fortuitously began in April 2018, a few months before the June 2018 global dust storm event. Layers of dust were found around 25-40 km altitude (Vandaele et al., 2019). TGO will operate as a communications relay for the second part of the ExoMars mission, the Rosalind Franklin rover. Rosalind Franklin is scheduled to launch in July 2020 with the primary goal to search for subsurface chemical and morphological life signatures. Both phases are outlined further below.

61 2.3. THE EXOMARS MISSION

2.3.1 Trace Gas Orbiter

The first phase of the mission consisted of Trace Gas Orbiter (TGO) and a test lander, Schiaparelli. TGO has a suite of four instruments that are used to achieve the mission goal of finding methane and other atmospheric trace gases at Mars. TGO performed aerobraking between March 2017 and February 2018 to circularise its initial orbit to its final 400 km science orbit. Aerobraking was paused in summer 2017 owing to Mars’ conjunction and resumed until February 2018. Routine commands and updates were not able to be reliably sent due to fear of deterioration (Scuka, 2017). Launched with TGO was an Entry, Descent and Landing Demonstrator Module (EDM), Schiaparelli. The EDM’s mission was to investigate local electricity and meteorology. Ultimately, it provided the opportunity to test technologies for future planetary landers. Unfortunately, the landing of Schiaparelli was unsuccessful. The IMU became saturated, and navigation data placed Schiaparelli below the surface. The combination of the parachute being released too early and thrusters firing for 10% of the anticipated time lead to systems being deployed at 3.7 km as if Schiaparelli had landed, but had in fact crashed.

TGO contains two IMUs, each containing three ring laser gyroscopes and three accelerometers. The operations of accelerometers and ring laser gyroscopes were outlined above in the context of MAVEN. The same working principles apply to TGO. Densities have been retrieved and are used in this study. The uncertainty in the derived density is the sum of a systematic part due to the uncertainty in CD, estimated to be 5% at these very low altitudes, and a noise and bias part due to the accelerometer. The systematic error has no impact on analyses of relative variations, e.g. wave perturbations. The bias and noise of the accelerometer were estimated through analysis of data outside the sensitivity range, i.e. above 130 km. The biases were estimated by computing averages before and after perihelion and were negligible (of the order 10−5 m/s2). The formal error cannot be computed based on the accelerometer specifications (as was done, in principle, for identical instruments on Venus Express in Mueller-Wodarg et al., 2016) as raw measurements are not available, but rather pre-processed accelerations for TGO. The formal noise of the Venus Express accelerometers, after processing of the velocity increments one second apart, was 0.001 m/s2 (1σ). Using that cut-off value leads to valid TGO densities to a maximum altitude of 115 km. However, after careful inspection of the acceleration and the resulting density profiles, the noise on the TGO accelerations appears to be on average twice lower, 0.0005 m/s2 assuming that lower value at the cut-off threshold leads to a maximum valid altitude of 120±4 km. Another way of determining the valid altitude range of the TGO densities is by using a comparison with a model, Mars-GRAM 2005 (MG05).

62 2.3. THE EXOMARS MISSION

The TGO-to-MG05 density ratios were computed for all proﬁles. The density ratios start to present a typical noise behaviour, minimal density ratios followed (preceded) by fast and large oscillations for the outbound (inbound) leg, for altitudes above 120-130 km. This is illustrated in Figure 2.3.1.

Figure 2.3.1: The TGO-to-MG05 density ratios for a proﬁle in January 2018 (blue line). x-axis is CNES Julian date. Altitude is shown on secondary y-axis (grey line).

TGO carries a suite of instruments capable of detecting trace gases within Mars’ atmosphere. The Nadir and Occultation for Mars Discovery (NOMAD) instrument consists of three spectrometers; these can detect methane and hydrocarbons (Vandaele et al., 2011). The Atmospheric Chemistry Suite (ACS) complements NOMAD by using infrared instruments to examine the chemistry and structure of the atmosphere (Korablev et al., 2018). The Color and Stereo Surface Imaging System (CaSSIS) is assigned to investigating the surface of Mars by capturing high-resolution images. This enables sources and sinks of trace gases to be identiﬁed (Thomas et al., 2017). Finally, the Fine Resolution Epithermal Neutron Detector (FREND) ﬁguratively digs into the surface. The detector is tasked with identifying reserves of subsurface hydrogen up to one metre below the surface (Mitrofanov et al., 2018).

63 2.4. CONCURRENT MAVEN AND EXOMARS DATA

2.3.2 Rosalind Franklin Rover

The second stage of the ExoMars mission is to land the Rosalind Franklin rover on the surface of Mars with the end goal of searching for the existence of past life on Mars. The launch date is set for 25th July 2020 (as of December 2020). Densities may be recoverable from accelerometers during the rover’s descent from which a vertical temperature proﬁle can be derived and compared to model outputs. This has been done previously with Pathﬁnder and ExoMars Schiaparelli (Magalhães et al., 1999; Aboudan et al., 2018). Beyond this, the Rosalind Franklin rover will not explicitly complement the work presented in this study, but will without a doubt improve our understanding of the Martian surface.

2.4 Concurrent MAVEN and ExoMars Data

During TGO’s aerobraking phase, MAVEN continued its science mission. For the first time, Mars’ upper atmosphere has been simultaneously sampled by two spacecraft. This exciting prospect allows the decoupling of long-term spatial and temporal variations in the upper atmosphere to begin. A more global picture of the density and temperature structure of the atmosphere can be formed. It should be noted that Mars Express is still in orbit and performs occultations to determine vertical neutral density profiles up to ∼50 km (e.g. Tellmann et al., 2006). The effects of significant events at Mars, such as coronal mass ejection (CMEs) or dust storms, can be studied nearly concurrently at two separate locations. With two spacecraft, there is a higher probability of observing any noticeable effects of such events. Thiemann et al., 2015 examined the dayside neutral density response in the upper atmosphere to solar flares and found significant heating caused by the flares, responding and recovering rapidly. With two spacecraft the effect of these flares could have been studied at two separate locations concurrently. Circulation may cause heating on the nightside and different latitudes may respond differently. In Chapter 7, these datasets are combined to investigate density and wave structures. Figure 2.4.1 shows TGO and MAVEN’s periapsis coverage in (a) altitude, (b) local time and (c) latitude during TGO’s aerobraking phase. In panel a, the lowering of TGO is visible in April 2017 as it descends from ∼120 km to its characteristic periapsis altitude of ∼105 km. The effects of conjunction are clear in summer 2017. MAVEN’s periapsis altitude remained relatively invariant at ∼150-170 km, with two dips to ∼130 km. No nominal DD campaigns were undertaken during this period. Panel b shows local solar time coverage. All times were sampled by TGO and nearly twice by MAVEN. In February 2018 both spacecraft sampled the midnight-dawn sector simultaneously. Panel c shows latitudinal coverage. TGO predominantly sampled the southern hemisphere, proceeding closer towards to pole as the aerobraking campaign advanced.

64 2.4. CONCURRENT MAVEN AND EXOMARS DATA

During this period, MAVEN principally remained in the northern hemisphere, however, moved in the southern hemisphere during the latter three months of the aerobraking campaign. Furthermore, sampled similar latitudes concurrently with similar local times in February 2018.

Figure 2.4.1: TGO (green) and MAVEN’s (blue) periapsis (a) altitude, (b) local time and (c) latitude during TGO’s aerobraking phase.

TGO probes deep into the atmosphere, typically down to ∼105 km. This is ∼15 km lower than MAVEN’s DD orbits and larger than Mars’ average scale height; therefore, it is expected to see potentially very diﬀerent behaviour. As discussed in Jakosky et al., 2017, the homopause location is reasoned to hover around 100 km, but cannot be resolved by accelerometer measurements alone. Although ACS is capable of deriving vertical CO2 density (and temperature) proﬁles, these are only retrievable at the morning and evening terminators in the 10-80 km altitude range. The homopause is unlikely to be found in this range, but rather ∼75-125 km (Jakosky et al., 2017). Towards the latter end of TGO’s aerobraking phase, MAVEN and TGO sampled similar regions concurrently. This overlap is exploited in

65 2.5. SUMMARY

Chapter 7 to garner complete thermospheric profiles from the two distinct altitude ranges. Both density and temperature profiles can be derived by hydrostatically connecting the profiles. These profiles are useful for understanding the unsampled structure but also for comparison with models as a method of validation. Complete profiles are of importance for modelling diffusion.

2.5 Summary

In this chapter, the MAVEN and ExoMars missions have been outlined, including a summary of their objectives. The instrumentation used to gather in situ atmospheric data has been discussed. A summary is shown below.

• MAVEN is the ﬁrst spacecraft to primarily probe the upper atmosphere of Mars. Its on board suite of instruments allows the thermosphere to be characterised by composition. Its coverage in altitude, local time, and latitude has been presented.

• NGIMS is the main source of data throughout this study. NGIMS measures the species with

masses 2-150 amu, which covers the major constituents in Mars’ upper atmosphere, with CO2, Ar

and N2 density data used throughout this study. The accelerometer on board MAVEN has been discussed.

• NGIMS data are compared to accelerometer data by interpolating onto a fixed altitude grid and taking the ratio at each altitude. Densities are more alike at low altitudes (large densities) but differ significantly at high altitudes. Along-track densities are typically within ∼20% of each other.

• The ﬁrst part of the ExoMars mission, TGO, is introduced. TGO undertook an aerobraking campaign to circularise its orbit from which densities have been derived from accelerometer measurements. During the latter part of TGO’s aerobraking campaign, it concurrently measured a similar region to MAVEN; the potential science associated with this fortunate occurrence is highlighted.

66 Chapter 3

Data Analysis and Model Comparison

3.1 Introduction

First, as temperature is not a directly measured quantity by either spacecraft, a technique is introduced to derive temperature profiles from density data. This technique is verified using density and temperature data extracted from the Mars Climate Database (MCD). Potential drawbacks and uncertainties with this technique are discussed. The MCD is used further to compare with NGIMS observations of individual species, such as CO2, Ar and N2, as well as Ar/CO2,N2/CO2 ratios, to establish if there any systematic difference between the MCD and observations. Finally, an interesting property within TGO density profiles is observed; the maximum density is consistently located away from the closest approach. This effect is quantified, and potential explanations are proffered.

3.2 Deriving Temperature Proﬁles From Density Data

Temperature is not a parameter directly measured by MAVEN. It therefore needs to be derived from measured densities. The hydrostatic equation (Equation 1.7, Chapter 1) relates vertical changes in pressure to density. Here, p, z, ρ and g are pressure, altitude, density, and gravitational acceleration, respectively. Integrating the hydrostatic equation with altitude downwards allows one to determine a pressure proﬁle; from this, a temperature proﬁle can be determined using the Ideal Gas Law. Given a column of atmosphere, the pressure at any given altitude, z, is derived by adding the weight of the atmosphere above, expressed by

Z ztop 0 0 0 P (z) = P (ztop) + ρ(z )g(z )dz (3.1) z

67 3.2. DERIVING TEMPERATURE PROFILES FROM DENSITY DATA

0 where P (ztop) is the pressure at the top of the column, ρ(z ) is the mean density in height element dz0 and g(z0) is gravitational acceleration at altitude z0.

During its flyby through Mars’ atmosphere, MAVEN travels both vertically and horizontally. Near periapsis, MAVEN is travelling quasi-horizontally, so any changes in density are likely to be due to horizontal structures, rather than vertical. Mueller-Wodarg et al., 2006 and Stone et al., 2018 discussed the effect of correcting along-track densities to account for horizontal structures. Stone et al., 2018 found a shift of ∼10 K after applying corrections, as such profiles are uncorrected and should be treated with caution. Further, for wave studies, a systematic shift will not significantly affect the results. Another issue to address in temperature derivation is the initial upper boundary condition, P (ztop). As Equation 3.1 is integrated downwards, and pressure is equal to the weight of the atmosphere above, an initial pressure is needed and shown later to be non-negligible. An initial temperature is required to determine

P (ztop) and is estimated from the top 10 km of the region studied, assuming to be isothermal. The scale height, H, is determined for this region by constructing a plot of log(ρ) in altitude and taking the gradient in this region using the method of least squares. The temperature can be calculated from the scale height using Equation 3.2 and assuming a mean molecular mass of m (equal to 43.03 amu).

mg T = H (3.2) k where terms have been previously introduced. This derived temperature can be used in the Ideal −12 Gas Law to retrieve the corresponding pressure. P (ztop) values are typically of the order 10 Pa at

∼240 km. Several scale heights below ztop, the initial choice of P (ztop) becomes unimportant and proﬁles from varying upper boundary conditions converge, as shown in Mueller-Wodarg et al., 2006 and

Snowden et al., 2013. The derived P (ztop) value is used in Eq. 3.1 to derive the pressure profile using a vertical step of 0.1 km. The Ideal Gas Law is then implemented to derive the temperature profile. Figures 3.2.1a and b show how temperature profiles converge when the upper boundary temperature condition is varied by ±25 K and ±50 K. From these offset temperatures, new pressure profiles are derived. In this case, temperatures converge within 40 km. This is likely to vary depending on the initial upper altitude. This has important implications for TGO temperature derivations where densities are only available over a 15 km range.

The error associated with temperature has been found numerically rather than analytically, following the method of Mueller-Wodarg et al., 2006. For each leg, 1000 random density proﬁles were

68 3.2. DERIVING TEMPERATURE PROFILES FROM DENSITY DATA

Figure 3.2.1: Temperature profiles from orbit 1060 derived from (a) inbound and (b) outbound Ar densities. The black line signifies the temperature profile derived using the upper boundary condition described. Profiles are shown for upper boundary conditions shifted by ±25 K and ±50 K. Temperature profile derived by Stone et al., 2018 is shown by the green dashed line.

created as follows. 1000 density proﬁles were produced assuming ρ(z) = ρobs(z) + ∆ρ(z) where ρobs(z) is the observed nominal density and ∆ρ(z) a perturbation chosen randomly to lie within the range

-σρ(z) ≤ ∆ρ(z) ≤ σρ(z). σρ(z) is the combination of error in density measurement and random uncertainty associated with the measurement. From these new proﬁles, temperature proﬁles were derived using the method described by Equation 3.1. Temperature errors are assumed to equal one standard deviation at each altitude level, with error bars being small due to small associated uncertainties. σ values are altitude dependent, with values of less than 10 K near periapsis and ∼25 K around 200 km.

Inbound and outbound temperature proﬁles inferred for orbit 1060 are shown in Figures 3.2.1a and b. Ar density data are used due to its inert nature. Clear wave-like behaviour can be seen, and the general trend is in agreement with what is to be expected (e.g. Bougher et al., 2015; Bougher et al., 2017). Near-isothermal behaviour at higher altitudes is observed in Figure 3.2.1b as conduction becomes dominant in this region. These are typical proﬁles with temperature values between 100 and 300 K dependent on location, local time and season. Uncertainties at higher altitudes are around 15

69 3.3. DRAWBACKS OF CURRENT TEMPERATURE DERIVATION TECHNIQUE

K and reduce to around 5 K near periapsis. The temperature profile presented in Figure 6 in Stone et al., 2018 from orbit 1060 is identical to the profile presented here; both studies have used different techniques to determine P (ztop). They determine upper boundary temperature and pressure values by fitting the density at high altitudes, assuming isothermality, to an equation of the form,

GMmi 1 1 Pi = Po,i · exp − (3.3) kTi r ro where Pi is the pressure of the ith species, Pi is the pressure of the ith species at the lower boundary of the ﬁtted region. G, M, mi, k are the gravitational constant, Mars mass, the mass of species i and

Boltzmann constant, respectively. Ti is the temperature of the ith species. r and ro are the distances above Mars’ surface and centre to the lower boundary of the fitted region, respectively. This temperature profile derived by Stone et al., 2018 is shown by the green dashed line in Figure 3.2.1a. Their upper boundary temperature is ∼50 K cooler than found in this study; this is likely due to the number of data points considered for the boundary condition. However, as expected, temperature profiles converge after several scale heights. The agreement between the green profile (Stone et al., 2018) and our converging profiles validates our technique.

3.3 Drawbacks of Current Temperature Derivation Technique

The above technique Equation 3.1 only considers vertical variations in density when deriving temperature profiles; however, MAVEN’s orbit trajectory becomes quasi-horizontal with respect to Mars’ surface as it approaches periapsis. The variations in the apparent vertical density profile are caused by vertical and horizontal variations and therefore may not be in hydrostatic equilibrium. Mueller-Wodarg et al., 2006 studied the effect of horizontal density variations on derived temperature profiles for Titan’s atmosphere. An artificial horizontal density gradient was introduced into an isothermal model, and densities were extracted along an imaginary spacecraft trajectory, and temperature profiles were derived in the manner explained above (Equation 3.1. Even with an ideal isothermal atmosphere, the extracted temperature profiles diverged away from the isothermal temperature by over 5 K. Even without knowledge of horizontal density variations in the atmosphere their effects can be seen by comparing an orbit’s inbound temperature profile to its outbound temperature profile. Physically, periapsis temperatures should be identical for inbound and outbound profiles during each orbit; the spacecraft is sampling the same region at the same time so profiles should converge to a single temperature, regardless of integrating inbound or

70 3.4. COMPARISON BETWEEN DERIVED AND EXTRACTED MCD TEMPERATURE PROFILES outbound data. This effect is exacerbated in a real atmosphere with non-uniform density gradients and waves. The extent of this effect can be quantified by determining the difference between inbound and outbound periapsis temperatures for each pass. These differences are denoted ∆T . Figure 3.3.1 shows ∆T as a function of periapsis solar zenith angle. On the dayside, ∆T is typically less than 50 K which for an atmosphere with along-track temperatures of ∼300 K gives a difference of ∼20%. Potentially earlier than expected, ∆T begins to increase fairly rapidly around 40°. By 80°, ∆T values are 80-90 K. This is significant if atmospheric temperatures are 300 K. Beyond 100° ∆T values gradually decrease to 60-70 K. Additionally, the trajectory length in solar zenith compounds this as passes spanning a large solar zenith range result in larger periapsis temperatures. Temperature gradients are investigated in more detail in Chapter 4.

Figure 3.3.1: Binned periapsis temperature diﬀerence between inbound and outbound proﬁles as a function of solar zenith angle

3.4 Comparison Between Derived and Extracted MCD Temperature Proﬁles

The Mars Climate Database (MCD) was introduced in Chapter 1, and its output is now compared with NGIMS densities. This is undertaken as a method of validation which is currently minimal in the upper

71 3.4. COMPARISON BETWEEN DERIVED AND EXTRACTED MCD TEMPERATURE PROFILES atmosphere. Solar minimum conditions are used within the MCD. Seasonal change is accounted for by the use of solar longitude within the model, which also accounts for Mars-Sun distance. Throughout the MAVEN mission, F10.7 varied between ∼20 and 80 sfu, according to Mars Initial Reference Ionosphere (MIRI) model (Mendillo et al., 2018). At Earth, during the MAVEN mission, F10.7 did not exceed 140 sfu; this is the value used as the MCD solar average condition, thus, as the majority of the mission possessed F10.7 values less than this, solar minimum conditions are used. Equivalent values are approximately 80 sfu at Earth. Furthermore, solar cycle 24 was quieter in terms of activity than previous cycles; therefore solar average was commensurate with typical solar minimum conditions. The MCD outputs, amongst other variables, the total pressure, temperature, density and volume mixing ratios; from these, the individual species’ densities can be determined. The MCD allows validation of techniques within a known environment. In this section, densities are extracted from the MCD using MAVEN spacecraft trajectories and then used to derive temperature profiles, as shown in this chapter. These are then compared to extracted temperature profiles along the passes. Figures 3.4.1a and b show derived and extracted temperatures, respectively. Temperatures are averaged in solar zenith angle and altitude with bin sizes of 5°×5 km. Figure 3.4.1a shows derived temperature profiles from along-track MCD densities. As expected, a clear trend in solar zenith angle is observed with the warmest temperatures (>220 K) at the subsolar point and the coolest on the nightside (∼150 K). The cause of the anomalously warm temperatures around 180 km at 40-60° is unknown. Figure 3.4.1b shows the extracted along-track temperatures from the MCD. These are consistently cooler compared to derived temperatures. This is in agreement with Stone et al., 2018 who found derived temperatures to be warmer than corrected temperatures, of which the extracted MCD temperatures can be taken as analogous. Figure 3.4.1c shows a more informative plot where the difference between the derived and extracted temperature has been calculated. At solar zenith angles below ∼30°, temperature differences are 20-40 K which are larger than expected for this region. The expected behaviour is that temperature differences should be largest across the terminator, where density gradients are expected to be most substantial. Locally, a slight increase in the difference is observed across the terminator, by up to 40 K. A more obvious increase at all altitudes would be expected. Although this finding does not support the expected behaviour, neither does it contradict the behaviour as the MCD density gradients are weaker than found in observations. With weakened gradients, temperature differences are reduced as observed in the above figures. Quantitatively, at 150 km, MAVEN densities decrease by just over an order of magnitude across the terminator, whereas the MCD estimates a more modest decrease of around a factor of two. Thus, density gradients are significantly less within the model. Overall, derived temperatures are typically

72 3.4. COMPARISON BETWEEN DERIVED AND EXTRACTED MCD TEMPERATURE PROFILES within ±20 K of ‘actual’ temperatures. This gives conﬁdence in our method of deriving temperatures. However, caution should still be taken when analysing observational temperatures; they are statistically likely to be warmer than actual temperatures given the results in Figure ?? in agreement with Stone et al., 2018.

Figure 3.4.1: (a) Binned derived temperatures using extracted along-track MCD densities from MAVEN trajectories. (b) Binned extracted along-track MCD temperatures. (c) Diﬀerence between derived and extracted temperatures. A bin size of 5°×5 km is used in all panels.

73 3.5. COMPARISON BETWEEN MCD AND IN-SITU DENSITY DATA

3.5 Comparison Between MCD and In-Situ Density Data

3.5.1 Comparison with Viking Landers’ Densities

CO2, Ar and N2 densities are extracted from the MCD along MAVEN trajectories taking into account altitude, local time, latitude, longitude and solar longitude. Both Viking 1 and Viking 2 possessed on board upper atmospheric mass spectrometers (UAMS) which allowed neutral densities within the atmosphere to be sampled during each lander’s descent. Viking 1 landed on 20 July 1976 and Viking

2 on 3 September 1976. Nier and McElroy, 1977 present these neutral density proﬁles for CO2,N2,

CO, O2 and NO between 100-200 km, along with early estimates for diﬀusion coeﬃcients. Number densities shown have a lower limit of ∼106cm−3; thus, densities for less dominant species (NO and

O2) are shown only up to ∼135 km and 160 km, respectively. CO2 is measurable up to ∼200 km. For each species, data are available at increments typically ∼10 km. Nier and McElroy, 1977 includes drawn lines that are the least-squares fit of a straight line to the data, and it is this line to which MCD comparisons are made; therefore, any wave activity is not shown. This best fit line acts as a background profile, therefore removes perturbations caused by wave activity. It must be noted that Viking 1 and 2 are landers, therefore produce one vertical profile each, as such MCD densities are extracted vertically upwards from the landers’ touchdown location (Viking 1: 22.48° N, -49.97° E, 16 hr LT and Ls=97° .

Viking 2: 47.97° N, -225.74° E, 10 hr LT and Ls=117.6° ). Figures 3.5.1a and b show CO2 (green) and

N2 (magenta) data gathered from the Viking 1 and Viking 2 landers, respectively. Solid (dashed) lines show Viking (MCD) data. Densities between Viking 1 (Figure 3.5.1a) and extracted MCD densities show a remarkable resemblance at altitudes 140-200 km for both studied species. Typical densities fall in the range 1013-1015m−3. From both Viking and MCD data, the atmosphere appears isothermal as shown by a constant scale height. Below 140 km, Viking and MCD densities diverge, suggesting a cooling in the MCD. The opposite behaviour is seen from Viking 2 results. Viking 2 still behaviours isothermally, but is cooler than predicted by the model above 140 km. At 200 km, MCD densities are over an order of magnitude larger than gathered by Viking 2. Densities become more comparable with decreasing altitude. Similar density structures are observed below 140 km where densities diﬀer by less than a factor of ﬁve. Similar temperatures are observed.

74 3.5. COMPARISON BETWEEN MCD AND IN-SITU DENSITY DATA

Figure 3.5.1: CO2 and N2 densities as a function of altitude taken from the MCD and (a) Viking 1 and (b) Viking 2. CO2 and N2 densities are shown by green and blue lines, respectively. Viking (MCD) data are shown by solid (dashed) lines, respectively.

3.5.2 Comparison with NGIMS Densities

In this section, NGIMS to MCD ratios are determined for all available orbits presented such that a global comparison can be made. This acts as further validation of the MCD. This section aims to answer the following question: Is there a systematic diﬀerence between NGIMS and MCD densities?

Data are binned in solar zenith angle and altitude with a bin size of 5°×5 km. This bin size allows orbit to orbit variability to be removed while retaining any larger trends. Figures 3.5.2a-c show NGIMS to MCD density ratios for CO2, Ar and N2, respectively, as a function of solar zenith angle and altitude. In each plot, the colour scale is centred around one, the value taken if NGIMS densities equal those output by the MCD. Ratios above one (red) indicate the MCD is underestimating densities. A discussion of each species’ ratio follows.

Figure 3.5.2a shows the ratio of MCD to NGIMS CO2 densities. There is clear day/night asymmetry in the ratios, as on the dayside ratios are typically larger than one with values increasing towards lower solar zenith angles up to a factor of ﬁve at the subsolar point. On the nightside densities typically diﬀer

75 3.5. COMPARISON BETWEEN MCD AND IN-SITU DENSITY DATA

Figure 3.5.2: Ratio of (a) CO2, (b) Ar, and (c) N2 densities between NGIMS and MCD data. Ratios are centered about unity. A bin size of 5°×5 km is used.

by a factor of two; this is fairly invariant in zenith angle. The strong contrast in densities is potentially due to heating and circulation issues, with the MCD typically producing cooler temperatures. Figure

3.5.2b shows a comparison of Ar densities. Whereas for CO2 there was a clear day/night asymmetry, no such trend is observed. Instead, it appears that overall Ar is consistently overestimated across nearly all zenith angles by typically over a factor of two than those found from NGIMS. Again, this overestimation increases towards the nightside. Underestimations are seen below 30° solar zenith angle. This region is one of the least sampled; therefore, the uncertainty is larger than around the terminator. MCD densities are approximately a factor of two larger. Figure 3.5.2c shows N2 ratios and similar behaviour to that presented for Ar. N2 ratios are overestimated for solar zenith angles bar those below ∼30°. The only appreciable diﬀerence between Ar and N2 ratios is more N2 bins have values closer to unity. A subtle altitude trend can be seen with ratios minimally diverging away from unity with increasing altitude. The day/night asymmetry in the CO2 ratios suggest the daily cycle is not fully understood and captured

76 3.5. COMPARISON BETWEEN MCD AND IN-SITU DENSITY DATA

by the MCD. Ar and N2 discrepancies most likely manifest from this. For all three species, the largest discrepancies occur at the sub-solar point. Thus, it is most likely the local time dependency is not being successfully captured.

Ar/CO2 and N2/CO2 ratios using MCD and NGIMS data are compared next. The aim of this exercise to understand how MCD relative abundances compare to observational data, shown identically to Figures 3.5.2a-c. Figures 3.5.3a and b show Ar/CO2 ratios taken from MCD and NGIMS data, respectively. Note the colour scale diﬀerence from the previous ﬁgures. Ar densities are consistently less than CO2 densities; therefore, a scale centred around unity is not used. MCD Ar/CO2 ratios reveal a trend in solar zenith angle with dayside ratios of ∼0.075, increasing to over 0.1 on the nightside. A similar trend is observed in the NGIMS data; however, ratios are about a factor of two smaller than values output from the MCD. Day and nightside ratios are ∼0.025 and 0.05, respectively. As well as day/night asymmetry there appears to be an altitudinal dependence, especially on the nightside where ratios are maximised to values around 0.1. The clear impact of scale height is evident here as the heavier

CO2 densities drop oﬀ more rapidly than Ar, thus increasing the ratio observed. However, the ratios are not in agreement.

Figures 3.5.3c and d show N2/CO2 ratios taken from MCD and NGIMS data, respectively. Unlike for Ar, N2 densities are comparable to CO2; thus, the colour scale is centred on one. MCD results are discussed first. The observed structure is more complex than found for Ar/CO2. On the dayside CO2 is dominant by up to a factor of ten, shown by the swathe of blue coloured bins. On the nightside CO2 is dominant up to ∼180 km. Above this N2 quickly dominates by over a factor of two. Again, the influence of scale height is visible. Results from NGIMS data are in very good agreement with the MCD ratios. Unlike as predicted by the MCD, CO2 is the dominant species on the dayside up to 170 km, suggesting the MCD is predicting cooler temperatures than observed. Evans et al., 2015 used dayglow observations by IUVS to derive CO2 and N2 density profiles from 18 October 2014 on 18 November

2014. By averaging in latitude and longitude, N2/CO2 ratios at 170 km range from ∼0.02 to 0.05. This is in good agreement with the averaged values found in this study.

The above two sections have compared in-situ spacecraft data with MCD data taken from the same trajectories. For the Viking comparison, the MCD does not successfully capture the in-situ densities for all altitudes; this is unanticipated given the MCD is validated against Viking landing data. More noticeable diﬀerences are observed in MCD/NGIMS comparisons. The MCD does not successfully capture trends

77 3.5. COMPARISON BETWEEN MCD AND IN-SITU DENSITY DATA

Figure 3.5.3: Ratio of Ar/CO2 derived from (a) MCD and (b) NGIMS data. Ratio of N2/CO2 derived from (c) MCD and (d) NGIMS data. A bin size of 5°×5 km is used.

in solar zenith angle with an underestimation (overestimation) on the dayside (nightside), which is likely a consequence of the MCD unable to recreate the local time dependency. The relative abundance of

Ar to CO2 is most alarming. The deficiency to capture these trends can be somewhat justified by the validation undertaken to constrain MCD densities (and temperatures), as the model top of the MCD has been extended upwards on numerous occasions from ∼90 km to ∼300 km from its inception to recent years (Forget et al., 1999; González-Galindo et al., 2015; Millour et al., 2018). As has been done in the lower atmosphere with landers and rovers, upper atmosphere densities need constraining by observational data. Currently, MAVEN provides the only substantial dataset that characterises the composition of the upper atmosphere, thus with only one version since MAVEN’s arrival (as of December 2020), the task of validating high altitudes has most likely just begun. Hopefully, our work highlights the current deficiencies with the model such that the respective team can address them. Overall, it is not surprising there is currently a systematic difference between model and observational densities, as

78 3.6. PEAK OFFSET IN TGO PROFILES this is the ﬁrst documented validation exercise. With time, these comparisons will allow the community to improve their models with newly added physics as we learn more about the atmosphere.

3.6 Peak Oﬀset in TGO Proﬁles

During the derivation of along-track densities from accelerometer data, it was observed that the location of maximum density did not always coincide with the closest approach. Gravity waves introduce horizontal density variations that may exceed vertical density changes, causing this apparent behaviour along the spacecraft trajectory. This offset has been explored and quantified using the difference in time between these two events. For each orbit, a background density profile is fit. Here, a third-order polynomial is fit to the logarithm of the density profile. Figures 3.6.1a-c show three density profiles derived during TGO’s aerobraking period. Periapses occurred at 2017-12-22 20:57:50, 2018-01-25 15:39:55 and 2018-02-05 15:54:44, respectively. Dashed vertical lines on each show two events. These are the point of closest approach and the maximum modelled density. Each profile displays a different offset characteristic. Figures 3.6.1a, b, and c show an offset of 25 s, 0 s and -15 s between closest approach and maximum density, respectively. Here, the positive (negative) offsets occur when the closest approach is prior (post-) point of maximum density. Figure 3.6.1d shows each orbit’s trajectory in local solar time (LST) and latitude. Colours correspond to respective density profiles in Figures 3.6.1a-c. Circles, squares, and crosses signify the start, closest approach, and end of the trajectory, respectively. These are shown on the density profiles, likewise. In light of discussion Chapter 2, data are restricted to below 120 km.

These oﬀsets are non-trivial and persistent through TGO’s aerobraking phase and are therefore investigated further. As this eﬀect is thought to be potentially caused by horizontal density gradients, the distances travelled by TGO in latitude (Slat) and longitude (Slon) along each pass are considered.

A ratio of Slat/Slon is computed for each pass. Hence, a ratio below one signiﬁes TGO has travelled more distance in longitude than latitude, and vice versa for ratios larger than one. Figure 3.6.2 shows the absolute time oﬀset as a function of this ratio. The ratio is shown in log scale.

The majority of passes traversed farther in latitude than longitude, apparent by a substantial portion data above a ratio of one. In this regime, offsets can range from 0 s to around 60 s with a peak in offsets in the range 20-40 s. This equates to an offset distance of approximately 100 km. In the cases

79 3.6. PEAK OFFSET IN TGO PROFILES

Figure 3.6.1: (a) TGO density proﬁle shown in time from closest approach and altitude (solid red line). Pass occurred at 2017-12-22 20:57:50. Circle, square and cross signify the start, point of closest approach and end of pass. Fitted density proﬁle is shown by dashed red line. ∆T is time between closest approach and maximum density. (c) and (d) follow the same format as (a), but for passes at 2018-01-25 15:39:55 and 2018-02-05 15:54:44. (d) Latitude and local time locations for passes shown in (a)-(c), coloured accordingly.

where TGO travelled further in longitude than latitude (ratio below one), different behaviour is observed. Close to one, offsets are commensurate to those already discussed. However, as longitude becomes the dominant direction of travel, time offsets lessen. The majority of offsets under this regime are less than 20 s, with smaller offsets typically associated with lower ratios.

From the above result, it can be inferred that the conjectured horizontal background densities are more prevalent and dominant in the latitudinal direction. One possible reason speculated is the diﬀerent timescales that densities vary in longitude and latitude. In the former direction, planetary rotation en- sures strong contrasts in density do not arise between the dayside and nightside (Bougher et al., 1988c).

80 3.6. PEAK OFFSET IN TGO PROFILES

Figure 3.6.2: Time oﬀset as a function of ratio of latitude to longitude traversed during pass

This is also evident later in Section 7.3.1. Moreover, for the latter case, a latitudinal gradient is likely induced in response to seasonal behaviour and remains established for longer than gradients in longitude.

A short study was performed to understand how the geometry of Mars affects the observed densities. A simple hydrostatic model was created for two planetary formations - spherical and ellipsoidal. The ellipsoidal model was based approximately on Mars with an equatorial (polar) radius of 3390 km (3370 km). With the model atmosphere above these surfaces, density data were collected along TGO orbits. Owing to an ideal atmosphere the spherical planet produces expected profiles; the only important factor dictating measured density is the altitude. Because of this, the closest approach is coincident with maximum density for all orbits. A different outcome is recognised when an ellipsoidal atmosphere is used. In this case, there is frequently a discernible offset between closest approach, as observed in the data. Similar behaviour was seen for ascending and descending behaviour, as above. However, for the radii stated above, offsets were significantly shorter than found observational; the majority were less than 5 s. For model offsets to be commensurate with observational values, the difference between the radii needs to be several tens of kilometres, which is not realistic for Mars, even including the rough topography. The planetary geometry does alter the offsets, however to a much lesser degree than experienced. There are other factors beyond this which most likely exacerbate this effect. The impact

81 3.7. SUMMARY of speciﬁc topography has also been explored. No correlation was found between oﬀsets and pronounced topography, such as mountainous regions or vast ridges.

3.7 Summary

In this chapter, the data analysis techniques used throughout this study have been presented. NGIMS data are compared to the Mars Climate Database. An oﬀset is observed between closest approach and maximum density in TGO proﬁles. The main results are outlined below.

• MAVEN does not directly measure temperatures so have been derived from NGIMS density data. A method has been presented, which integrates density downwards producing a vertical pressure profile. Subsequently, the Ideal Gas Law is used to derive a temperature profile. The advantages and drawbacks of this technique have been discussed. Using densities extracted from the MCD along spacecraft trajectories, temperatures have been obtained using the integration method. Overall, derived temperatures are typically within ±20 K of extracted temperatures, and gives confidence in our implemented technique.

• Comparisons between NGIMS and MCD densities are made. It appears that CO2 is overabundant,

whilst Ar and N2 are both under calculated. Possible drawbacks of the model have been discussed.

MCD Ar/CO2 and N2/CO2 ratios have been compared to identical orbits’ ratios from NGIMS. The local time dependence on density appears not to be captured successfully. Subsolar MCD densities are up to a factor a ﬁve smaller than observed by NGIMS. This behaviour is reversed on the nightside.

• Examination of TGO density profiles has revealed significant offsets between the maximum observed density and closest approach density. In an ideal atmosphere, there is no offset; maximum density is found at closest approach. It has been speculated strong latitudinal background density gradients preferentially cause this finding. Potential other causes have been discussed.

82 Chapter 4

Background Density and Temperature Analysis

4.1 Introduction

This chapter investigates background density and temperature structures and trends using data from NGIMS. A simple solution to solving the disparate periapsis temperatures scenario is proposed by making use of MAVEN’s short orbital period, as this allows average temperature profiles to constructed from a set of consecutive orbits given sampling location changes relatively slowly. This chapter examines temporal trends on three distinct timescales: diurnal, monthly and seasonal. The former is possible due to MAVEN sampling the full range of solar zenith angles multiple times. The second due to MAVEN’s short orbital period, allowing the atmosphere to be sampled continually (∼5 orbits per day) at similar orbit-to-orbit locations. The latter is feasible due to MAVEN’s lengthy nominal and extended missions. By this virtue, occasions arise when latitudes and local times are sampled numerous times, allowing these factors to be decoupled from the overall trends in density and temperature. By presenting atmospheric variability over different timescales, it offers a platform from which models can be constrained. For example, what effect does the 27-day solar rotation have on the thermosphere? Is this visible in the model data? What are the implications of seasonal behaviour in the upper atmosphere? These are crucial for understanding the underlying physics controlling atmospheric structure and are explored in this chapter.

83 4.2. AVERAGING TEMPERATURE PROFILES

4.2 Averaging Temperature Proﬁles

In Chapter 3, it was shown that inferred inbound and outbound periapsis temperatures are rarely identical when physically they should be. By considering campaigns of consecutive orbits, average temperature profiles can be determined with more agreeable periapsis temperatures, which are more physically mean- ingful. This is demonstrated by using orbits undertaken during DD1 (orbits 714-747 - details in Table 2.2.1). Figure 4.2.1a shows MAVEN’s trajectory through solar zenith angle and altitude for orbits during DD1. Red (blue) signifies inbound (outbound) orbits. Periapsis solar zenith angles are typically between 105° and 115° with MAVEN spanning 30° . MAVEN sampled a local time and latitudinal range of 17.5- 19.7 hr and 20.7-61.7°. Figure 4.2.1b shows derived temperature profiles from DD1, using the method presented in Chapter 3, as faded lines. Colour coding is conserved. Orbit-to-orbit variability is seen with temperatures ranging between 100 K for outbound passes to over 300 K for some inbound passes. Similarly, each profile exhibits large variations likely caused by pervasive wave activity in the atmosphere. These perturbations are explored further in Chapter 5. Considering just a single temperature profile may give an unrealistic profile for a given zenith angle range. To get a clearer idea of typical background structures, temperature profiles from DD1 are averaged to create single inbound and outbound profiles, shown by the dashed lines in Figure 4.2.1b. As expected, temperatures close to periapsis are in agreement. This technique is therefore useful for determining an average temperature profile from a range of consecutive orbits where wave activity and strong horizontal density gradients are present. Inbound and outbound behaviour over a short duration can be compared owing to minimal local time, latitude and seasonal variations. By considering consecutive orbits, realistic average temperature structures can be derived. Here, for example, temperatures across the temperatures range from 150-300 K, whereas nearer the nightside the structure isothermal around 150 K. These conclusions could not unambiguously be drawn by considering only individual profiles.

A slightly different approach in deriving average temperature profile is now outlined. From the same range of orbits, average inbound and outbound Ar density profiles are created using a bin size of 2 km, as used above. From these average density profiles, temperature profiles are derived using the method described in Chapter 3. These newly obtained temperature profiles are shown by dotted lines in Figure 4.2.1b. These are in good agreement with the averaged temperature profiles. For an isothermal atmosphere, this is expected. However, by averaging out divergences between true and derived temperature profiles caused by horizontal density variations, it is equivalent to initially averaging

84 4.3. INVESTIGATING DIURNAL TEMPERATURE VARIATIONS

Figure 4.2.1: (a) Trajectories of DD1 orbits (714-744) in solar zenith angle and altitude. Red (blue) lines show inbound (outbound) trajectories. (b) Derived inbound and outbound temperature profiles from DD1. Average profiles are shown by dashed lines. Temperature profiles derived from average density profiles are shown by dotted lines.

out horizontal density variations and then deriving a single proﬁle. This result demonstrates that either technique can be applied, with the same structures derived. Either way, it is better to characterise temperatures by averaging, not considering only individual proﬁles

4.3 Investigating Diurnal Temperature Variations

Any planetary body which is illuminated by the Sun can be divided into two regions - a lit dayside and a dark nightside. The terminator is deﬁned as the locus of points on a planet or moon where the line through its parent star is tangent. For an observer on the surface of a planet, the Sun disappears behind the solid body at a solar zenith angle of 90°. This assumes a perfectly spherical shape and treats the Sun as a point source. The terminator zenith angle increases with altitude. Beyond the terminator, the atmosphere is no longer directly solar heated.

The diurnal nature of temperature variations is investigated and will address the following open question: What are typical dayside and nightside temperatures at the Red Planet, and how do they compare

85 4.3. INVESTIGATING DIURNAL TEMPERATURE VARIATIONS with modelling efforts? One method to understand such structures is by considering fixed altitudes and investigating the temperature variation in solar zenith angle. Inbound and outbound background temperatures are interpolated at 160-200 km in 10 km increments. Background temperatures are derived by fitting a hyperbolic tangent function to individual temperature profiles; this removes wave activity Hedin et al., 1983. The reasons for studying these altitudes stem from both practical and scientific interest. Practically, nearly all orbits have a periapsis altitude of 160 km, or lower and therefore more data are available for analysis, at the selected altitudes, MAVEN is sampling vertical variations, more so, than near periapsis, and finally, these altitudes are several scale heights below the considered upper boundary, so this eliminates uncertainty in the upper boundary condition. Scientifically, this is the least-studied region within the atmosphere, thus will extend our understanding. With this in mind, Figure 4.3.1 shows interpolated background temperatures as a function of solar zenith angle. Thousands of data points are presented, thus for clarity, a hyperbolic tangent function has been fitted to each altitude level, and are shown in corresponding colours.

The dayside is discussed first. Temperatures range from ∼150 K at 160 km to over 300 K at 200 km. As background temperatures have been used, variability due to wave activity is minimal. As a consequence of this, orbit-to-orbit variability is most visible alongside seasonal behaviour. The latter is explored later in this section. Average temperatures, shown by the hyperbolic fits, span a smaller range from 200 K at 160 km to 230 K at 200 km. It is clear that average temperatures become more similar with increasing altitude; this is clear evidence of the atmosphere becoming isothermal. The reasoning for this was highlighted in Chapter 1; as the density in the thermosphere is tenuous, the mean free path of particles becomes comparable to the scale height towards the exobase; thus particles travel vast distances before colliding, so a large region of the atmosphere is isothermal due to conduction (Schunk and Nagy, 2009). Further, vertical conduction is large within the thermosphere, and this isothermal behaviour is shown below. Solar radiation also decreases with altitude; thus, less heating occurs. Tem- peratures are relatively invariant on the dayside up until ∼75 °. The behaviour at the terminator is explored in more detail in the next section. Temperatures decrease by ∼40-50 K on the nightside, with the coolest temperatures seen at the lowest altitudes. The range of average temperatures is more compact, spanning only 20 K. However, similar variability as observed on the dayside is apparent. One remark is the removal of wave activity from temperature profiles insignificantly changes average profiles, and similar orbit-to-orbit variability is still observed.

86 4.3. INVESTIGATING DIURNAL TEMPERATURE VARIATIONS

Figure 4.3.1: Temperatures interpolated onto the 160 km, 170 km, 180 km, 190 km and 200 km altitude levels and shown against solar zenith angle. A hyperbolic tangent function is ﬁt to each altitude level and coloured accordingly.

The behaviour exhibited by the thermosphere is one that is primarily solar driven. If the atmosphere were heated only by local solar absorption, temperatures on the night side would be significantly cooler, as found for Venus (Bougher et al., 1990). Modelling studies, such as Bougher et al., 1990, have investigated the general circulation at Mars and the subsequent effect on temperature. Bougher et al., 1990 saw diurnal behaviour with temperature peaks near 1500 LT (195-305 K) and troughs around at 0500 LT (145-177 K). These values are in good agreement with the results presented in this study. Bougher et al., 1990. carried out a numerical experiment to highlight the importance of planetary rotation on temperature dynamics by neglecting the effects of Mars rotation, and the results resembled behaviour modelled for Venus by Bougher et al., 1988a. Near-symmetric day to night wind and temperature distributions were found for this scenario, which is not observed in the data. More enhanced day-night density and temperature contrasts are found when rotation is neglected. Therefore, rotation buffers the

87 4.3. INVESTIGATING DIURNAL TEMPERATURE VARIATIONS day-night temperature contrast. Understanding day/night temperatures allow atmospheric dynamics to be understood fully. Temperature variation across the terminator may lead to useful insight about the dynamics in this region. During the discussion above, it was noted that temperature structures vary between the dayside and nightside, and this is brieﬂy explored now. Temperatures derived for solar zenith angles below 30° and above 150° are taken as typical dayside and nightside temperatures, respectively. The altitude range has been extended down to 120 km to include the DD orbits. The mean and standard deviation are calculated for each altitude level. Figure 4.3.2 shows the average dayside and nightside temperature proﬁles.

Figure 4.3.2: Temperatures binned in altitude for solar zenith angles less 30° (red) and greater than 150° (blue). Shaded regions show one standard deviation.

The dayside is warmer than the nightside as outlined earlier. The vertical structure in both regions is more apparent in this format. Near isothermal behaviour is observed above 170 km with the average temperatures increasing moderately with altitude from 220 K to 240 K. Below this, temperatures

88 4.3. INVESTIGATING DIURNAL TEMPERATURE VARIATIONS decrease more rapidly down to ∼150 K at 130 K. This hyperbolic-like behaviour has been assumed for fitting purposes on, for example, Venus (Hedin et al., 1983). This behaviour has been explained in Chapter 1. The standard deviation also decreases with decreasing altitude; this is likely a manifestation of both sampling and environmental reasons. The former is due to fewer orbits at these lower altitudes, thus little opportunity for significant variability. The latter could be borne from the effective thermostat in the thermosphere, which restricts substantial temperature changes. The nightside exhibits a similar trend to the dayside, but with less rapid cooling with decreasing altitude. Temperatures range from 100 K to 160 K. Bougher et al., 1990 noted that dayside temperatures appear to vary much more than global mean values, implying a small response by Mars nightside temperatures to changing solar fluxes. Less variation is seen for dayside values here. Modelling efforts have shown that the thermosphere is a capable thermostat via cooling mechanisms (Bougher et al., 1990). There are two similar reasons behind this. The first is the general temperature trends. The upper thermosphere is heated at different rates throughout a sol, as demonstrated by a difference of 70 K between day and night at 200 km. A descent through the thermosphere leads to a convergence of day and nightside temperatures. The dayside profile only reaches 130 km; however, a simple extrapolation would lead to further convergence between the profiles. The convergence to common temperatures suggests an effective cooling mechanism in and below this region on the dayside. The optical depths for EUV and UV wavelengths approach one, so no more dayside heating occur are low altitudes. CO2 cooling is dominant at Venus, however, due to Mars’ 10-fold smaller O abundance on Mars than Venus, CO2 cooling is rendered less effective for moderating solar flux changes on Mars (Bougher, 1995). It is believed that winds and conduction are more effective than the cooling mentioned above (Bougher and Roble, 1991). This effective thermostat restricts severe day/night temperature contrasts. Further evidence is the uncertainty in profiles. At the top of the thermosphere, one standard deviation on the day- (night-)side is 60 K (115 K). This is in part due to the choice of the upper boundary condition and highly variable solar fluxes. The amount of flux varies with season, heliocentric distance, local time and solar cycles. The range of temperatures rapidly decreases with descending altitude. By 130 km, the day and night side standard deviations are 20 K and 30 K, respectively. This narrow range of temperatures shows how efficient cooling mechanisms are to keep lower thermospheric temperatures within ∼30 K. These results are in very good agreement with those found by Bougher, 1995, as they found highly varying exobase temperatures (170-305 K) and less varying temperatures around 120-130 km of 160-190 K over the solar cycle.

Along-track density proﬁles have been extracted from the MCD, and temperature proﬁles derived

89 4.4. INVESTIGATING DIURNAL HORIZONTAL TEMPERATURE GRADIENTS from these. From Chapter 3, it was shown derived temperature profile differ from extracted temperatures, thus for a fair comparison with NGIMS results, derived profiles are used. Data taken at solar zenith angles below 30° or above 150° are binned in altitude, as undertaken for NGIMS data. The averaged temperature profiles are shown by dashed lines in Figure 4.3.2. Near the subsolar point (red), the MCD successfully captures the observed behaviour below ∼150 km with rapid cooling of 50 K over 20 km. Above 150 km, observations continue to show a dependence on altitude for temperature, as further warming of 50 K is seen up to 190 km. The MCD implies near-isothermal behaviour of 200 K above 150 km. The MCD clearly is too cool on the dayside by ∼20 K. On the nightside (blue), the MCD consistently predicts warmer temperatures by up to ∼25 K at 130 km, reducing to ∼10 K at 190 km.

Derived temperatures from NGIMS densities are as expected, based upon previous data as described above and with comparison to models. As alluded to in Chapter 3, and a more surprising result, is that there is no clear systematic diﬀerence in the model and observed temperatures; the MCD is cooler (warmer) on the dayside (nightside) than observed in the data.

4.4 Investigating Diurnal Horizontal Temperature Gradients

Average temperature profiles, as shown above, are used here to quantify horizontal temperature gradients in solar zenith angle, with a particular focus across the terminator. As before, orbits from DD1 are used to aid with the explanation. Their trajectories through solar zenith angle and altitude are shown in Figure 4.4.1a. Red (blue) lines are inbound (outbound) legs. Two initial solar zenith angle ranges of width 2° are used to filter temperature data, as shown by the black dashed boxes in Figure 4.4.1a, for example. The corresponding inbound and outbound temperature data and averaged temperature profiles are shown in Figure 4.4.1b. The temperature gradient is determined at each altitude level by dividing the difference in average inbound and outbound temperature by the change in solar zenith angle (°). Figure 4.4.1c shows a vertical profile of temperature gradients based on the average inbound and outbound temperatures in Figure 4.4.1b. All gradients are negative, which suggests temperatures are decreasing towards the nightside, as expected. Gradients range from 0 K/° to -9 K/° with an apparent increase in variation with altitude. This is repeated for all combinations of solar zenith angle ranges; the inbound range is kept constant whilst the outbound range is shifted by 1° . Once all outbound ranges have proceeded, the inbound range is shifted by 1°. Each gradient also has a zenith angle associated with it, given by the average zenith angle of the ranges. By cycling through all zenith angles, many

90 4.4. INVESTIGATING DIURNAL HORIZONTAL TEMPERATURE GRADIENTS gradients can be determined from just a small range of orbits.

Figure 4.4.1: Left pane: Trajectories of orbits 714-744 through solar zenith angle and altitude. Red (blue) show inbound (outbound) trajectories. Dashed black boxes show the solar zenith angle ranges used to determine temperature gradients. Middle panel: Temperature data (dots) from shown solar zenith ranges. Dashed lines show average temperature proﬁles. Right panel: Horizontal temperature gradient in K per solar zenith angle degree.

Figure 4.4.2 shows as global overview of gradient data binned in solar zenith angle and altitude. Temperatures decrease most rapidly near the terminator as solar insolation is signiﬁcantly reduced. Up to ∼75° temperature gradients rarely exceed ± 5K/°with no clear trend in zenith angle or altitude. Closer to the terminator, gradients increase by a factor of at least two to a maximum of -10 to -15 K/° with a noticeable decrease in altitude. Beyond the terminator, nightside gradients are similar to dayside values.

91 4.5. INVESTIGATING THE EFFECTS OF THE 27-DAY SOLAR CYCLE ON ATMOSPHERIC DENSITY

Figure 4.4.2: Horizontal temperature gradients in solar zenith angle binned by solar zenith angle and altitude. Bins which contain data are bordered.

4.5 Investigating the Eﬀects of the 27-Day Solar Cycle on Atmospheric Density

The following timescale considered is related to the rotation of the Sun. This section aims to answer the question as to whether solar rotation effects are observable in the thermosphere. The Sun goes through both decadal and monthly cycles of change, as well as unpredictable events such as coronal mass ejections (CMEs) and flares. During the 11.6-year solar cycle, the level of solar radiation varies between solar maximum and minimum (Clette et al., 2014). The appearance of the Sun varies during the 11.6-year cycle, with sunspot numbers significantly increased during solar maxima. Coronal mass ejections are large clouds of plasma which may be released from the Sun, and as plasma leaves the Sun it drags the magnetic field with it. The number and severity of CMEs increase during solar maxima and is maximised during the declining phase. Currently, it is not possible to study this cycle in its entirety with MAVEN data alone as data cover less than half the solar cycle, and few places have been sampled more than once, as will be shown in the next section. A more examinable period is the 27-day solar cycle caused by differential rotation of the Sun. The equatorial region rotates faster than the polar regions with periods of 24 days and 30 days, respectively. Magnetic field lines are forced to twist due to dif-

92 4.5. INVESTIGATING THE EFFECTS OF THE 27-DAY SOLAR CYCLE ON ATMOSPHERIC DENSITY ferential rotation which creates active regions that release enhanced solar energy, including periodicities in extreme ultraviolet (EUV) radiation responsible for heating the thermosphere (Hall and Hinteregger, 1970; Forbes et al., 2006). Hall and Hinteregger, 1970 studied the 27-day rotation effects using the Orbiting Solar Observatory; this orbiting satellite is located at 550 km above the Earth’s surface and has a wavelength range 1310 to 270 Å. In the 27-day variation reported in their study, an increase of about 40% in the solar EUV is identified while the 10.7-cm flux increased from 111 to 201. EUV flux is typically scaled by the Mars-Sun distance; however, the periodic nature is retained. As noted in Forbes et al., 2006, relatively little is known about the solar rotation effects on the thermosphere. However, many studies have examined these effects on the Martian ionosphere. For example, Withers and Mendillo, 2005 studied the response of the electron density peak to solar rotation and found a periodicity a ∼26 days.

The approach outlined in Forbes et al., 2006 is used here to identify the solar rotation effects on the Martian thermosphere. They compare the response of Earth (at 420 km) and Mars’ (at 320 km) thermospheres to solar rotation effects. Earth’s thermospheric data is derived from the Challenging Minisatellite Payload (CHAMP) accelerometer measurements. Mars data is inferred from the precise orbit determination of MGS. Concurrent measurements were taken between 01 January to 31 December 2003 and compared; these results are discussed later. Densities are interpolated to respective altitudes. Short-term variations caused by pervasive wave activity, amongst others, are averaged out by calculating a 27-day rolling mean. The window is centred about the date and is shifted by one day. Any potential solar rotation effects are isolated by subtracting the interpolated data from the rolling mean. In order to derive relative perturbations, the residual densities are divided further by the mean densities. To remove large variability, as in Forbes et al., 2006, a 5-day rolling average is determined from the residual. Figure 4.5.1a shows interpolated Ar densities at 190 km for all orbits taken during 2015. The 27-day rolling average is shown by blue crosses. The large variation seen between DOY 150 and 250 is primarily due to sampling the nightside. Predictably, the 27-day rolling mean captures the general trend successfully.

In the following, Earth days are used as found in NGIMS data ﬁles and periods are converted to Martian sols. Figure 4.5.1b shows the mean residual density after the subtraction of the 27-day rolling mean and application of the further 5-day rolling mean. There is a clear periodic motion between DOY 260-340 in the 5-day mean values. This covers nearly three solar rotations. A sinusoidal function is ﬁt using the method of least squares to the averaged residual data; this is a simple method to determ-

93 4.5. INVESTIGATING THE EFFECTS OF THE 27-DAY SOLAR CYCLE ON ATMOSPHERIC DENSITY

Figure 4.5.1: (a) Interpolated Ar density data at 190 km (red circles) for 2015 and 27-day rolling mean (blue crosses). (b) The 5-day rolling mean of residual densities (red circles) and a sinusoidal ﬁt between DOY 240 and 340 (blue line)

94 4.5. INVESTIGATING THE EFFECTS OF THE 27-DAY SOLAR CYCLE ON ATMOSPHERIC DENSITY ine amplitudes and periods. An example fit is shown by the blue line in Figure 4.5.1b. For this fit, the amplitude is 11.8% with a period of 26.6 days. The same procedure is performed with data from 2016, 2017 and 2018 using data at 160 km, 170 km, 180 km, and 190 km for all years. Intervals that show clear periodic nature, as shown for 2015 data, are selected, and sinusoidal functions are fit as before. Table 4.5.1 shows five intervals that have been manually identified that exhibit clear wave-like behaviour along with their respective fitted parameters. Amplitudes vary greatly over the four sampled years. Amplitudes varied greatly with year from under 4% in 2016 to nearly 30% in 2018. The average is 14.3±8.4%. For each chosen interval amplitudes generally increase with increasing altitude. The rate of increase is not constant across the years, nor for each interval. For example, in 2015, the amplitude decreased by 2.9% over 30 km, however, in 2018, the amplitudes decrease by 13.2% over the same range. Forbes et al., 2006 only presents results at 390 km; therefore, direct comparisons cannot be made. Nor can results found here be extrapolated upwards due to inconsistent trends in altitude. Seem- ingly larger amplitudes with higher altitudes imply that these regions are more susceptible to solar-driven effects. The mean period is 25.5±1.9 days. Withers and Mendillo, 2005 note a 27-day period at Earth corresponds to a 26-day period at Mars due to a difference in their orbital periods. This may explain the reduced average observed period. By identifying intervals where there is clear periodic behaviour, Forbes et al., 2006 perform fits to data; however, they do not explicitly extract nor state amplitudes and periods. They find relationships between the F10.7 index and density changes instead. Nonetheless, by inspection, amplitudes are ∼10-20% but can extend to over 40% within these intervals. Periods are ∼30 days; however, this is restricted by the manual subdivision of the DOY scale. The overall agreement between the two datasets suggests that strong solar rotation effects are present within the thermosphere.

There are several occasions where parameters could not be fit. One factor is the lack of data. During 2016, periapsis altitude was raised to above 180 km; therefore, data are not available below this altitude. Where fits are available, data are taken from the dayside where the atmosphere is directly heated by the Sun, thus limiting the opportunity to study this effect. Even with missing data, much can be inferred from the limited results. This response to the solar-rotation impacts is not exclusive to Mars, as alluded to with quoted studies. Guo et al., 2007 used retrieved densities from CHAMP accelerometer measurements. Explicit periodic behaviour is observed within the Earth’s atmosphere at 410 km. Maximum amplitudes of oscillations are less than 50% but typically more significant than those found at Mars. This is anticipated from the decrease in solar flux with distance from the Sun. Although not investigated at Mars, Guo et al., 2007 used several solar activity proxies such as soft X-ray, XUV,

95 4.5. INVESTIGATING THE EFFECTS OF THE 27-DAY SOLAR CYCLE ON ATMOSPHERIC DENSITY

Year DOY Altitude (km) Amplitude (%) Period (Days) Period (Sols)

160 8.9 27.9 27.1 170 11.2 26.8 26.0 2015 240-340 180 11.7 27.5 26.7 190 11.8 26.6 25.8 160 ††† 170 ††† 2016 260-320 180 * * * 190 3.7 27.7 26.9 160 5.7 19.8 19.2 170 5.3 22.8 22.1 2017 250-300 180 8.4 23.7 23.0 190 11.7 23.4 22.7 160 16.1 23.3 22.6 170 18.7 24.3 23.6 2018 50-90 180 27.6 23.2 22.5 190 29.3 23.0 22.3 160 * * * 170 15.1 17.7 17.2 2018 240-290 180 * * * 190 14.9 26.6 25.8

Table 4.5.1: Thermospheric response to solar rotation eﬀects. Table outlines selected intervals for which periodic activity is identiﬁed. Fitted wave amplitudes and periods are shown in percent and days, respectively. † - Not enough data. * - Data not periodic

96 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS and F10.7 and found thermospheric densities correlate well with these solar irradiances variations. The observation of periodic behaviour in density data at timescales of solar rotation is not unexpected, given behaviour observed in electron data (Withers and Mendillo, 2005) and neutral data at higher altitudes (Forbes et al., 2006). However, this is the ﬁrst study of its kind in this region, and shows that the eﬀects are less profound at lower altitudes.

4.6 Investigating Seasonal Density and Temperature Variations

The longer-term trend with season is now examined, and the seasonal effects are quantified - how much do densities and temperatures vary season? Are the effects negligible? If not, how much do they differ throughout a Martian year? In order to study the variation in the background atmosphere due to solar longitude, the effects caused by latitude and local time need to be removed. The general trend of temperature in latitude and local time for each season or part thereof could be found and systematically removed from temperature profiles, then averaged temperature profiles from each season could be compared to examine the seasonal effect. This technique relies heavily on the statistics of the thermosphere. Decoupling all these factors and deducing profiles which are purely dependent on the season is difficult. An alternative method is proposed below.

4.6.1 Identifying Regions Sampled Multiple Times by MAVEN

Orbits have been identified that sample similar latitude and local times, but different solar longitudes. This process is simplified further by removing the effect of altitude by considering one fixed altitude along each orbit. In the following study, all data are interpolated to 200 km. On the requirement that each orbit has a periapsis below 200 km, each orbit will contribute two data points for analysis at two separate latitudes and local times - one for inbound and one for outbound. The next step identifies groupings of orbits that have similar inbound and/or outbound locations. An initial range of orbits is considered over which latitude and local time at 200 km do not vary dramatically, for this a range of 10 orbits is chosen which equates to around two days worth of data. From this group of orbits, the maximum and minimum latitudes and local times are found. The second range of orbits is scanned through located at least 200 orbits later. Again, the maximum and minimum latitude and local time are computed and are compared to those from the first range. Orbit ranges are classed as overlapping if the maximum latitudes are within 2° of each other, and likewise, minimum latitudes must be within 2° of each other. Maximum local times must be within 0.5 hr. Similarly for minimum local

97 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS times. Ranges are manually inspected to see whether sets can be combined. As each orbit contributes two data points, there are three possible occasions where orbits may overlap. These are by comparing inbound to inbound, outbound to outbound and inbound to outbound legs. All three are considered here and shown in Tables 4.6.1-4.6.3, respectively, alongside the date, orbit, Ls, latitude and local time ranges of each overlapping period. A visualisation of overlapping occasions in local time and latitude is provided in AppendixA. These ranges are not exclusive to solely studying density and temperature. They can be utilised to study the seasonal trend in any measured quantity. It should be reiterated that these overlap regions apply to 200 km and will inevitably vary when considering other altitudes.

Date Orbit (#) Ls (°) Latitude (◦) Local Time (hr)

30 Nov 2014 - 06 Dec 2014 333-365 243.6-247.5 72.4 N-74.3 N 3.7-5.7 24 Jun 2017 - 01 Jul 2017 5300-5340 24.0-27.5 72.3 N-74.4 N 3.8-6.0 23 Dec 2014 - 28 Dec 2014 455-481 258.4-261.5 60.4 N-63.6 N 23.9-0.0 06 Feb 2016 - 12 Feb 2016 2635-2670 105.4-108.4 60.2 N-64.0 N 23.9-0.0 26 Feb 2015 - 06 Mar 2015 795-838 298.5-303.4 13.2 N-18.3 N 15.8-16.6 26 Mar 2017 - 03 Apr 2017 4825-4870 339.3-343.8 13.3 N-18.7 N 15.7-16.5 17 Apr 2015 - 29 Apr 2015 1059-1125 327.2-334.0 25.0 S-19.8 S 10.7-11.8 08 Oct 2015 - 21 Oct 2015 1995-2060 52.2-57.6 26.6 S-18.0 S 10.7-11.8 12 Dec 2015 - 21 Dec 2015 2335-2385 80.4-84.5 20.1 N-26.3 N 5.3-6.1 29 May 2016 - 06 Jun 2016 3240-3280 160.4-164.4 20.1 N-26.2 N 5.3-6.0 16 Apr 2016 - 22 Apr 2016 3010-3040 138.4-141.2 55.7 N-59.9 N 10.0-10.7 25 May 2017 - 30 May 2017 5141-5168 9.8-12.2 55.5 N-60.1 N 10.0-10.7 10 Aug 2016 - 17 Aug 2016 3635-3674 201.3-205.6 33.5 S-29.2 S 22.4-23.1 15 Jan 2017 - 23 Jan 2017 4460-4500 299.8-304.3 34.6 S-28.2 S 22.2-23.0

Table 4.6.1: Seven pairs of occasions where MAVEN sampled the same region of the atmosphere in latitude and local time during inbound legs at 200 km.

98 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

Date Orbit (#) Ls (°) Latitude (◦) Local Time (hr)

08 Dec 2014 - 13 Dec 2014 376-401 248.8-251.6 62.4 N-65.3 N 8.4-9.2 14 May 2016 - 20 May 2016 3156-3192 152.3-155.7 62.8 N-66.5 N 8.4-9.3 03 Aug 2015 - 09 Aug 2015 1648-1676 22.4-24.8 66.5 S-63.3 S 0.9-1.7 06 Jan 2017 - 11 Jan 2017 4413-4436 294.4-297.0 67.4 S-65.2 S 1.1-1.8 27 Sep 2015 - 02 Oct 2015 1934-1964 47.1-49.6 65.2 S-61.8 S 13.8-14.6 04 Nov 2016 - 10 Nov 2016 4082-4114 254.7-258.6 64.0 S-60.3 S 13.7-14.6 27 Jan 2016 - 04 Feb 2016 2584-2622 101.2-104.3 19.5 N-25.0 N 1.9-2.5 14 Jul 2016 - 19 July 2016 3486-3515 185.4-188.5 21.1 N-25.9 N 1.9-2.4 23 Sep 2016 - 28 Sep 2016 3866-3895 228.4-231.9 33.2 S-29.5 S 18.9-19.5 26 Feb 2017 - 04 Mar 2017 4678-4713 323.9-327.6 34.8 S-29.5 S 19.0-19.6 24 May 2016 - 30 May 2016 3210-3243 148.8-160.7 57.2 N-61.0 N 7.2-7.9 04 Jul 2017 - 09 Jul 2017 5356-5382 28.9-31.2 56.5 N-59.8 N 7.1-7.7

Table 4.6.2: Six pairs of occasions where MAVEN sampled the same region of the atmosphere in latitude and local time during outbound legs at 200 km.

99 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

Date Orbit (#) Ls (°) Latitude (◦) Local Time (hr)

16 Nov 2014 - 17 Nov 2014 260-266 234.8-235.5 70.0 N-70.5 N 9.7-9.9 07 May 2016 - 09 May 2016 3123-3131 149.0-149.8 68.9 N-59.5 N 10.1-10.4 16 Mar 2015 - 23 Mar 2015 891-929 309.2-313.4 3.1 N-9.0 N 14.2-1439 20 Apr 2017 - 27 Apr 2017 4960-4993 352.7-355.8 3.7 N-7.3 N 14.2-14.7 07 May 2015 - 14 May 2015 1167-1208 338.2-342.2 36.3 S-30.4 S 9.3-10.0 06 Nov 2015 - 15 Nov 2015 2146-2195 64.8-68.8 37.6 S-31.0 S 9.2-10.0 02 Jul 2015 - 03 Jul 2015 1469-1476 6.8-7.4 70.6 S-70.0 S 2.8-3.1 29 Dec 2016 - 02 Jan 2017 4368-4389 289.1-291.6 71.5 S-69.7 S 2.7-3.5 23 Aug 2015 - 30 Aug 2015 1753-1789 31.5-34.7 57.1 S-52.6 S 15.5-16.3 21 Oct 2016 - 28 Oct 2016 4013-4046 246.2-250.3 55.8 S-51.8 S 15.5-16.3 28 Oct 2015 - 05 Nov 2015 2100-2141 61.0-64.3 12.6 S-7.4 S 9.4-10.0 12 May 2015 - 19 May 2015 1198-1233 341.2-344.7 11.0 S-6.5 S 9.5-10.1 29 Dec 2015 - 06 Jan 2016 2430-2468 88.2-91.4 65.1 N-39.5 N 3.7-4.4 24 June 2016 - 30 June 2016 3379-3411 174.3-177.6 36.2 N-41.2 N 3.8-4.4 23 Feb 2016 - 25 Feb 2016 2728-2738 113.3-114.2 69.7 N-70.5 N 21.2-21.6 24 Aug 2017 - 25 Aug 2017 5623-5632 51.5-52.2 71.6 N-72.2 N 21.4-21.7 16 Jun 2016 - 22 Jun 2016 3333-3371 169.7-173.5 5.9 N-11.6 N 3.7-4.4 07 Jan 2016 - 15 Jan 2016 2477-2518 92.2-95.5 4.4 N-10.2 N 3.7-4.4 27 Aug 2016 - 05 Sep 2016 3727-3772 211.8-217.1 45.2 S-40.1 S 20.5-21.4 09 Feb 2017 - 16 Feb 2017 4589-4625 314.3-318.2 46.2 S-41.4 S 20.6-21.4 14 Oct 2016 - 19 Oct 2016 3973-4001 241.4-244.8 68.1 S-65.2 S 14.9-15.9 19 Sep 2015 - 25 Sep 2015 1891-1925 43.5-46.3 69.4 S-66.1 S 14.8-15.9 10 Dec 2016 - 17 Dec 2016 4272-4306 277.8-281.8 60.8 S-56.8 S 2.5-3.3 24 Jul 2015 - 28 Jul 2015 1591-1611 17.5-19.2 58.9 S-56.3 S 2.6-3.1 01 Feb 2017 - 09 Feb 2017 4546-4590 309.5-314.4 22.3 S-16.9 S 20.6-21.3 04 Sep 2016 - 11 Sep 2016 3768-3804 216.6-220.9 21.5 S-15.7 S 20.7-21.4 12 Apr 2017 - 18 Apr 2017 4916-4947 348.4-351.4 25.6 N-29.3 N 14.4-14.9 19 Mar 2015 - 26 Mar 2015 906-945 310.9-315.1 26.0 N-30.6 N 14.4-15.2

Table 4.6.3: Fourteen pairs of occasions where MAVEN sampled the same region of the atmosphere in latitude and local time during inbound (upper rows) and outbound (lower rows) legs at 200 km.

100 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

4.6.2 Density Variability with Season

Now that latitudinal and local time variations have been removed, the seasonal eﬀect is investigated. For each range in Tables 4.6.1-4.6.3, the mean density and solar longitude are calculated. There- fore, for each overlap there are ρ1, ρ2, Ls1 and Ls2 values. A new quantity denoted ρs is given by

|ρ1 − ρ2|/(ρ1 + ρ2). ρs produces a value between 0 (signifying densities within an overlapping pair are identical) and 1 (signifying densities are very diﬀerent).

Figure 4.6.1 shows density variation, ρs, in solar longitude. Mars’ orbit is shown by the black circle. The arrow shows the direction of Mars’ orbit. Grey dashed lines mark out four seasonal reference points (Ls=0°, 90°, 180°, and 270°). For each overlapping pair shown in Tables 4.6.1-4.6.3, a line joins the two diﬀerent solar longitudes from which ρs was calculated; therefore there are 27 lines from the 27 pairs.

Each line is coloured by ρs. For example, the near-vertical green line to the left of the Sun is the pair- ing 23 December 2014-28 Dec 2014 and 06 February 2016 - 12 February 2016 (second row, Table 4.6.1).

The expectation is that overlapping ranges with similar solar longitudes (shorter lines) should yield low ρs values as Mars has not precessed far through its year and vice versa, diﬀerent solar longitude

(longer lines) should have larger ρs values associated with them. There are several occasions where similar locations were sampled between Ls=90° and Ls=180°, as shown in the upper-left portion of Figure

4.6.1. ρs values are expectedly low, barely exceeding ∼0.3. During these times, the Mars-Sun distance is maximal; thus, influences are likely to be minimal. A grouping of pairs is observed with similar Ls differences between northern spring and northern summer. ρs values during these seasons are typically no less than 0.6. Thus, it can be inferred that densities vary to a more considerable degree in this region. The last primary result this plot reveals is the potential effect of the ’dust storm season’ on densities. As discussed in Chapter 1, the dust storm season straddles perihelion (Ls∼271°). Lines emanating from this region take ρs values greater than 0.8; this is true for those extending to Ls∼45° which signals a definite seasonal variation, but also those that stretch from Ls∼280-290° to only Ls∼0-20°. These latter solar longitudes differences are similar to those shown in the upper left. ρs values are substantially different, suggesting the dust storm seasons plays a significant role in driving density changes.

Studies so far have not rigorously studied seasonal variation in such a manner. Liu et al., 2017 studied the seasonal variation of longitudinal structures using NGIMS data. Although seasonal density variations

101 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

Figure 4.6.1: Density variations throughout a Martian year. Each line represents an overlapping period shown in Tables 4.6.1-4.6.3. One line is an occasion where MAVEN sampled the same region of the atmosphere in latitude and local time. Lines have feet at sampled solar longitudes. Lines are coloured by how diﬀerent densities are between sampled periods. 0 (1) is no (large) change.

were not explicitly explored in their study, seasonal variations can be inferred from their work. Similar latitudes and local times were sampled in May 2015 and November 2015; these cover substantially more orbits. Solar longitudes for the two months were Ls∼340° in May, close to northern spring equinox, and Ls∼70° in November, close to northern summer solstice and aphelion. Using densities presented in their study, ρs values at 200 km for these months are ∼0.75. This is in line with expectant values from Figure 4.6.1. The orbital ranges used in this study are suﬃciently large to produce comparable results to a study using a month’s worth of data. The increase in densities around perihelion owing to an expansion in the atmosphere caused by lofted dust. To achieve ρs values upwards of 0.8, densities must vary by a factor of 10. Furthermore,

102 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS to achieve values above 0.98, which is an upper limit in our study, the discrepancy in densities must be a factor of 100. Such large seasonal changes have not been quantiﬁed observationally

4.6.3 Temperature Variability with Season

An identical examination to that above is now performed using temperature data. Temperatures are interpolated onto the 200 km altitude level. Figure 4.6.2 shows an identical plot to Figure 4.6.1, however, seasonal variability in temperature is quantified as |T1 − T2|, where T1 and T2 are average temperature values for the sampled regions. Whereas for density variations, differences vary by over an order of magnitude, average temperatures typically vary by no more than ∼100 K, therefore only absolute temperature differences are taken forward.

The main contrast between seasonal density and temperature variations is the relative variability throughout a Martian year. This is further evidence that the thermosphere is an effective thermostat, restricting temperatures to within a fixed range. Explicit behaviour is not apparent as it was in the previous section with variation during the dust storm season not evident. Consistent values are observed between northern summer and autumn, with typical differences of 40-60 K. The above results have been achievable due to MAVEN’s extensive mission length; more pairings will occur if additional, currently unused, data from 2019 onwards are utilised. Hence, model comparisons are necessary. Bougher et al., 2015 studied seasonal variations using the Mars Global Ionosphere-Thermosphere Model (M-GITM). While M-GITM has the capabilities to discern effects caused by the 11-year solar cycle, the consequence of such an external factor cannot be yet be identified in the data. Bougher et al., 2015 present results from solar minimum, moderate and maximum conditions. MAVEN arrived during the declining solar phase (moderate to minimum); as such, it is these conditions from Bougher et al., 2015 that are used for comparison (Lee et al., 2017). Exospheric dayside (lower zenith angles) are considered first in Bougher et al., 2015. For solar moderate (minimum) conditions, temperatures lie in the range 260-300 K (190-220 K). As this is for an idealised situation, one would expect to see more substantial variation due to wave activity, e.g. gravity and thermal waves. The most considerable variations, as seen in observations, are between perihelion and aphelion (Ls=251° and 71°, respectively). Many of the data emerging from around perihelion are taken on the dayside, thus, on the whole, are comparable with Bougher et al., 2015. Bougher et al., 2017 used NGIMS and Imaging Ultraviolet Spectrograph (IUVS) data to examine seasonal and solar activity trends in scale heights and temperatures. One key finding in agreement with results here is significant heating between aphelion and perihelion of several tens of

103 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

Figure 4.6.2: Temperature variations throughout a Martian year. Each line represents an overlapping period shown in Tables 4.6.1-4.6.3. One line is an occasion where MAVEN sampled the same region of the atmosphere in latitude and local time. Lines have feet at sampled solar longitudes. Lines are coloured by how diﬀerent temperatures are between sampled periods.

104 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

K. One of the more substantial differences is observed between Ls∼260° and Ls∼105°. These occurred in December 2014 (end of solar maximum) and February 2016 (start of solar minimum), respectively (Table 4.6.1 - second row). The M-GITM predicts a temperature difference above 200 K; part of this substantial difference can be attributed to temperatures modelled during peak solar conditions, rather than declining phases. Cross-spacecraft comparisons can be made as initially presented in Bougher et al., 2000. The most pertinent spacecraft for this particular comparison are Viking 1 and 2 during minimum conditions at Ls∼95-120° and Mariner 9 nominal mission during solar maximum conditions at Ls∼300°. Respective temperatures are 186 K, 145 K and 325±40 K; these are per expected differences found in this current study. The next two largest differences cannot be attributed to different solar phases. Apart from the highlighted cases above, it can be assumed that a large portion of the pairings occur during solar minimum and moderate conditions. According to the M-GITM, temperature differences should scarcely exceed 70 K. Further, spacecraft temperature profiles during solar minimum vary by a similar amount, thereby showing agreement with MAVEN results presented here. The results found here indicate further that the M-GITM is a robust model which can successfully account for seasonal variations. Martian seasons are affected by both planetary obliqueness and distance from the Sun. If the former is temporarily neglected, the effect of the latter can be explored and is undertaken below. Given the clear seasonal dependence on density, as shown in the previous section, the lack of trend in temperature is unexpected. This highlights how effective the atmosphere is at controlling temperature via its thermostatic features, e.g. thermal conduction and CO2 cooling. This lack of trend is worth studying further.

Further Investigation Into Seasonal Temperature Variations

At any given distance from the Sun, the solar ﬂux (F ) is inversely proportional to the Mars-Sun distance (R) squared. If it assumed that thermospheric temperature (T ) is proportional to F then T ∝ R2, then the constants of proportionality need not be known if comparisons between the two scenarios are made. 2 The expectation is then T1/T2=(R2/R1) , For each pair shown in Tables 4.6.3-4.6.1, the ﬁrst range is subscript one, the latter range two. This relationship is tested now using the pairs in Tables 4.6.1-4.6.3.

For each overlap, a value T1/T2 is determined using temperatures from earlier. To get the uncertainty in this value a random temperature from range one is divided by a random temperature in range two and repeated 1000 times from which the standard deviation is calculated and taken to be the uncertainty. 2 This is repeated for all overlap occasions. Figure 4.6.3a shows T1/T2 against (R2/R1) . The expected 2 result is T1/T2=(R2/R1) which is shown by the black dashed line. This is the expected behaviour for

105 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS a purely, constantly heated atmosphere. Overall, the behaviour exhibited by the data is in agreement with the expected trend to within the tolerance of the uncertainty.

A measure of the differences between the actual and expected T1/T2 values are determined for each 2 pair. The expected value is given by (R2/R1) , as governed by the above law, and the difference is 2 therefore |T1/T2-(R2/R1) |. Figures 4.6.3b and c show these differences as a function of local time and latitude, respectively. Solar zenith angle is not used as this varies within each pair owing to planetary obliqueness and M-S distance. From the basic theory explained early in this section, it may be expected that only the dayside follows the behaviour as only this portion of Mars is directly heated by solar radiation. There is a slight trend with local time with a grouping of points located around noon with 2 low |T1/T2-(R2/R1) | values (<0.25). As expected, this implies more direct heating on the dayside. Slightly larger values are seen in the dawn and dusk sectors. Figure 4.6.3c plots the differences in latitude. Near the equator, differences are typically ∼0.1. Differences increase towards the northern polar region as differences can exceed 0.3. Differences in the southern hemisphere are of similar value to near the equator. Near the poles, solar radiation passes through more atmosphere to reach a given altitude compared to at the equator, as shown in Chapter 1. By sampling the same season, local time and latitude should result in small differences. Overall, the behaviour exhibited is what is to be expected by a solar-driven atmosphere.

4.6.4 Southern Polar Warming

In Section 4.6.3, results have shown that there are certainly seasonal variations in density and temperature. The unanticipated small diﬀerences between expected and actual T1/T2 values in the southern hemisphere lead to an interest in potential polar warming. This is inspired by a study by Bougher et al., 2006. Initially, only the orbits shown in Tables 4.6.1-4.6.3 were used, however this severely limited conﬁdence in results. Thus, a new approach was taken, whereby all data could be included. Four altitude levels are selected - 160 km, 170 km, 180 km, and 190 km and data are interpolated accordingly. Although passes probe deeper than these altitudes, good coverage is available for all latitudes. Data are then categorised into one of four bins. Orbits can either be on the dayside (06 - 18 LST) or nightside (18-06 LST) and either near perihelion (1.38-1.52 AU) or near aphelion (1.52-1.66 AU). Increasing the number of bins reduces the number of orbits per bin; thus, four bins are used for brevity and clarity. Figures 4.6.4a-d show temperature as a function of latitude for the four considered altitudes. Here, red (blue) lines symbolise orbits near perihelion (aphelion) and solid (dashed) lines signify dayside (nightside)

106 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

2 Figure 4.6.3: (a) T1/T2 against (R2/R1) at 200 km. Crosses are average T1/T2. Error bars are 2 one standard deviation. The dashed line shows the expected fit of T1/T2=(R2/R1) . (b) Difference 2 between average T1/T2 (or (R2/R1) ) and expected value as a function of local time. Error bars are one 2 standard deviation. The dashed line is a best fit. (c) Difference between average T1/T2 (or (R2/R1) ) and expected value as a function of latitude. Error bars are one standard deviation.

orbits. A rolling mean is employed with a 5° window.

Figure 4.6.4a shows temperature at 160 km. The expected behaviour with the warmest temperatures found near perihelion on the dayside is seen. Substantial warming occurs across the equator with temperatures exceeding 240 K. Coolest temperatures are observed on the nightside around perihelion, extending down to 160 K. Aphelion temperatures are fairly invariant throughout the day, with temperatures between 160 K and 200 K. Figure 4.6.4b shows temperatures at 170 km. Temperatures across all cases are more alike at this altitude and begin to exhibit behaviour observed at higher altitudes. The dayside perihelion temperatures remain the warmest. A peak of 20 K in the dayside aphelion temperature is apparent around 0-40°N. This is most likely due to northern summer occurring near aphelion, thus being directly heated. Northwards of ∼40°S, nightside perihelion and aphelion are near identical with temperatures generally 180-200 K. Southwards of ∼40°S sees an interesting trend. Signiﬁcant warming of ∼30 K is discernible towards the south pole. In the opposite, and more expected manner, nightside

107 4.6. INVESTIGATING SEASONAL DENSITY AND TEMPERATURE VARIATIONS

Figure 4.6.4: Average temperatures on the dayside (solid lines) and nightside (dashed lines) near perihelion (red) and aphelion (blue) interpolated at (a) 160 km, (b) 170 km, (c) 180 km and (d) 190 km as a function of latitude.

108 4.7. SUMMARY aphelion temperatures cool by ∼30 K towards the south pole. Dayside warming/cooler is observed but occurs nearer the south pole. Figures 4.6.4c and d show very similar behaviour to that observed at 170 km (panel b). The cooling around aphelion agrees with ﬁndings from MGS during the southern winter solstice (Ls=70-90°); temperatures near 120 km increase slightly from the equator (130–140 K) toward mid-latitudes (up to 160 K), while dropping to 100 K near the South pole (Keating et al., 2003). ODY data revealed strong northern polar warming within the 100-130 km altitude range during its aerobraking campaign (Ls=265°–310°). At 110 km, warming increased from ∼100 K to 170-200 K, maximising on the nightside. At 120 km, warming was still observed but to a lesser degree; temperatures reached 160-170 K. Obvious northern warming is not seen for any of the four cases presented here. Bougher et al., 2006 suggested a strong inter-hemispheric circulation during northern winter to be responsible for this warming. This is driven by the stronger insolation and dust heating near perihelion. This circulation most likely explains the strong polar warming, not previously observed at these altitudes. Bell et al., 2007 modelled this further using the M-GITM to understand vertical dust transport. Bougher et al., 2006 did not simulate southern warming in light of aerobraking ﬁndings; however, this should be considered in the future.

4.7 Summary

In this chapter variations in background densities and temperatures are investigated primarily on three timescales: diurnal, 27-day and seasonal.

• Clear diurnal behaviour is observed with dayside temperatures in the region 150-300 K, increasing with altitude. Nightside temperatures are found to be typically between 100 and 250 K. Evidence of an eﬀective thermostat is presented with dayside and nightside temperatures appearing to converge in the lower thermosphere. Temperature gradients are most signiﬁcant across the equator taking values of ∼10-15 K/°. This is expected within a solar-driven thermosphere.

• The eﬀect of the 27-day solar rotation has been explored. The removal of a 27-day rolling mean reveals a strong periodic trend, with densities varying by up to 10%. This is in agreement with results at higher altitudes. This trend is not always visible within the data, inferring some spatial and temporal dependence. The most apparent periodicities occur on the dayside.

• The seasonal variation in density has been investigated using the overlapping orbits. Commensur- ate with small diﬀerences in sampled solar longitudes, density diﬀerences are comparatively small.

109 4.7. SUMMARY

This is true during Northern summer and autumn. The most considerable density diﬀerences occur when one of the two ranges in a pair is sampled during the dust storm season (around perihelion). This is true even for solar longitudes that are separated by 90°.

• Seasonal temperature variations have also been studied. The general trend is ambiguous. However, a general agreement with the sparse previous measurements during solar minimum and the Mars Global Ionosphere-Thermosphere model (M-GITM) is observed. In line with the results from M- GITM, temperatures typically vary by no more than ∼60 K across solar minimum and moderate. As MAVEN approached during the declining phase, it is unknown how much temperatures would vary by.

• Evidence of southern polar warming on the nightside near perihelion is presented. Temperatures increase by up to 30 K. This has not been observed in data before. However, it has been explained using dust-induced circulation as proposed by Bougher et al., 2006.

Whilst this chapter has investigated density and temperature variations of substantial time scales (one day to several months), the next chapter probes variations along each orbit. These variations are interpreted as waves and are characterised to understand them fully.

110 Chapter 5

Gravity Waves in the Martian Upper Atmosphere

5.1 Introduction

In this chapter, gravity waves within the Martian atmosphere are introduced, and their role described therein. This chapter aims to answer the following questions: what are typical amplitudes and dominant wavelengths of thermospheric gravity waves? How do these vary with zenith angle and season? This will hopefully lead to the improve initialisation conditions and gravity wave inclusion in GCMs should lead to a more accurate representation of the atmosphere. Gravity waves are extracted from NGIMS data. Waves in the Martian atmosphere are time-varying structures with spatial scales, as measured via wavelengths, of tens to hundreds of kilometres in the vertical and horizontal direction. These wavelengths and amplitudes are extracted from the data, and their diurnal and seasonal variations are explored. Waves are expected to grow with altitude, as described in Chapter 1; this is tested by examining how amplitudes vary with altitude. As topography is a known mechanism of wave generation at the surface, possible correlations between amplitude and topography are explored. Finally, waves from consecutive orbits are shown to demonstrate wave propagation within the atmosphere.

Gravity waves are imperative to study in the context of the Martian atmosphere, especially within the upper atmosphere. As described in Chapter 1, wave amplitudes grow with altitude to conserve momentum. It is within the upper atmosphere that these waves begin to dissipate and break, thus depositing substantial momentum and energy within this region. This can lead to the slowing of ﬂows

111 5.2. ATMOSPHERE PERTURBATIONS and warming/cooling of the atmosphere. Therefore, gravity waves as a source of momentum and energy are crucial to our understanding of the upper atmosphere. On a more practical level, more spacecraft will unquestionably arrive at Mars in the not-too-distant future. Waves are related to variability in the atmosphere; understanding this variability is essential for predicting atmospheric conditions encountered by future spacecraft to Mars. Where do we see the largest gravity waves? What are their typical amplitudes? These questions are answered below.

5.2 Atmosphere Perturbations

To extract perturbations from the temperature and density profiles, unperturbed background profiles need to be determined. Only Ar profiles are used in this analysis. England et al., 2016 showed that near-identical wave structures are observed in at least CO2, Ar and N2 profiles. Inbound and outbound legs are treated separately and therefore have different background profiles. There are many options which have been considered and used previously, including running averages (Creasey et al., 2006b; Fritts et al., 2006). Temperature is highly variable in the thermosphere, so there is not a single function which can be used universally for all temperature profiles. The general behaviour shows an increase in temperature with altitude, which, at high altitudes, becomes isothermal (Bougher et al., 2017). A hyperbolic tangent function is often used for the background temperature in the thermosphere, given by Equation 5.1,

z − zmin T (z) = Tmin + (Tmax − Tmin) tanh (5.1) ∆z where Tmin and Tmax change depending on location, local time and season, z is the altitude above the surface, zmin is periapsis altitude and ∆z is the altitude range where the temperature is not isothermal. A hyperbolic tangent function is used as this allows the isothermal behaviour at high altitudes in the thermosphere and exosphere to be captured. This function will also successfully capture the rapid decrease in temperature in the 120-140 km region. This function contains no oscillations and reduces the risk of introducing artificial waves to the fit. The background temperature is fit using the method of least squares. The isothermal temperature calculated earlier (Equation 3.2) is used as an initial value for

Tmax and the temperature at periapsis as Tmin. ∆z is initially set as 100 km. All three are optimised to give the best-fit background profile using the method of least-squares. A representative set of orbits were examined, and the profiles were captured successfully by the fit. Figures 5.2.1a and d show the

112 5.2. ATMOSPHERE PERTURBATIONS inbound and outbound temperature profiles for orbit 1060. Temperature increases with altitude as heat is conducted downward. The isothermal behaviour can be seen in panel d with a value of 260 K. Panel a does not display such clear behaviour, suggesting the upper atmosphere continues to be heated at higher altitudes. The profiles have clear waves present. To extract perturbations from the density profiles, an exponential function could be fit, but this assumes the atmosphere to be isothermal, which has been shown not be the case. A third-order polynomial is chosen and fit to the logarithm of the density. This low order polynomial is chosen to reduce the possibility and impact of edge effects. Inbound and outbound density profiles are shown for orbit 1060 in Figures 5.2.1b and e.

Normalised perturbations are determined by subtracting the data from the background profile and normalising by dividing this residual by the background profile. As seen in Figures 5.2.1c and f, gravity waves are composed of smaller waves with varying wavelengths. The main properties considered here are amplitude and wavelength. A fast Fourier transform (FFT) is performed on the extracted normalised perturbations allowing the wave properties to be identified. A single FFT is performed over the entire altitude range for each leg. Due to wave growth/decay, amplitudes do not remain constant for a given wavelength. Extracted amplitudes are averages over the sampled range since a straightforward Fourier transform does not allow for accounting of wave decay. Using the amplitudes and wavelengths from the four most dominant waves, a new wave can be constructed using the wavetrain described by Equation 5.2.

3 X 2π An sin z + φn (5.2) λ n=0 n th ◦ where An, λn and φn are the amplitude, wavelength and phase of the n wave. φn is initially set to 0 for all n. The phase of each composite wave is unknown and therefore needs to be fit for comparisons with the observed perturbations. This is determined by least-squares fitting. The fits were automated given the large number of orbits being analysed, with manual checks performed on a representative sample set. In some cases, two waves could capture the gravity wave successfully, in others more were needed. It was found that, overall, gravity waves were generally captured sufficiently well with four waves. By considering four waves, the varying wavelengths can be captured. By fixing the number of waves, comparisons between properties can be made, and the fitting process is done automatically without human checks. As discussed, four waves are used to reconstruct gravity waves. The initial wavetrain is used as an estimate for the best fit wavetrain. The wavetrain is refined further using the method of least squares by adjusting amplitudes, wavelengths and phases of each wavetrain during the fit.

113 5.3. EFFECTS OF SPACECRAFT TRAJECTORY ON INFERRED GRAVITY WAVE WAVELENGTHS

Figures 5.2.1c and f show the perturbations (faded lines) and their wave fits (dark lines) for both the inbound and outbound leg of orbit 1060. This orbit has been shown as it highlights ’typical’ gravity waves found throughout this study. The inbound wave profiles (Figure 5.2.1c) clearly exhibit behaviour described earlier; temperature (red) and density (blue) waves are in near perfect antiphase as described by Equation 5.3, discussed in Section 5.4. Both structures in the temperature and density fields are captured well by the wave fits. The perturbations are centred around zero, which shows waves have been successfully extracted from the background profiles. Wave amplitudes are around 10%, and wavelengths are 20-30 km. As shown later, this wave is typical. The amplitudes are larger than uncertainties which suggest physical waves are present. The density amplitude around 160 km is underestimated by about 5%. There are shorter wavelengths of around 5 km which have not been captured. These are visible up to around 180 km. Given their relatively small amplitudes of a couple of percent, we do not consider them in this analysis. Pressure perturbations are shown by the grey dashed line. The amplitude of such waves is typically an order of magnitude lower than density and temperature amplitudes. The outbound wave profiles (Figure 5.2.1f) show an example of a long-wavelength gravity wave. Temperature (red) and density (blue) are still in anti-phase like the inbound leg but to a lesser degree. The general trend of the wave is captured well. Amplitudes are about 10%, and vertical wavelengths have values between 60 km and 80 km; as discussed later in this chapter, these wavelengths are longer than typical values. Smaller-scale perturbations with visible wavelengths of a few km are visible but not included in the analysis. Their amplitudes are at least an order of magnitude smaller than the more dominant waves and therefore not considered here. The similarity between fitted temperature and density perturbations in respective inbound and outbound legs are shown by similar amplitudes and wavelengths in Table. 5.2.1. This gives confidence in the methods used.

5.3 Eﬀects of Spacecraft Trajectory on Inferred Gravity Wave Wavelengths

In this short section, the eﬀects of trajectory on measured gravity wave wavelengths are investigated. This is aided by the use of the MCD which initialises gravity waves in a random direction. Although this scenario is highly idealised, the results highlight potential problems with current techniques used to derive wavelengths. Five scenarios are considered where wavelengths of 5 km, 10 km, 15 km, 20 km and 25 km are used. As shown above, these are typical wavelengths. As gravity waves are dir-

114 5.3. EFFECTS OF SPACECRAFT TRAJECTORY ON INFERRED GRAVITY WAVE WAVELENGTHS

Figure 5.2.1: Panels (a) and (d) show temperature profiles (red solid line) for inbound and outbound legs, respectively. Red dashed lines are fitted background profiles. Panels (b) and (e) are Ar abundance profiles (blue solid line) for inbound and outbound legs, respectively. Blue dashed lines are fitted background profiles. Panels (c) and (f) show the inbound and outbound extracted waves. Red are temperature structures and blue are density structures. Faded lines show the actual waves. Dark lines show the fitted wavetrains. The grey dashed lines show pressure perturbations. Data is taken from ◦ ◦ ◦ orbit 1060. Periapsis location: -2.1 latitude, 149.9 longitude, 12.1 LST, 327.3 Ls. Error bars are one standard deviation of the random temperature profiles.

ected randomly in the MCD, the only possible way to guarantee accurate wavelength measurements is to ﬂy vertically through the wave. An orbiting spacecraft does not this. At periapsis, MAVEN is moving quasi-horizontally, therefore would not measure a vertical wavelength. This section attempts to measure the vertical wavelength along a spacecraft trajectory. In Section 5.2, a robust technique used to extract gravity wave characteristics from data is described. This technique determines the most dominant wavelengths for an entire leg. As the eﬀect of spacecraft trajectory on the measurement of wavelength is sought, ideally wavelength as a function of a trajectory parameter is wanted. One such

115 5.3. EFFECTS OF SPACECRAFT TRAJECTORY ON INFERRED GRAVITY WAVE WAVELENGTHS

A1 A2 A3 A4 λ1 λ2 λ3 λ4

T 11.3 6.2 5.6 5.5 23.6 32.6 16.3 20.9 Inbound ρ 10 7.6 7.1 3.9 25.3 16.8 33.7 19.1 T 8.3 3.3 1.7 1.7 73.4 47.9 37.1 17.8 Outbound ρ 11 4.2 2.8 2.3 56.1 37.2 24.7 122

Table 5.2.1: Amplitude and wavelengths of constituent waves that form the wave extracted from orbit 1060. Inbound and outbound leg values are shown. A are amplitudes (%) and λ are wavelengths (km)

parameter that is used now is the angle to the planetary normal. This is 90° at periapsis and increases away from closest approach. As gravity waves in the MCD are periodic at the initial wavelength, a simple analysis can reveal wavelength as a function of angle to the normal. Peaks (maximum) in density are identiﬁed, and the diﬀerence in altitude between adjacent peaks is determined, giving an estimate of the wavelength. The average angle to the normal between adjacent peaks is used as a measure of the angle. Thus, several values for the wavelength can be measured along the trajectory. Figure 5.3.1a shows apparent wavelength as a function of angle to normal for 5 km, 10 km, 15 km, 20 km and 25 km model wavelengths. Data points darken with increasing wavelength length. In all cases, the measured wavelength near periapsis (90°) is ∼0 km, as expected. A horizontally moving spacecraft cannot detect vertical variations. Below angles of ∼92°, all measured wavelengths are identical, regardless of the model wavelength. Therefore, using these data to determine vertical wavelengths is futile. The measured wavelengths increase away from periapsis as the spacecraft begins to travel with a vertical component with respect to the Martian surface. The measured wavelengths appear to plateau to values less than the model wavelengths. With longer orbital data, wavelengths at higher altitudes could be measured. To understand the general behaviour of how successfully wavelengths are captured, measured wavelengths are normalised by the known model wavelength. Figure 5.3.1b shows normalised wavelengths, λ˜. Similar behaviour is seen between all wavelengths. λ˜ values are ∼0 near periapsis, as expected. These increase with increasing trajectory angle. λ˜ plateaus around 0.8 at around 96°. This is equivalent to an altitude of ∼240 km. Therefore, over an entire trajectory, wavelengths are almost certainly always underestimated if they are purely vertical.

116 5.4. COMPARING TEMPERATURE AND DENSITY PERTURBATIONS

Figure 5.3.1: (a) Estimated wavelengths as a function of angle of trajectory to Mars’ normal for simulated 5 km, 10 km, 15 km, 20 km and 25 km vertical wavelengths. (b) Estimated wavelengths normalised by the original known simulated wavelength as a function of angle of trajectory to Mars’ normal.

As explained in Chapter 8, this work could be explored further with the introduction of MCD v6.0, where wave can propagate horizontally.

5.4 Comparing Temperature and Density Perturbations

Using the Ideal Gas Law, the perturbations of a gas with pressure p, density ρ, temperature T and mean molecular mass m may be expressed as

δρ δp δm δT = + − (5.3) ρ p m T As only Ar is considered here, δm is zero. As seen from Figures 5.2.1c and f, density and temperature perturbations appear primarily in antiphase for all altitudes. Using Equation 5.3, we may calculate δp/p and obtain typical values of up to 1%, whereas δρ/ρ reach 10% and δT/T reach slightly smaller, but similar values as Eq. 5.3 needs to balance. δp/p values are calculated using the same method to extract density perturbations. This shows that pressure perturbations are overall a factor of about 10 less than

117 5.4. COMPARING TEMPERATURE AND DENSITY PERTURBATIONS density and temperature perturbations.

Histograms were constructed to get an overview of gravity wave properties in the upper atmosphere. Figures 5.4.1a and b show the amplitudes of wave structures in the temperature and density ﬁelds, respectively, without spatial or temporal distinction. Each bin has a width of 2.5%. The histograms are in agreement with each other. The median temperature and density amplitudes are 10% and 8%, respectively. Standard deviations are 11% and 10%, respectively. A broad peak in amplitude is seen around 10%. To understand the distribution of waves further, the histogram is broken down into the four waves which comprise each ﬁtted wavetrain. Less dominant waves are shown by faded lines. The most dominant constituent wave has the broadest distribution in both density and temperature. This highlights the variability in characteristics and is discussed further later. Density amplitudes are systematically smaller than temperature amplitudes by about 2-4%.

Figures 5.4.2a and b show the distribution of gravity wave wavelengths. They have been broken down identically to Figures 5.4.1a and b. As found for the case of amplitudes, the results for temperature and density wavelengths are in very good agreement with each other. From Equation 5.3, perturbations in density and temperature fields are expected to be in anti-phase. Due to this, density and temperature wavelengths must match to ensure waves remain in anti-phase. The histograms take into account all waves are nearly centred on the median values of 27 km and 24 km for temperature and density, respectively. Standard deviations are 26 km and 24 km, respectively. A clear second peak is observed in Figure 5.4.2a around 80 km. The largest apparent perturbations may be due to the chosen temperature function not capturing temperature profile. The subsequent residuals may be interpreted as a large wave by the Fourier transform. Much can be learned about the lower thermosphere by analysing the DD campaigns. For wavelengths to be captured with confidence, they need to be shorter than the altitude range examined. During the DD campaigns, the spacecraft sampled a more extended altitude range, down to ∼120 km, hence allowing us to extract longer wavelengths potentially. We analysed the DD orbits using the techniques described in Section 5.2. However, we did not detect longer wavelengths from the DD data, instead, finding characteristics similar to those from higher periapsis orbits. As shorter wavelengths are thought to be filtered out with altitude, we may have expected to see shorter wavelengths at lower altitudes. This is found not to be the case, implying they may have already been filtered out.

118 5.4. COMPARING TEMPERATURE AND DENSITY PERTURBATIONS

Gravity waves have vertical and horizontal components; however, these cannot be independently determined due to the unknown and varying angle between the wave phase velocity and spacecraft velocity. If we interpret the structures to be caused by vertical variations, then typical wavelengths are found to be 10-30 km. By interpreting structures as horizontal waves, wavelengths are around 100-300 km. Henceforth, we focus on vertical wavelengths. A discussion and comparison with previous results now follows. Creasey et al., 2006a found vertical wavelengths to be bimodally distributed with peaks between at 8-10 km and 13-15 km, which are around a factor of two less than here. As wavelengths scale with scale height, normalised wavelengths need to be considered. Similar scale heights are observed near the surface (Lewis, 2003), and in the upper atmosphere, thus different wavelengths are being observed. They used occultation data from MGS and retrieved temperature profiles below 30 km altitude. In their study, waves appear periodic in the vertical dimension. We, therefore, interpret variations as vertical waves. Previous studies have shown shorter wavelengths to be filtered by the mean flow, which may be occurring here. Perturbations with shorter wavelengths induce local temperature gradients which may exceed the environmental lapse rate and cause waves to break at lower altitudes. Larger wavelengths pass through the flow and are seen in the thermosphere. Creasey et al., 2006b reveal dominant horizontal wavelengths of 100-300 km along the orbital path. There has not been a comprehensive study of vertical wavelengths in the thermosphere, so comparisons between techniques cannot be made. Another possibility is secondary wave production. Near the surface, the topography is likely a prolific source of gravity wave generation; however, waves may break, causing the generation of secondary waves. This has been discussed in the context of Earth (Moudden and Forbes, 2011). In Gardner and Schunk, 2011 a large-scale gravity wave is studied in a global thermosphere-ionosphere model to determine the 3-D characteristics of the wave as it propagates upward through the Earth’s thermosphere. Waves are initiated around 100 km. They found that as the gravity wave breaks, it deposits energy, and a second wave is generated from the original gravity wave. The newly generated gravity wave has a wavelength which exceeds the original. On Mars, if waves are breaking around 100 km, secondary wave generation may explain the longer wavelengths observed in the upper atmosphere. Waves appear saturated on the dayside so wave breaking may be occurring below 120 km. There is no definitive evidence for this, but the results from Gardner and Schunk, 2011 may explain what is happening at high altitudes in Mars’ atmosphere. On the nightside waves continue to grow with breaking occurring around 180-200 km; secondary waves be produced in this region. Equally, short wavelengths (<20 km) are theoretically dissipated below 100-120 km with longer vertical wavelengths (50-100 km) propagating up to 150-200 km (Imamura et al., 2016). The most dominant wavelengths here are around 30-50 km. The waves

119 5.4. COMPARING TEMPERATURE AND DENSITY PERTURBATIONS observed near the surface are signiﬁcantly shorter than noted here (Ando et al., 2012; Creasey et al., 2006a). Results presented provide evidence for either (or both) wave dissipation and secondary wave production.

Figure 5.4.1: Panel (a) shows a histogram of gravity wave amplitudes extracted from temperature structures. Grey shows the distribution of all gravity wave amplitudes extracted. Red shows the breakdown of the total into the four most dominant waves. Less dominant waves are shown by lighter red. Grey is the sum of all reds. Panel (b) same as (a) but showing amplitudes extracted from density structures. T 0 and ρ0 are temperature and density amplitudes, respectively.

Amplitudes observed here are of the order of those found in previous studies which have used MGS, Odyssey (ODY) and MAVEN datasets (Creasey et al., 2006b; Creasey et al., 2006a; Fritts et al., 2006; Yiˇgit et al., 2015a). Fritts et al., 2006 used MGS and ODY data and found gravity wave amplitudes of 5-50%. From Figure 5.4.1a and b we observe that amplitudes rarely exceed 30%, but do reach 50%. This discrepancy may be explained by the diﬀerent regions of the atmosphere, which were sampled by MAVEN and MGS. MGS typically sampled a lower region of the atmosphere with periapsis altitude around 100-120 km. Terada et al., 2017 applied a smoothing technique to NGIMS Ar density data to extract perturbations. They found root-mean-square amplitudes of 6-30% with an average value of around 15% for vertical waves. These are in agreement with the results found in this study, especially the most dominant waves. The very good agreement between our results and those found by Terada

120 5.5. ALTITUDINAL EFFECTS ON GRAVITY WAVES

Figure 5.4.2: Panel (a) shows a histogram of gravity wave wavelengths extracted from temperature structures. Grey shows the distribution of all gravity wave wavelengths extracted. Blue shows the breakdown of the total into the four most dominant waves. Less dominant waves are shown by lighter red. Panel (b): as (a), but showing wavelengths extracted from density structures.

et al., 2017 give us confidence in the technique used. We find that structures in the temperature and density fields are typically in anti-phase; however, in the cooler regions, pressure perturbations become large enough to see significant effects. As the mean molecular mass is constant (44 amu), pressure perturbations were calculated by the addition of density and temperature perturbations. Pressure perturbations are typically no more than 50% of the respective density and temperature perturbations. Unlike on Titan, where pressure perturbations are taken to be negligible, pressure perturbations in Mars’ atmosphere are typically several percent (Mueller-Wodarg et al., 2006).

5.5 Altitudinal Eﬀects on Gravity Waves

We investigate how gravity waves evolve vertically within the atmosphere. For each orbit, we split the orbit into 30 km regions, each shifted by 10 km allowing Fourier transforms to be applied in diﬀerent regions as a method of understanding growth and/or decay. For example, we may study the 140-170 km, 150-180 km, 160-190 km regions of a leg. For each section, we identically extract perturbations,

121 5.5. ALTITUDINAL EFFECTS ON GRAVITY WAVES as described in Section 5.2. We determine dominant amplitudes and wavelengths for each section. The average solar zenith angles for each section are determined.

Figure 5.5.1: Gravity wave amplitude as a function of altitude. Amplitudes are separated in solar zenith angle with each panel covering 30◦ SZA. Amplitudes are extracted in 30 km section as explained in Section 5.5.

We consider six solar zenith angle regions; each region spans 30◦ in SZA. The amplitudes determined above are initially binned into one of the six solar zenith angle regions. Amplitudes are then binned in altitude and the mean calculated. Figures 5.5.1a-f shows the result. We observe amplitudes on the dayside to remain fairly constant in altitude with typical values around 10%. As discussed further later in this chapter, it is thought that processes which act to grow amplitudes are well balanced with dissipative processes. On the nightside, we observe that amplitudes grow from around 10-15% at 120 km to over 20% at 180 km. For altitudes above 180 km on the nightside, we ﬁnd amplitudes to begin to decrease by several percent.

122 5.5. ALTITUDINAL EFFECTS ON GRAVITY WAVES

By considering the conservation of momentum in a conservative atmosphere, amplitudes are expected to grow exponentially with altitude as density decreases. Our results suggest that the growth process is well balanced by dissipative processes in the thermosphere, such as an increased viscosity. As temperature increases, decay processes are enhanced, balancing growth. On the nightside, we observe growth in amplitudes up to around 180 km. From this result, it appears the effect of dissipative processes are reduced, allowing growth processes to dominate there. The amplitudes do not increase exponentially; therefore wave decay is still occurring. Beyond 180 km on the nightside, amplitudes begin to decrease by 2-5%. This behaviour is consistent on the nightside and is potential evidence for wave breaking. The induced temperatures gradients may exceed the adiabatic lapse rate, causing wave motion to be no longer sustained. The breaking of gravity waves will deposit momentum into the atmosphere, potentially causing changes in the flow. The effects of such breaking will form part of a future study. Using the gravity wave scheme employed by Yiˇgit et al., 2008; Yiˇgit et al., 2015a investigated the amplitude growth/decay in the Martian atmosphere. They found amplitudes grow rapidly from the surface up to around 100 km and amplitudes are modelled to be on average about 50% at this altitude. Upwards of 100 km, the average amplitude decreases rapidly, returning to values below 10% at 140 km. We do not observe such decreases in amplitude at these altitudes. Gravity wave propagation is strongly affected by background winds (Yiˇgit et al., 2015a). This is a factor which has not been investigated in this study but may account for some of the behaviour observed. Winds in the upper atmosphere are substantially changed by the presence of gravity waves. This is caused by momentum deposition above the mesopause by gravity waves. Both the easterly and westerly jets are impacted by gravity waves with the easterlies are weakened (Medvedev et al., 2013). Yiğit and Medvedev, 2017 modelled the effect of gravity waves on Earth’s thermosphere. Tidal amplitudes increase or decrease depending on latitude due to interactions with gravity waves.

Fritts et al., 2006 used the assumption of saturated gravity waves to estimate net horizontal momentum flux, from which momentum deposition can be derived. This can be presumed to occur on the dayside (Figure 5.5.1a-c). As the B-V frequency has not been explicitly calculated in this study, it is taken to be 2×10−2 s−1 (from Medvedev and Yiğit, 2019). Momentum fluxes calculated in the thermosphere are a few hundred m2s−2 for small amplitudes (∼0.1), reaching 1000 m2s−2 at amplitudes close to 0.5. Fritts et al., 2006 find values of ∼2000 m2s−2. As similar amplitudes were used in Fritts et al., 2006( ∼0.2) as used here, the likely candidate for the discrepancy is the ratio of horizontal to

123 5.6. GLOBAL CHARACTERISTICS OF GRAVITY WAVES vertical wavelengths. In this study, vertical (horizontal) wavelengths are taken to be 10-30 km (200-300 km, taken from England et al., 2016), whereas Fritts et al., 2006 took horizontal wavelengths of ∼100 km. This may explain subtle diﬀerences, but overall values are in good agreement.

5.6 Global Characteristics of Gravity Waves

The previous section looked at the general properties of gravity waves; this section will look at how location, local time and season affect gravity wave characteristics. As DD campaigns make up a small portion of the total number of orbits and have similar amplitudes and wavelengths to non-DD orbits, they have been included in the following analysis. Solar zenith angle has been used to describe the location of MAVEN. The temperature of the atmosphere is expected to decrease with increasing distance from the Sun. For example, mid-afternoon equatorial temperatures near 200 km vary from 190-390 K between aphelion and perihelion throughout the solar cycle (Bougher et al., 2015). Terada et al., 2017 have highlighted the effect temperature has on the growth of gravity waves in the thermosphere. Warmer regions of the atmosphere restrict amplitude growth as dissipative processes are enhanced with warmer temperatures. The combination effects of solar zenith angle and M-S distance may, therefore, affect wave properties, which we will examine in the following section.

The data were 2-D binned in solar zenith angle and M-S distance, and the median amplitudes and wavelengths were calculated for each bin. Bin sizes of 11.25◦×0.025AU were used, giving a total of 192 bins. 80 out of 192 bins contain data. The coverage is good in M-S distance. Figures 5.6.1a and b show polar plots of gravity wave amplitude and wavelength, respectively, as a function of solar zenith angle and M-S distance. In each polar plot, the upper semicircle presents results from temperature structures and lower semicircles from density structures. The azimuthal component is the solar zenith angle, and the radial is M-S distance. Temperature is then decreasing both radially outwards and towards larger zenith angles.

Temperature amplitudes are considered ﬁrst (upper semicircle, Figure 5.6.1a). Below solar zenith angles of about 45◦ coverage of M-S distance is limited; values range between 1.45 and 1.6 AU, so perihelion and aphelion are not sampled. In this region, amplitudes are found to be less than 5% with little variation in either solar zenith angle or M-S distance. The most sampled quadrant is between 45◦

124 5.6. GLOBAL CHARACTERISTICS OF GRAVITY WAVES and 90◦ with only coverage missing from the 1.45-1.475 AU bin. There is greater variation in this region compared to the previously discussed region. Near periapsis, amplitudes are similar to low solar zenith angle values (<5%). The effect of M-S distance is more evident in this quadrant. Moving towards aphelion leads to amplitudes increasing by a factor of around 2 to about 10%. The next quadrant (90◦-135◦) shows a large increase in amplitudes with values typically greater than 15%. The effect of M-S distance seems to be weakened in this region. Amplitudes are fairly constant. The final quadrant (135◦-180◦) is the least sampled and as such little can be concluded from it. M-S distance is only sampled at distances less than 1.5 AU and amplitudes are greater than 15%. Considering the contours of constant solar zenith angle and M-S distance reveals their relative importance in affecting gravity wave growth. As shown in Chapter 4, temperature is well correlated with solar zenith angle. There- fore, there is a relationship between gravity wave characteristics and temperature, which is discussed later. There is a larger variation in amplitude over the solar zenith angle range than over M-S distance. The most well-sampled distance is around perihelion of Mars, with only low solar zenith angle data missing. Here, amplitudes range from their minimum values (<2% at 45◦) to their maximum (>15% around 170◦). This range of values is much larger than over M-S distance range. This large and rapid change in amplitude suggests that gravity waves exhibit highly variable behaviour. Amplitudes vary greatly by several factors throughout a sol. A near-identical trend is found in the density structures (lower semicircle, Figure 5.6.1a). Density amplitudes are typically larger than their temperature equi- valents, as also shown in Table 5.2.1. This is most obviously seen around solar zenith angles around 45◦.

Figure 5.6.1b shows 2-D binned vertical wavelengths as a function of solar zenith angle and M-S distance. The same bins are used as discussed for amplitude analyses. Temperature wavelengths (upper semicircle, Figure 5.6.1b) are considered ﬁrst. Compared to presented amplitude results, there is not a clear trend with either variable. There is a slight pre-terminator increase in wavelength towards aphelion. Given that this trend is not seen elsewhere, it is likely due to factors other than temperature. Median wavelengths are fairly constant with values between 20 km and 30 km. Possible reasons are discussed later.

The effect of gravity waves on the atmospheric temperature has been explored in great detail using models (e.g. Medvedev et al., 2011; Medvedev and Yiğit, 2012). Gravity waves affect the mean flow in the upper atmosphere by closing jets and, in some cases, reversing the flow. Dependent on location and gravity wave dynamics, gravity waves can warm or cool the atmosphere via dissipation. We have found

125 5.6. GLOBAL CHARACTERISTICS OF GRAVITY WAVES

90 90 a b 135 45 135 45

T T 180 1.4 1.5 1.6 0 180 1.4 1.5 1.6 0

135 45 135 45

90 90

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0 5 10 15 20 25 30 X (km) 0

Figure 5.6.1: Panel (a) shows a polar plot of the gravity wave amplitudes from temperature (top semicircle) and density (bottom hemisphere) data as a function of solar zenith angle and M-S distance. Panel (b) is same as (a) but showing gravity wave wavelengths. The four most dominant waves are considered from each orbit.

that gravity wave amplitudes show clear trends with solar zenith angle and M-S distance. Processes which dissipate waves are enhanced in the warmest regions; therefore amplitudes are smaller here. Dis- sipative processes that decay gravity waves include eddy and molecular viscosity, thermal conduction, radiative cooling, and ion drag (Yiˇgit and Medvedev, 2010). A trend suggests that regions, where waves have been damped, have been warmed. An explicit relationship between amplitude and temperature has not been computed in this study. Terada et al., 2017 derived temperatures for each orbit and found amplitudes increase during cooler orbits. They suggest the anti-correlation between amplitude and temperature is primarily caused by breaking/saturation of gravity waves due to convective instability. They derive a threshold of convective instability for the perturbation number density. In the short-wave limit, assuming a temperature of around 250 K and vertical wavelength 25 km, the threshold for amplitude is about 11% which increases to 18% for a temperature of 150 K. The threshold condition is proportional to wavelength, so the larger amplitudes are likely associated with larger wavelengths. In the long-wavelength limit, where amplitudes are typically larger, the threshold is about 86%. This value is not exceeded in this study.

126 5.6. GLOBAL CHARACTERISTICS OF GRAVITY WAVES

Given the results presented here, SZA/LST plays a more dynamic role in controlling amplitude than M-S distance given the more rapid, larger temperature changes. Dissipative processes such as molecular diffusion, whose coefficient increases with EUV flux, are enhanced with temperature (Yiˇgit and Medvedev, 2010). Therefore, cooler regions in the atmosphere can support most gravity waves, whereas gravity waves will dissipate in the warmer regions. Using the LMD MCD, we find viscosity to be maximum where the temperature is maximum. The increased viscosity may explain the damped amplitudes in the warmer regions. Creasey et al., 2006b extracted gravity waves from MGS accelerometer data. They looked at seasonal effects by investigating data at similar latitudes and local times. They found larger amplitudes in northern autumn compared to northern spring. They suggest aerobraking during spring/summer as waves are most damped, which is in agreement with findings here; aerobraking should occur in the warmest regions. Density is also highest in these regions. Yiˇgit et al., 2015a studied

NGIMS CO2 perturbations in the upper atmosphere. They were far more restricted in the number of orbits available; however, they found amplitudes to be inversely proportional to scale height which agrees with the results presented previously. Overall, from this study and others, temperature appears to be moderately important in controlling gravity wave amplitudes in the Martian atmosphere shown by the strong correlation with solar zenith angle. It should be noted that horizontal background winds are more important in controlling the upward propagation of gravity waves. If the background horizontal wind speed equals the gravity wave phase speed, the wave can no longer propagate (Fritts and Alexander, 2003; Lindzen, 1981). This may explain the variation in observed amplitudes. This section has answered the posed open questions with wave amplitude and wavelength distributions shown. As discussed in this chapter, derived amplitudes are comparable to previous studies, so not surprising. However, the wealth of data increases our confidence in determined amplitudes. This is the first substantial study to derive vertical wavelengths, and as such adequately answers the open question. Vertical wavelengths are a factor of 10 shorter than horizontal wavelengths, as theoretically predicted. The open question of diurnal and seasonal variation of wave characteristics is surprisingly clear, with obvious day/night asymmetries in amplitudes, which has not been shown before. As waves are filtered as they propagate upwards by background flows, it is not too unexpected that there is not a similar day/night trend.

127 5.7. EFFECT OF TOPOGRAPHY ON GRAVITY WAVES

5.7 Eﬀect of Topography on Gravity Waves

One source of gravity waves is ﬂow over topography, so we investigate the vertical evolution and search for potential links with topographical features. We use the data produced in Section 5.5. Figures 5.7.1a and b show gravity wave amplitudes in latitude and longitude for both the lower (120-150 km) and upper (150-180 km) regions, respectively. We have superposed a topography map to compare with gravity wave amplitudes. Figure 5.7.1a shows amplitudes extracted in the lower region. We see the coverage is mainly between 15◦S and 40◦N with good coverage in longitude. Data are also seen below 40◦S. The Tharsis region is centred near the equator in the western hemisphere. This region contains Arsia Mons, Pavonis Mons, and Ascraeus Mons located at 8.35◦S 120.09◦W, 1.48◦N 112.96◦W and 11.92◦N 104.08◦W. These volcanoes are visible on the superposed map. Olympus Mons is located at 18.65◦N 133.8◦W.

Figure 5.7.1b shows amplitudes in the upper region. The coverage is much better with all latitudes being sampled. We observe similar results as in the lower region. In similar regions, amplitudes are comparable between the two altitude regions suggesting that waves remain constant. There appears to be a latitudinal dependence on amplitude seen in both altitude ranges. This dependence is clearer in 5.7.1b due to more coverage at these altitudes. Terada et al., 2017 determined wave amplitudes using a diﬀerent method, but found a similar dependence. They removed the temperature dependence to produce corrected amplitudes. These corrected amplitudes still show a visible, but weaker dependence on latitude. The increase in amplitudes in the Northern hemisphere is therefore potentially caused by a sampling bias; the atmosphere was likely sampled during cooler periods in the Northern hemisphere. Even with the removal of this bias, the dependence is still visible. The Southern hemisphere has more topography than the Northern hemisphere. As the topography is one of the main drivers behind gravity waves, the latitudinal dependence is contradictory to what is expected. The slight longitudinal dependence in the Northern hemisphere agrees with our understanding of gravity wave generation. Amplitudes over the mountainous Tharsis region appear enhanced, especially at higher altitudes. This is in agreement with Terada et al., 2017, even after their corrections.

Data and modelling studies have tried to elucidate the connection between gravity wave activity and topography (e.g. Creasey et al., 2006a: Miyoshi et al., 2011). Creasey et al., 2006a looked at waves in the troposphere and found gravity wave activity to be higher in some areas of elevated topography such

128 5.7. EFFECT OF TOPOGRAPHY ON GRAVITY WAVES

Figure 5.7.1: (a) Averaged amplitudes determined from binning in latitude and longitude using amplitudes extracted between 120 and 150 km. (b) Same as (a), except amplitudes extracted in the 150-180 km region are used.

as the Tharsis region, however in other relatively similar areas of topography the activity is comparatively lower. Seasonally averaged latitude-longitude plots of amplitude and wavelength were produced, but no direct link with topography was found in either case. As latitude and longitude are well sampled by

129 5.8. COMPARING WAVE ACTIVITY OVER SUCCESSIVE ORBITS

MAVEN, the distribution of amplitudes in Figures 5.6.1a and b would be expected to be more random if there was a link in this region. The strong trend with solar zenith angle and M-S distance shows the possible importance of temperature in controlling gravity waves; once a gravity wave has been generated it is the conditions within the atmosphere which control its evolution. Wave amplitudes are significantly larger in the warmer regions of the atmosphere. Waves deposit their momentum directed mainly against the local wind, therefore providing wave drag on the mean flow (Kuroda et al., 2015). The dissipation of energy into flow may erase any potential evidence of its origin.

There is inherent bias while analysing potential topography dependencies on gravity wave properties. Although density and temperature variations have been interpreted as vertical gravity waves, MAVEN spans tens of degrees in latitude during each pass due to its horizontal component. For each orbit, we have sliced the wave, as in Section 5.5, and associated each with the average longitude and latitude for that section. By slicing up the wave, each bin will contain wave data from multiple waves. This allows local time effects to be averaged out, and in theory, leaves the topography dependence. This should show stronger relationships with topography than considering the entire leg and using periapsis latitude and longitude. Bias due to spacecraft trajectory on gravity wave amplitudes is less than for wavelengths. Close to periapsis MAVEN is travelling quasi-horizontally, so although we have interpreted waves as vertical, the variations are due to horizontal variations. This will affect the measured wavelengths. We have not accounted for this trajectory bias. This problem is lessened away from periapsis; the higher altitude wavelengths are likely more accurate. We find no correlation between wavelength and topography.

5.8 Comparing Wave Activity Over Successive Orbits

Hitherto, each extracted wave has been treated independently. In this section waves from consecutive orbits are compared to each other. This process allows potential wave evolution to be studied within a relatively short time period of MAVEN’s orbit (∼4.5 hr). This is of particular importance when investigating the lifetime of waves - do they persist for several hours? Or are they too short to sample twice?

This may have implications for the formation of thermospheric CO2 clouds, for example.

This is undertaken in the following way. Two waves are considered; the ﬁrst is denoted as Υ1 which is the density wave of the ith orbit. The second is Υ2 taken from the i + 1th orbit. The likeness

130 5.8. COMPARING WAVE ACTIVITY OVER SUCCESSIVE ORBITS

Figure 5.8.1: Examples of waves from two consecutive orbits exhibiting similar characteristics. (a) Waves extracted along inbound passes for orbit 4092 (red) and 4093 (blue). (b) Waves extracted along inbound passes for orbit 6833 (red) and 6834 (blue)

, of the waves is quantified by computing the correlation coefficient between Υ1 and Υ2. And this is repeated for all orbits. A normal distribution is observed with a median around zero. Thus, indicating no consistent correlation between consecutive waves. There are some cases where consecutive waves have large correlation coefficients. This suggests waves can remain fairly stationary between consecutive orbits. Figures 5.8.1a and b show two examples where consecutive waves appear to be near-identical, suggesting the wave is not propagating. This is possible to see in the global structure of the waves where similar dominant wavelengths and amplitudes are seen in phase. Amplitudes in both cases are ∼20%, and vertical wavelengths are ∼30 km. Smaller-scale structures vary between orbits. Identical waves, like those shown, account for only ∼0.5% of all cases.

131 5.8. COMPARING WAVE ACTIVITY OVER SUCCESSIVE ORBITS

Some basic conclusions based on the above can be made. There are no cases where three consecutive orbits exhibit near-identical wave characteristics; hence it can be inferred that such structures can survive up to ∼9 hours. There are no occasions where successive inbound-inbound waves occurred on the same orbit as consecutive outbound-outbound passes. Each subsequent orbit is sampled at a diﬀerent longitude than the previous; however, local times are very similar between consecutive orbits. Tidal modes may be weakened, therefore enhancing the persistence between successive orbits.

A more likely scenario is that after 4.5 hours, waves have propagated upwards and this may be captured on the next orbit. This is attempted in this section, whereby a comparison between two orbits is as follows. Υ1 and Υ2 are interpolated onto a ﬁxed altitude grid with spacing 0.1 km which is the approximate resolution of NGIMS data. With Υ2 kept stationary as the ’reference’ wave, Υ1 is shifted upwards by 0.1 km as if it were propagating in an ideal manner. A new correlation coeﬃcient is calculated between the waves. An example is shown in Figure s5.8.2a-d. Figure 5.8.2a shows the extracted inbound density perturbations from orbit 3811 (faded red line) and 3812 (faded blue line). Similarities are observed between the two waves; amplitudes are ∼20%, and vertical wavelengths are

∼30 km. Figures 5.8.2b-d show the wave extracted from orbit 3811 (Υ1) shifted by 5 km, 10 km, and 15 km, respectively. Faded lines show the original waves. Bright lines show the shifted waves. The first, non-shifted waves are shown by faded lines. After a 5 km shift, the two waves are strongly in phase. It could be inferred that MAVEN has sampled the same wave on consecutive orbits, but shifted upwards. After a further 10 km shift, the waves are in anti-phase with each other. This is repeated for all waves, and the correlation coefficient is calculated for all shifts. By restricting required coefficients to values over 0.9, an emergent trend is seen. Correlation coefficients are maximised after a 30-40 km shift. If an orbital period of ∼4.5 hrs is used, then wave propagation occurs at a speed of ∼6.5-9 km/hr. This is the vertical group velocity of the wave. .

The implications of consecutive waves being similar are now addressed. Temperature profiles derived using NGIMS data exhibit temperatures below the CO2 condensation point (R Yelle 2019, personal communication). This may be the first evidence of CO2 clouds in the thermosphere. Such clouds have been identified in the mesosphere by SPICAM (Forget et al., 2009). Temperature is an important factor in cloud formation; however, there are more subtle aspects that need to be considered. One is density; there need to be sufficient CO2 particles for nucleation to take place. From Section 5.1 it is seen that temperature and density are in strong anti-phase; by their very nature, the lowest temperature regions

132 5.8. COMPARING WAVE ACTIVITY OVER SUCCESSIVE ORBITS

Figure 5.8.2: (a) shows the original waves from orbit 3811 (red) and 3812 (blue). (b), (c) and (d) show the wave from orbit 3811 shifted upwards by 5 km, 10 km and 15 km, respectively. The original waves are shown by faded lines. Bright lines show shifted waves.

allow for the best chance of cloud formation due to the highest densities. Another consideration is the lifetime of waves which the above work has attempted to address. More speciﬁcally, how long do these pockets of low temperature last? Naturally, a longer lifetime leads to an increased chance in cloud formation. Two aspects are considered - similarity between consecutive orbits’ waves and low temperatures. In doing so, the ﬁrst criterion that is to be met is that perturbations are similar over consecutive orbits. From Figure 1.5.3 the CO2 saturation threshold temperature is shown. At 100 km the required temperature for saturation is ∼100 K. A basic extrapolation up to altitudes considered here results in a saturation temperature of ∼50-80 K. An assumption that a minimum temperature of 100

K is needed to achieve cloud formation is used. CO2 proﬁles have been constructed using the method outlined in Chapter 3.

133 5.8. COMPARING WAVE ACTIVITY OVER SUCCESSIVE ORBITS

Several occasions have been identified which meet the above criteria that consecutive waves need a correlation coefficient greater than 0.75, and absolute temperatures need to be less than 100 K. Figure 5.8.3a shows extracted inbound waves from orbit 6107 (red) and 6108 (blue). Periapsis locations are 5.6°S, 10.8 LST and Ls=90°, and 5.9°S, 10.7 LST and Ls=91°for orbit 6107 and 6108, respectively. A large perturbation is seen around 190 km in both waves. Average amplitudes are ∼50-75%, and a long wavelength of ∼50 km is observed. Figure 5.8.3b shows the individual temperature profiles for the orbits mentioned above, coloured accordingly. On the first pass, temperatures at minimised to ∼70 K at 198 km and ∼80 K at 196 km on the following pass. The consistency between consecutive wave and consecutive temperature profiles is indicative of persistent behaviour lasting several hours. These profiles provide evidence for potential cloud formation, having met two criteria.

Figure 5.8.3: (a) Extracted inbound density waves from orbit 6107 (red) and 6108 (blue). Periapsis locations are 5.6°S, 10.8 LST and Ls=90°, and 5.9°S, 10.7 LST and Ls=91°for orbit 6107 and 6108, respectively. (b) Inbound temperature proﬁles for orbit 6107 (red) and 6108 (blue).

134 5.9. WAVE CHARACTERISTIC COMPARISON WITH OTHER PLANETS

The results found in this section are conceivably the most surprising so far in this thesis, given consecutive waves have not been studied before. The implications of studying waves in such a way are profound. Firstly, vertical group velocities can be calculated more accurately allowing wave dynamics to be observationally explored. Secondly, potential cloud formation can be studied further.

5.9 Wave Characteristic Comparison with Other Planets

As brieﬂy mentioned earlier in this chapter, gravity waves are not exclusive to the Red Planet. This short section aims to review studies at Venus, Earth, Jupiter, Saturn and Titan and draw comparisons between them.

As one of our closest neighbours, Venus has been well sampled. Radio occultation proﬁles from Magellan revealed perturbations around the cloud tops (∼65 km) with amplitudes and vertical wavelengths of 4 K and 2.5 km, respectively. This amplitude is equivalent to 1-2% assuming a background temperature of 200-250 K, as suggested in Hinson and Jenkins, 1995. Although interesting, 65 km marks the approximate bottom of the mesosphere and thus studies within the upper atmosphere need to be considered for comparison (Pätzold et al., 2007). Garcia et al., 2009 used the Visible and Infrared Thermal Imaging Spectrometer-Mapper (VIRTIS-M) on-board Venus Express to explore gravity waves within the lower thermosphere (110-140 km). Amplitudes were found to be ∼0.5%. Horizontal wavelengths possess an extensive range from 90 to 400 km. More recently, Venus Express (VEX) undertook a two- week aerobraking campaign in Venus’ lower thermosphere (130–140 km). Densities were recovered from accelerometer data, and analysis similar to that found in this chapter was performed. Mueller-Wodarg et al., 2016 found amplitudes and horizontal wavelengths of ∼10% and ∼100-200 km, respectively.

Earth is the most well-studied planet for gravity waves, and as such, myriad articles have detailed experimental results. A select few publications are discussed. Space shuttle re-entry accelerometer data implied amplitudes in the mesosphere/thermosphere of typically less than 5% (Fritts, 1989, Fritts, 1989). Due to the trajectory of these shuttles, only horizontal wavelengths were inferred; typical lengths are 10-1000 km in the 60-140 km region. Garcia et al., 2009 used accelerometer data from Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) to retrieve thermospheric densities and subsequent relative density perturbations. During solar minimum conditions, maximum amplitudes of 6% around ∼270 km were found. However, more typical amplitudes are less than half this, which is in agreement

135 5.9. WAVE CHARACTERISTIC COMPARISON WITH OTHER PLANETS with Park et al., 2014 who used a similar technique using data from CHAMP located around 300-400 km. This study found amplitudes of <2%, suggesting attenuation with altitude. Horizontal wavelengths are found to be ∼150-600 km.

Galileo is only one of two spacecraft to orbit Jupiter, arriving in 1995 and finally succumbing to Jupiter’s harsh radiation environment in 2003 when it was purposefully flown in the Gas Giant. Young et al., 1997 used directly-measured temperatures profiles from the Atmospheric Structure Instrument (ASI) on board the Galileo probe to infer gravity waves in Jupiter’s thermosphere. Temperature perturbations are ∼50-80 K superimposed on a 600-800 K background temperature, consequently amplitudes are ∼5-10%. Vertical wavelengths are ∼90-150 km. By modelling these waves, Young et al., 1997 required amplitudes of ∼2-7% in the troposphere to explain amplitudes in the thermosphere. This agrees with wave growth seen for Mars. A further study by Young et al., 2005 used ASI data in the stratosphere and found temperature fluctuations of ∼5%.

Titan is Saturn’s largest moon and the second largest in the solar system behind Ganymede. It is the only known moon with a dense atmosphere. Titan’s atmosphere has been sampled in-situ by both flybys and landers. Hinson and Tyler, 1983 first inferred gravity wave signatures in Titan’s lower atmosphere in occultation data from Voyager 1. Mueller-Wodarg et al., 2006 used in-situ data from the Ion and Neutral Mass Spectrometer (INMS) on board Cassini from two Titan flybys (24 October 2004 and 16 April 2005). Closest approaches occurred at 1176 km and 1025 km with altitudes up to 1600 km. Strong perturbations in N2 and CH4 densities were found and interpreted as vertically propagating waves. Spectral curves were fit to fluctuations with typical vertical wavelengths ranging from 170 to 360 km and density and pressure amplitudes reaching 4–12%. Temperature perturbations were 5-10 K. A second opportunity to study waves in was provided by the descent of the Huygens probe through Titan’s atmosphere. Temperature and density profiles were recovered from the Huygens Atmospheric Structure Instrument (HASI) data. Above 500 km, temperature perturbations of 10–20 K about a mean of about 170 K were observed (Fulchignoni et al., 2005). These equate to amplitudes of ∼6-11% which are very similar to values found by Mueller-Wodarg et al., 2006. Likewise, Lorenz et al., 2014 used Huygens temperature descent data and retrieved constant perturbations of ∼2 K between 60 km and 140 km. Wavelengths are 3-8 km. These are significantly different from those found by (Mueller-Wodarg et al., 2006). One reason is likely the sampling range; the range is not large enough to deduce wavelengths found by Mueller-Wodarg et al., 2006. Additionally, it is expected for shorter wavelengths to be damped

136 5.9. WAVE CHARACTERISTIC COMPARISON WITH OTHER PLANETS with altitudes, leaving the longer wavelengths to remain at higher altitudes from the original ensemble.

During its nominal mission, Cassini did not graze Saturn’s atmosphere as done during Titan’s flyby. After 13 years, Cassini was running out of fuel and instruments exceeded their expected lifetime; thus, a decision was taken to dispose of Cassini in Saturn’s atmosphere purposefully. Cassini continued to gather data until it burnt up in the atmosphere. For the first time, Mueller-Wodarg et al., 2019 discovered atmospheric waves in Saturn’s thermosphere using INMS. A spectral fit to perturbations reveal the presence of waves with amplitudes reaching 5–10%. If interpreted as vertical (horizontal) waves, wavelengths would range from 100–300 km (1550–3500 km). No other studies are available for comparison.

Finally, Hinson and Magalhães, 1993 discovered inertio-gravity waves in Neptune’s atmosphere with the aid of Voyager 2 occultation data. Amplitudes are minimal, taking values of 0.1-1 K which equate to a few percent in an atmosphere with temperatures typically less than 80 K.

This section is not an exhaustive review of planetary gravity waves, however, does provide an overview of typical wave characteristics. Data are severely sparse for some bodies; however, notwithstanding this, conclusions can be made. Wavelengths across the solar system exhibit enormous variation compared to altitude, from a few km to several hundred km. Planetary size appears indicative of the expectant wavelengths. The vast vertical extent the Gas Giants’ atmosphere allow such large waves to be generated and sustained. Terrestrial planets are much smaller and as such have vertical wavelengths an order of magnitude lower. Mars’ are 10% that of Jupiter’s. Such large waves on Saturn would be planetary-size on Mars. On the contrary, amplitudes are not comparable with body size. The most obvious comparison is with the largest body, Jupiter, and Mars; Jupiter is 20 times larger (by radius) than Mars. However, amplitudes are comparable. It is not unusual for Mars’ nightside amplitudes to be double those found on Jupiter. Earth is twice as large (by radius) than Mars’ but typically possesses amplitudes much less than the Red Planet. These simple conclusions reveal the relative importance of wave generation mechanisms. Mars has signiﬁcant topographical features compared to Earth, thus may explain such large amplitudes. The implication of such large amplitudes includes the importance of waves in atmosphere dynamics. From Fritts et al., 2006, a simple relationship is proﬀered with amplitude being proportional to the Brunt-Väisälä frequency and inversely proportional to gravitational acceleration and vertical wavenumber. Given Mars’ gravity is nearly a factor of three smaller than all

137 5.10. SUMMARY the planets’ discussed above, this may explain the disparity between planets’ wave amplitudes assuming similar Brunt-Väisälä frequencies.

Observations of perturbations are not limited to neutral density profiles. Mayyasi et al., 2019 showed evidence of ion-neutral coupling within Mars’ thermosphere as indicated by correlated ion and neutral profiles from NGIMS. These correlations imply that neutral perturbations drive oscillations in the plasma. This phenomenon is not evident in all profiles, however. Interactions with magnetic fields and the solar wind induce additional structures which are not visible in neutral profiles.

5.10 Summary

In this chapter, perturbations from proﬁles of densities and temperatures have been extracted and interpreted as vertical gravity waves. The main ﬁndings are highlighted below.

• Perturbations have been extracted from density and temperature proﬁles and interpreted these as vertically propagating gravity waves. The amplitudes and vertical wavelengths of structures in the density and temperature ﬁelds have been examined. They have been found to average amplitudes and vertical wavelengths to be around 10% and 25 km respectively, with slightly larger values in density perturbations.

• It has been shown how solar zenith angle and Mars-Sun distance aﬀect the thermospheric gravity wave amplitude. A strong correlation between solar zenith angle and gravity wave amplitudes has been found. With an increase (decrease) in solar zenith angle (temperature), we observe an increase in amplitude. The enhancement of dissipative processes such as diﬀusion and viscosity occurs with increasing temperature. This is one proposed explanation.

• The evolution of gravity waves in altitude has been examined by extracting amplitudes and wavelengths in 30 km sections along each leg. At solar zenith angles below around 90◦ amplitudes appear invariant with altitude. From the conservation of momentum, amplitudes are expected to grow with altitude. Therefore, decay processes appear to balance growth. Amplitude growth has been observed with increasing altitude at solar zenith angles beyond 90◦. Amplitudes begin to decrease above 180 km, which may present evidence of breaking.

• As gravity waves play an essential role in the Martian atmosphere, the predicted evolution of gravity waves in diﬀerent regions within models could be compared to the results presented in this

138 5.10. SUMMARY

study. This would potentially help to improve gravity wave schemes.

• Waves extracted from consecutive orbits have been compared in an attempt to understand wave lifetimes. In ∼1% cases waves on successive orbits exhibited structures too similar to be a coin- cidence. One possible explanation is that other wave modes (tides) are weakened. In a smaller subset of cases, there is evidence of cold pockets (<100 K) of air surviving several hours. This

aids the potential for CO2 cloud formation.

139 Chapter 6

Eﬀects of June 2018 Dust Storm on the Martian Upper Atmosphere

6.1 Introduction

Global dust storms are rare, global events at Mars, with the last but one dust storm occurring in 2007. Fortuitously, MAVEN was operational during the June 2018 dust storm. NGIMS continued to collect data throughout the dust storm, creating a new dataset to study. This chapter exploits data from this grand event, including studying individual species’ responses to the dust storm. Previous studies have shown evidence of upper atmospheric expansion due to heating in the lower atmosphere, such as during dust storms. Results are compared to those found from other instruments on board MAVEN, such as the Imaging Ultraviolet Spectrometer (IUVS), and to previous studies, such as regional dust events sampled during aerobraking periods (Bougher et al., 1997). The rate at which dust storms effects decay is calculated and compared to previous studies. Given the rarity of such events, modelling efforts of storms are discussed and compared. It is crucial to understand dust storms in their entirety. Pertinently, Opportunity, unfortunately, perished as a consequence of the June 2018 dust storm preventing the rover garnering enough power via its solar panels owing to increased dust opacity. By understanding how long dust storms preside on Mars, it will be possible to test spacecraft to such extremes without the necessary power. Lastly, continuing the study of gravity waves, waves extracted during the dust storm are compared to those before the storm onset. Little is known regarding the potential alteration of gravity waves during a dust storm. Work speculated on Earth-based waves is utilised to understand any effects on waves at Mars. The open questions this chapter hopes to answer are how are gravity waves

140 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION affected by dust storms? Is there a significant change in the wave spectrum during a storm? How would this affect the thermal and dynamical structure of the thermosphere?

6.2 Dust Storm Growth and Atmospheric Expansion

On 30 May 2018, NASA’s Mars Reconnaissance Orbiter (MRO) detected a dust storm which progressed towards NASA’s Opportunity rover located at Perseverance Valley on the plains of Meridiani Planum (centred at 0.2°N 357.5°E). Opportunity was put in safe mode to conserve power as the dust storm blocked out the sunlight necessary to power its solar arrays and keep instruments warm. The dust storm had ballooned with such intensity that by 13 June 2018 it had reached NASA’s Curiosity rover at Gale Crater (5.4°S 137.8°E). Dust storms can be identified by rovers and landers on the ground with optical instruments by measuring the opacity level, or τ, of the atmosphere. Outside of the dust storm season, τ is typically below one. As the dust storm season approaches, τ increases as dust is lofted up into the atmosphere, as discussed in Chapter 1, with values rarely exceeding two. During the 2007 global dust storm, τ peaked around five, and during the 2018 dust storm, τ exceeded ten. By measuring the opacity, conditions within the atmosphere can quickly be assessed by science teams and appropriate action taken. During the global dust storm MAVEN continued to collect data. Post-event analysis of density data is possible, and evidence for the dust storm in the upper atmosphere is presented. As a dust storm develops, the atmosphere expands due to heating. Dust is lofted into the atmosphere up to several tens of kilometres and efficiently absorbs solar radiation. Dust storms present themselves as sudden and long-lived increases in densities compared to the background atmosphere.

Regional dust storms are more common than global dust storms and thus have a higher probability of being observed with an orbiting spacecraft. MGS was fortunate to gather in situ density data during its aerobraking phase throughout the Noachis dust storm (Keating et al., 1998). MGS Thermal Emis- sion Spectrometer (TES) detected the regional dust storm on 25 Nov 1997 in the southern hemisphere around the Noachis Terra region (40°S 20°E). Density increases were observed in the lower (∼60 km) and upper atmosphere (∼126 km); these coincided with warming and hydrostatic expansion. Relative pressure increases were a factor of 2 (3) in the lower (upper) regions. Therefore, the lower atmosphere accounts for 2/3 of the atmospheric inﬂation. Additional heating above 60 km is required for further expansion (Bougher et al., 1999). Bougher et al., 1999 used and expanded on the study by Keating et al., 1998 by attempting to reproduce observations using two models (MGCM and MTGCM) out-

141 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION lined in Section 1.9 (Bougher et al., 1997). Seasonal-orbital and latitudinal variations were modelled Bougher et al., 1997 and compared to MGS accelerometer data. The general behaviour of the storm was captured relatively successfully. The underlying and unpredictable large variability caused by pervasive wave activity is not reproduced within the models. As described earlier, dust is injected into the lower atmosphere, and the system is allowed to evolve. At 130 km MGS densities increased by 200%, with the model predicting a modest increase of ∼70%. Similarly, the F1-ionospheric peak is underestimated; the model increase is 3 km compared to an observational rise of 8 km. This modest expansion corresponds to a lessened temperature increase. TES observed warming of 10-15 K, whereas modelled zonally averaged temperatures are 7-10 K. Bougher et al., 1997 cite "(a) missing aerosol heating of the atmosphere below 30 km during the Noachis storm, (b) missing dynamical heating at Northern mid-latitudes above 60 km during the storm, and (c) missing wave eﬀects (including longitudinally ﬁxed planetary waves and gravity waves)" as potential shortcomings of their model.

This section aims to examine how individual species are impacted by the global dust storm. Inbound and outbound CO2,N2 and Ar densities have been interpolated at 180 km, with similar behaviour observed at other thermospheric altitudes. Background densities have been binned using a width of 0.5° Ls. This creates a smooth time series by removing orbit-to-orbit variability. Figures 6.2.1a and b show these interpolated data from Ls=165° to Ls=210°. A large period is shown to highlight variation caused by sampling location. For this study, the first detection of the storm is taken at Ls=189° (vertical dashed line), in agreement with Elrod et al., 2019. There are several reasons for this choice. Firstly, there is a gap in data at this solar longitude; MAVEN was put into safe-mode by the science team as the dust storm spread. Secondly, although Opportunity first detected the dust storm on 30 May 2018 (Ls∼185° ), it took over two weeks for the storm to develop and circumnavigate Mars fully. Therefore, the chosen solar longitude is a compromise between these two significant dates. The dotted line signifies an apparent peak in the storm around Ls=193°. The following effect is discussed in more detail in later sections. Densities increase to a maximum just before Ls=180°. This is caused by sampling move towards the dayside, and a reduction in densities is seen beyond this caused by MAVEN proceeding towards the nightside. This decreasing trend is interrupted by the dust storm; a sudden increase is observed, which is not expected to arise purely due to benign seasonal or geographic changes in sampling locations. This is indicative that the effects of a dust storm are being observed in the upper atmosphere. At the begin- ning of the dust storm, NGIMS undertook two ten orbit campaigns to determine wind measurements by swinging the boresight direction by ±8°(Benna et al., 2019). Due to this, regular neutral densities

142 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION cannot be produced. Hence, there are missing data. Although all species presented here have increases associated with them, an unexpected decrease in O densities was by Elrod et al., 2019. One explanation proﬀered is an oxygen sink in the form of water ice clouds.

Figure 6.2.1: Binned CO2 (blue), N2 (blue) and Ar (red) densities at 180 km as a function of solar longitude for (a) inbound and (b) outbound passes. The onset is shown by the grey dashed lines around Ls=189°. The initial growth peak is shown at Ls=193° by the grey dotted lines

Two ranges of orbits are considered to isolate the effects of the dust storm. The first is a pre-onset range from 1-3 June 2018 (Ls=185-189°). This period is used when pre-storm conditions are required and contains around 20 orbits. The second is a post-onset range from 12-15 June 2018 (Ls=192-194°). This range straddles Ls=193°which has been taken as the peak of the storm in the upper atmosphere. Now, the effect of the dust storm is studied for all altitudes by interpolating background densities onto a fixed altitude grid with spacing 2 km, from which the mean density and standard deviation at each altitude level are calculated for inbound and outbound legs. All orbits within the pre-onset and post- onset range are utilised. Variability in profiles during the dust storm is studied later. These average profiles are shown in Figures 6.2.2a (inbound) and 6.2.3a (outbound). Ar, CO2 and N2 are coloured red, green and blue respectively, with pre-onset densities and standard deviations shown by solid lines and shaded boxes, respectively and post-onset densities and standard deviations shown by dashed lines and

143 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION hatched boxes, respectively. Colours are kept consistent. In line with Figures 6.2.1a and b, densities are generally larger during the dust storm for a given altitude, typically taking values nearly one standard deviation away from pre-onset values, suggesting a signiﬁcant increase. The largest increase is seen for

CO2. The ratio is taken between post-onset and pre-onset densities at each altitude level to quantify the increase in densities for each species. Figures 6.2.2b (inbound) and 6.2.3b (outbound) show these ratios as function of altitude. N2 varies the least with post-onset density increases of up to 20%. Ar varies by ∼30-50%, followed by CO2, which varies by ∼50-70%.

Figure 6.2.2: Averaged inbound CO2, Ar and N2 density proﬁles for pre-storm (solid) and storm (dashed) conditions. Shaded (hatched) boxes show one standard deviation for pre-storm (storm) conditions. Right: Ratio of storm to pre-storm densities as a function of height for CO2, Ar and N2

In both inbound and outbound profiles, there is an apparent mass dependence on the density increase. It was initially believed to be due to the expansion of the entire atmosphere, such that there was scale height dependence as heavier constituents increase more rapidly. This was assessed by dividing the post-onset to pre-storm density ratios by the respective mass, referred to as the relative ratio, and revealed an interesting result. For both inbound and outbound profiles, Ar and CO2 relative ratios are −1 near-identical taking values in the range 0.034-0.036 amu .N2 exhibits significantly different behaviour; for similar relative ratios to be observed in N2, a slight decrease in density is required during

144 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION

Figure 6.2.3: Averaged outbound CO2, Ar and N2 density proﬁles for pre-storm (solid) and storm (dashed) conditions. Shaded (hatched) boxes show one standard deviation for pre-storm (storm) conditions. Right: Ratio of storm to pre-storm densities as a function of height for CO2, Ar and N2

the global dust storm. The original claim that the atmosphere expands relative to each species scale height has been refuted. To further understand the potential mass dependence, Figure 6.2.4 shows the post-onset to pre-onset density ratios plotted as a function of molecular mass at 170 km. This dataset is extended by a result found by Elrod et al., 2019 who found O decreased by ∼20% during the global dust storm. A clear trend is observed with the lightest species behaving diﬀerently during the storm for a given altitude. Densities of species with masses less than ∼23 amu are predicted, and found for O, to be lower during the storm period. Elrod et al., 2019 suggests the idea that an oxygen sink is induced or enhanced during the storm, such as water ice clouds. With the addition of data in this study, it is more likely that dynamics drive the distribution, rather than chemistry. The fairly negligible increase in

N2 is unanticipated, even with the consideration of scaling by mass. This is an interesting, outstanding puzzle to solve with suggested work in the ﬁnal chapter.

In Chapter 1, it was discussed that the atmosphere expands during a dust event owing to heating in the lower atmosphere. Implications of this include physical processes that manifest at certain altitudes before the storm occurs at higher altitudes during storms, such as the electron density peak, as

145 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION

Figure 6.2.4: Post-onset to pre-onset density ratios taken at 170 km from Figures 6.2.2b and 6.2.3b as a function of molecular mass (blue circles). O has been added from Elrod et al., 2019 (red plus). Black dashed line shows line of best ﬁt.

shown by Wang and Nielsen, 2003. The vertical extent of atmospheric expansion can be quantiﬁed by considering at which altitudes the same densities are observed pre- and post-onset. For example, Ar densities of ∼1013m−3 are located at ∼170 km before storm onset. After the onset, the expansion of the atmosphere causes this density to be sampled at ∼175 km. This calculation has been performed for all sampled species and their densities. Figures 6.2.5a and b show the post-onset altitude as a function of pre-onset altitude for CO2 (green), Ar (red) and N2 (blue). Shown for reference is line showing post- onset altitudes equal to pre-onset altitudes (y=x, black dashed line). The vertical distance between each species’ line and y=x line gives the altitude shift. For CO2 the altitude shift is ∼6-8 km. For Ar, the altitude shift is ∼5-7 km. N2 has the smallest shift of no more than 4 km. The mass dependence described above has been applied to altitude shifts. Relative to each species’ scale height, the altitude shifts are found not to be equal.

Chaufray et al., 2019 performed a similar investigation using MAVEN/IUVS data obtained during the 2018 global dust storm event. IUVS measures Lyman-α emissions from interplanetary and Martian hydrogen at the limb and through the extended corona of Mars. From these brightness data, the CO2

146 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION

Figure 6.2.5: Post-onset altitude as a function of pre-onset altitude for (a) inbound and (b) outbound legs using results from Figures 6.2.2a and 6.2.3a. CO2, Ar and N2 altitude shifts are shown by green, red and blue lines, respectively. The no-shift scenario is shown by the black dashed line.

absorption optical thickness can be derived. Before the dust storm, the altitude at which the optical thickness was equal to one was relatively constant with a value of 114.5±2 km, where the uncertainty is one standard deviation. At the onset of the storm, this reference altitude increases up to 119±2 km. As expected, this is in very good agreement with the CO2 altitude shift found in this thesis. Chaufray et al., 2019 associate this with heating in the lower atmosphere. They estimate the global heating required using Equation 6.1. Constant heating is assumed within a deep region, ∆Z < 50km. This is derived in AppendixB.

hHi 1 β = 2 = hHi (6.1) hHi1 1 − 1 ln n2 ∆Z n1 where hHi1 is the average scale height prior to the onset within the heated region . Likewise, hHi2 is the average scale height after the storm onset. n2/n1 is the fractional increase in observed CO2 at a given altitude found to 1.9±0.2. Assuming a quiet time scale height of 8-12 km, the estimated temperature increase required in the lower atmosphere is ∼25-50 K. Their density increase of 1.9±0.2 is slightly larger than found in this thesis. One likely explanation is the diﬀerence in methods; most notably Chaufray et al., 2019 implement an isothermal temperature to derive densities. Although this

147 6.2. DUST STORM GROWTH AND ATMOSPHERIC EXPANSION is not entirely accurate, it is the best estimate.

Using NGIMS data, Liu et al., 2018 present different species’ variability during dust loading events, similar to Figures 6.2.2a 6.2.3a. As found here, there is a mass dependence in the variability; CO2 varies by less than 50% at 170 km, increasing up to 200% above 210 km. Although our variability is less than this, the difference could be attributed to the method used to determine quiet and storm periods. Liu et al., 2018 found thermospheric expansion, as found here, of ∼10 km and attribute the mass-dependent variability to differing respective scale height. They do not investigate further possible effects. As mentioned in in Chapter 1, atmospheric expansion is not an isolated effect of the neutral atmosphere. A recent study by Girazian et al., 2019 is apropos to atmospheric expansion during dust storm events. Data from the Mars Express (MEX) Mars Advanced Radar for Subsurface and Iono- sphere Sounding (MARSIS) experiment is used to evaluate altitude change in the ionospheric peak during the June 2018 global dust storm. At solar zenith angles similar to those sampled by MAVEN during this period (50-70°), the ionospheric peak altitude rises by 10-15 km based on a nominal peak of 137 km. The variability in the peak altitude during storm periods more than doubled; this suggests that dynamical processes that couple the lower and upper atmosphere are enhanced during dust storms. The enhanced inter-hemispheric circulation that permits polar warming presented in Chapter 4 is evidenced by Girazian et al., 2019. MARSIS and MAVEN (Radio Occultation Science Experiment - ROSE) sampled the dust season concurrently at different latitudes (30°S and 50°N, respectively). At the storm onset, both instruments observe a rise in ionospheric peak location simultaneously implying dust storms can affect a large area over a short time period. The dust storm was local to the southern hemisphere; however, the effects lasted longer in the northern hemisphere as indicated by a more rapid descent in ionospheric peak measurements by MARSIS. Qin et al., 2019 used MGS radio occultation profiles during MY27. The mean shift in electron peak from pre-onset to post-onset is from 135.1 km to

140.5 km. Given CO2 dominates in this region, it is unsurprising this is commensurate with neutral shifts.

The lower atmosphere temperature has been estimated, and this is expected to be signiﬁcantly warmer than in the thermosphere, as is investigated now. By inspection, the averaged density proﬁles are approximately linear in log-space. Therefore isothermal temperatures can be calculated from their respective scale heights. The pre- and post-onset temperatures for inbound passes are 177 K and 191 K for CO2, 187 K and 199 K for Ar, and 176 K and 180 K for N2, respectively. For outbound passes pre- and post-onset temperatures are 219 K and 225 K for CO2, 219 and 223 K for Ar and 217 K and 205 K

148 6.3. DUST STORM DECAY

for N2. By its very nature, the assumption of an isothermal atmosphere means altitudinal temperature variations cannot be observed. However, pre-onset temperatures are in 5/6 of the cases lower than post-onset temperatures. CO2 exhibits the most substantial temperature increase of 14 K during the inbound passes. During the inbound passes N2 has a temperature increase of 4 K, but a decrease of 12 K during the outbound passes. Again, mass dependence on temperature seems apparent here; thus, it could be inferred that O temperatures would decrease during the storm. Nevertheless, the increase in temperatures agrees with previous studies of heating within the atmosphere. Thus, the conclusion that upper atmosphere temperatures increases are not expected to be as substantial as for the lower atmosphere due to lack of increased direct heating can be made. We can infer that storm-induced heating is most intense below the homopause (∼25-50 K) with slight warming in the upper region. This is confirmed further by Jain et al., 2020 who explored MAVEN/IUVS limb scans. IUVS discovered a significant increase in peak airglow intensities, symptomatic of an increase in neutral densities. Jain et al., 2020 end by noting an increase in thermospheric temperature of ∼20 K. The prediction of intense lower atmosphere heating is verified by Guerlet et al., 2019 who used the Atmospheric Chemistry Suite (ACS) on board TGO and found a considerable increase of 50 K in the 5-45 km range, which is the prime region of dust heating. On a side note, the above study infers strengthened and dominant diurnal modes during storm periods, in contrast to dominant semi-diurnal modes during quieter periods. Similarly, Kass et al., 2019 exploited temperature and density data from MCS (Mars Climate Sounder) to explore warming/cooling around 25 km during global dust storm events. During quiet years, average temperatures are ∼180-200 K. During dust storm periods (June 2001 and June 2018), the zonal average temperatures increase to 220-230 K. The atmospheric warming of 30-50 K is in excellent agreement with that postulated in our study. On a different note, evidence of the dust storm ’shading’ the surface can be implied by considering surface temperatures. Using MCS data, Streeter et al., 2019 found an average global surface warming of 0.9 K, with local cooling on the dayside of up to 16 K. More intense heating above the surface evinces shading by the dust storm. The 2001 dust storm saw smaller warming/cooling due to its storm, with only increases/decreases in the surface temperature of 2-3 K (Cantor, 2007).

6.3 Dust Storm Decay

In Chapter 1, the main phases comprising a dust storm were discussed: onset, growth, and decay. The previous section investigated the onset, and now the decay phase is studied. Withers and Pratt, 2013

149 6.3. DUST STORM DECAY presents an exposition on dust storms and their decay rates. They focus on the magnitude and timescale of changes in upper atmosphere densities throughout the regional Noachis dust storm. They focused on aerobraking accelerometer data, UV stellar occultation data and radio occultation data from MGS. MGS accelerometer data are presented for 130 km, 140 km, 150 km and 160 km for both inbound and outbound legs. Data span from Ls ∼185-300°with the storm onset at ∼224°. Their technique is described now and explained in the context of NGIMS data. Figures 6.3.1a-d and 6.3.2a-d show interpolated background total densities at 170 km, 180 km, 190 km, and 200 km for inbound and outbound legs, respectively. Vertical dashed and dotted lines signify storm onset and storm peak, respectively, as in Figures 6.2.1a and b. Pre-onset densities are shown by stars in the range Ls=185-189°. During the growth stage of the storm, taken in this study to be Ls=189-194°, densities are shown by diamonds. Lastly, post-onset densities are shown by circles. Two exponential functions are fit such that time constants can be derived to get a measure of the decay timescale. The first timescale accounts for changes in density due to changing sampling location; densities generally decrease in solar longitude here due to moving towards the nightside. To ensure that only the seasonal trend is captured only data taken from Ls=185-189° and Ls=220-240° are used; this aims to omit dust storm influences. The fit is shown by solid orange lines in Figures 6.3.1a-d and 6.3.2a-d and its decay timescale is denoted τs. The second timescale is a combination of seasonal changes and abatement of the dust storm and is calculated using all densities post-onset (Ls≥193°) and denoted τfit. This fit is shown by the dashed orange line in Figures 6.3.1a-d and 6.3.2a-d. Given exponential functions have been used, the decay timescale of the dust storm can be isolated and derived using 1/τfit = 1/τs + 1/τcor. This formulation is taken from Withers and Pratt, 2013. The ratio (r) between the average peak storm density and pre-onset density is computed for each altitude level to quantify the severity of the global storm. The average peak storm density is calculated from all orbits in the range Ls=193-195°; this is the same range as used for post-onset densities in Figures 6.2.2a and 6.2.3b. The pre-onset density is taken from the seasonal fit (solid orange dashed line) at Ls=189°. Results for the Noachis regional dust storm are shown in Table 6.3.1. Timescales found from this current study are shown in Table 6.3.2.

Figure 6.3.3a shows τcor as a function of r. Results from this thesis are shown by circles and results found by Withers and Pratt, 2013 are shown crosses. The apparent dichotomy indicated by Tables 6.3.1 and 6.3.2 becomes less so when visualised in Figure 6.3.3a. Although r and τcor values are notably diﬀerent in both studies, a similar trend is observed across both dust storm events. In both cases, τcor decreases with increasing r; thus, more severe enhancements decay more rapidly. Severity here means

150 6.3. DUST STORM DECAY

Figure 6.3.1: (a), (b), (c) and (d) show interpolated inbound total densities at 170, 180, 190 and 200 km, respectively. Grey dashed lines show the first detection of the dust storm in the upper atmosphere (Ls∼189°). Densities prior to this onset are shown by stars. Densities during dust storm growth are shown by crosses. A peak in the storm is taken at Ls∼193° as shown by grey dotted lines. Decay time densities are shown by circles. Orange dashed lines show an exponential fit to post-onset densities. Solid orange lines show an exponential fit to the pre-storm and last 10° Ls densities and act as a seasonal fit.

the ratio between pre- and storm time densities. Further, and more intriguing, perhaps, is the likeness of the trends. Similar gradients are observed for both dust storms; these are -55°and -70°for results from this thesis and Withers and Pratt, 2013, respectively. Thus, it can be inferred that although there is not a single relationship that describes all dust storms, dust storm abatement phases are similar across dust storms. The most likely behaviour is that all decay phases have similar gradients to those presented here. Further behaviour that could be implied from the data, and veriﬁed with further storm data, is that decay phases are translated diagonally along a line from the lower left to the upper right. For example, decay data from another storm may lay along a line between the coordinates (1.6, 100°) and

151 6.3. DUST STORM DECAY

Figure 6.3.2: (a), (b), (c) and (d) show interpolated outbound total densities at 170, 180, 190 and 200 km, respectively. Grey dashed lines show the first detection of the dust storm in the upper atmosphere (Ls∼189°). Densities prior to this onset are shown by stars. Densities during dust storm growth are shown by crosses. A peak in the storm is taken at Ls∼193° as shown by grey dotted lines. Decay time densities are shown by circles. Orange dashed lines show an exponential fit to post-onset densities. Solid orange lines show an exponential fit to the pre-storm and last 10° Ls densities and act as a seasonal fit.

(2.3, 50°). Future work may elucidate relationships between dust storms. Withers and Pratt, 2013 note that taking the product of τcor and r produces a narrow range of values (205-222° Ls). This is not true here with the product producing values of 80-100°. Instead, τcor is now divided by r for both studies.

Figure 6.3.3b shows τcor/r as a function r. This exercise provides a compelling commonality between the two data sets with τcor/r for both studies taking values of 20-60°. Further studies will elucidate whether this is true for all dust storms. Decay timescales have been derived for the lower thermosphere during the 2018 global dust storm. Guzewich et al., 2019 used atmospheric optical depth measurements from Mastcam on board the Curiosity rover and found decay constant of 43±2 sols, equivalent to 25° Ls.

152 6.3. DUST STORM DECAY

◦ ◦ ◦ Altitude (km) Direction r(-) τfit ( ) τs ( ) τcor ( )

130 Inbound 2.24 42.93±2.78 80 93±3 130 Outbound 2.60 53.31±4.53 160 80±5 140 Inbound 2.45 39.64±1.72 90 71±2 140 Outbound 2.36 59.65±3.95 187 87±4 150 Inbound 2.44 41.65±1.98 76 93±2 150 Outbound 2.02 73.12±4.98 234 106±5 160 Inbound 2.08 50.94±3.24 100 104±3 160 Outbound 1.88 82.98±6.50 279 118±7

Table 6.3.1: Dust storm decay timescales determined for Noachis dust storm. r is ratio of peak storm density to pre-storm density. τfit is the decay timescale obtained by a direct exponential ﬁt to the data,

τs is the background decay timescale associated with changes in season and latitude, and τcor is the corrected decay timescale. All uncertainties are 1σ. Adapted from Withers and Pratt, 2013

Although this is comparable with fitted decay constants in the upper atmosphere, it is marginally lower than the corrected constants. There is inherent sampling bias; MAVEN sampled on the dayside around 50°S whereas Curiosity is located in Gale Crater (∼5°S), and it is not unexpected for different regions to recover at different rates. Further, Wolkenberg et al., 2020 compared dust storm decay rates using Thermal Emission Spectrometer (TES) on board MGS and the Planetary Fourier Spectrometer (PFS) on board Mars Express to compare global dust storm events in MY25 (2001), MY28 (2007) and MY34 (2018). The decay constants found for the respective years are 58°, 16° and 7°, and as found in both Withers and Pratt, 2013 and this study, the more severe the storm, the faster its recovery.

Other studies of global dust storm events have provided decay timescales for comparison. Dust opacity decay timescales found for Mariner 9 during the 1971 global dust storm were around 20° Ls, whereas lower atmospheric decay timescales found were longer taking values of around 36° Ls (Withers, 2006). Lemmon et al., 2015 found a constant of 43 sols using data from the Mars Exploration Rovers during the 2007 global dust storm. This constant is similar to the 51 sols calculated by Pollack et al., 1979 during the 1977 global dust storm. Cantor, 2007 made use data from of the Mars Observer

153 6.3. DUST STORM DECAY

◦ ◦ ◦ Altitude (km) Direction r(-) τfit ( ) τs ( ) τcor ( )

170 Inbound 1.52 20.88±5.76 29.47 71.61 170 Outbound 1.85 13.23±3.60 18.57 46.07 180 Inbound 1.59 17.29±3.18 23.58 64.84 180 Outbound 1.93 11.54±3.17 16.10 40.74 190 Inbound 1.66 15.37±4.29 20.65 60.09 190 Outbound 1.95 11.11±2.64 15.57 38.84 200 Inbound 1.48 15.38±2.78 19.50 72.89 200 Outbound 1.99 11.48±2.67 16.50 37.75

Table 6.3.2: Dust storm decay timescales determined for June 2018 dust storm. r is ratio of peak storm density to pre-storm density. τfit is the decay timescale obtained by a direct exponential ﬁt to the data, τs is the background decay timescale associated with changes in season and latitude, and τcor is the corrected decay timescale. All uncertainties are 1σ.

Camera (MOC) on board MGS to analyse the 2001 global dust storm event. Using the MOC, daily global maps were created from which over 5000 dust storms were identiﬁed, yet only one was a global dust storm event. Cantor, 2007 used atmospheric opacity (τ) to quantify storm conditions and assume an exponential decay during the abatement phase. Without accounting for seasonal variations in τ, decay constants ranged from 30-117 sols. From Table 1.4.2, the equivalent solar longitude timescale is ∼20°-70° Ls. Consequently, the decay phase lasted 60° Ls. These values are remarkably similar to those in this current study. The results imply that regional storms, such as the Noachis storm, have longer decay times compared to global dust storms. One possible explanation is that with a global dust storm, the complete shading of the surface removes the energy source, thus decaying more rapidly. The values attained in these other studies do fall into the behaviour described in this study. At the time of writing, this is the only study to quantify the 2018 dust storm decay timescale in this manner; it is unanimously agreed that the dust storm extended and ended around September 2018. Hence, no direct comparisons can be made. However, the dust storm’s decline has been hinted at being precipitous (Zurek et al., 2018). It is unclear as to whether the decay is steeper than the increase or sharper in comparison to previous dust storms.

154 6.4. DUST STORM EFFECTS ON GRAVITY WAVES

Figure 6.3.3: (a) Storm decay rate (τcor) as a function of density enhancement (r) from this study (circles) and Withers and Pratt, 2013 (crosses). (b) Storm decay rate normalised by density enhancement as a function of density enhancements

6.4 Dust Storm Eﬀects on Gravity Waves

This current study is one of few that studies the eﬀects of dust storms on gravity waves. Figures 6.4.1a and b show Ar gravity waves (blue lines) captured pre- and post-onset of the 2018 global dust storm using the same of orbits in Section 6.2. Waves are extracted by the method outlined in Chapter 5. The local maximum and minimum amplitudes are computed for each wave and then binned in 5 km intervals; this creates an envelope showing the average wave amplitude throughout each orbital range. This envelope is shown by the red dashed lines in Figures 6.4.1a and b. In Figure 6.4.1a shows waves taken pre-onset with average amplitudes of ∼10-20%, as expected from work in Chapter 5. There is no convincing growth in altitude. Figure 6.4.1b shows waves extracted in the post-onset range. Signiﬁcant growth is apparent at all altitudes with an average amplitude of ∼30-40%; this amounts to a factor of two increase compared to pre-onset waves. These are surprisingly large given the solar zenith angle. To ensure this behaviour is storm-induced the solar zenith angles of the two sampled regions are computed. A correlation between solar zenith angle and amplitude was shown in Chapter 5; larger zenith angles are associated with a larger amplitude. Figure 6.4.1d and e show the periapsis solar zenith angle for each orbit in the pre-onset and post-onset ranges, respectively. Pre-onset zenith angles range from

155 6.4. DUST STORM EFFECTS ON GRAVITY WAVES

53-57° and continue to increase to 65-70° during post-onset. From Chapter 5, such a relatively small increase in solar zenith angle should not induce a factor of two increase in amplitudes, as seen here. For further validation of increased storm-induced amplitudes, a quiet period is considered that samples the same solar zenith angles as during the dust storm, but two months earlier (April 2018). This removes the potential for seasonal effects to influence wave amplitudes. Figures 6.4.1c and f show Ar wave profiles and the solar zenith angle range during April 2018. Average wave amplitudes are ∼10-15%; this is in very good agreement with pre-onset amplitudes, thus confirming significant wave growth takes place during global dust storms. By extension, waves in-situ of regional dust storms most likely grow significantly. While moderate temperature increases are observed in the upper atmosphere, the posited dissipation processes in Chapter 5 are outweighed by the processes allowing significant wave growth. Elrod et al., 2019 noted increased turbulence and wave structures during this dust storm. Creasey et al., 2006b observed no noticeable change in wave-like perturbations during the Noachis storm. Local dust storms are more common than global dust storms; however, their locality reduces the probability of observation. As such, local dust storms can be studied using models. One such study performed by Spiga et al., 2013 investigated, what they proposed as, rocket dust storms. These localised storms form and inject dust high into the atmosphere (30-40 km). This creates a dust layer similar to that observed using Mars Reconnaissance Orbiter (MRO) date (Heavens et al., 2011). Spiga et al., 2013 identified the emission of mesoscale gravity waves due to rocket dust storms. Large temperature perturbations were observed.

There have been very few studies investigating the relationship between dust storms and gravity waves. One possible explanation is an increase in wind speed during a dust storm. Ryan and Henry, 1979 and Ryan and Sharman, 1981 use Viking Lander 1 and 2 data to characterise the response of the lower atmosphere to major dust storms at Mars. Prior to the dust storm, typical wind speeds at the Viking 1 site were less than 10 m/s, however, at the onset speeds increased to 17.7 m/s with gusts peaking at 25.6 m/s. As noted in the text, these are signiﬁcantly higher than previously recorded at the site. The Viking 2 landing site experienced slightly lower, but wind speeds notably increased at storm onset. Initially, wind speeds increased to 13.9 m/s with 21.2 m/s gusts, rising over the next few sols to 17.3 m/s and gusts of 25.7 m/s. Sánchez-Lavega et al., 2019 used ground-based images to understand the growth of the dust storm. At the onset, the storm expanded at a speed of 17±5 m/s, increasing to 40±5 m/s around 7-8 June. If this expansion is commensurate with surface winds, then a signiﬁcant enhancement in topographically-induced gravity wave activity is expected. Das et al., 2011 performed

156 6.4. DUST STORM EFFECTS ON GRAVITY WAVES

Figure 6.4.1: (a) Ar density perturbations (blue lines) extracted prior to the global dust storm onset using orbits with Ls=185-189°. (b) Ar density perturbations extracted post global dust storm onset using orbits with Ls=192-194°. (c) Ar density perturbations extracted at similar solar zenith angles to those sampled during the storm using orbits taken with Ls=159-161°. (d), (e) and (f) show periapsis solar zenith angles during the sampled periods.

an Earth-based study investigating gravity waves over the Thar Desert, located at the India/Pakistan border. They present evidence for a sudden enhancement of warming over a broad region of ∼0.8 K/day near 3.5 km altitude. This region is known to be a warm spot due to dust storms (Deepshikha et al., 2006). A significant perturbation is observed in the middle atmospheric temperature profiles, which is posed to be a potential source of gravity waves. As gravity wave generation requires a source of perturbation, localised heating due to dust storm is a plausible explanation. The results presented above show significant increases in gravity wave amplitudes during a dust storm, as in agreement with Das et al., 2011. The geographical location of each profile is considered to understand whether localised heating has an impact on waves at Mars. In both latitude and longitude, there was no clear trend with increase

157 6.5. SUMMARY wave activity; amplitudes are well mixed in location and time suggesting any local heating eﬀects which may occur in the lower atmosphere are not visible in the thermosphere. Das et al., 2011 found speciﬁc wavelengths (18-35 km) became prominent during the dust storm, which is not seen outside this region or during quiet periods. For the three sampling periods studied here, wavelengths are determined using the method in Chapter 5. From inspection, the general distributions of wavelengths are indistinguishable between the sampling period. From this, it can be inferred that dust storms enhance amplitudes but do not alter the wave spectrum.

As the first observational study of gravity waves during a global dust storm, it was unknown as to how wave characteristics would react to dusty conditions. The results are therefore new, exciting and surprising in equal measure. As suggested, increased winds may lead to a growth in wave activity; it is worth considering the use of a low-level wind/topography product to predict gravity wave activity. Revised open questions are stated in Chapter 8. It has been stated ad nauseam that gravity waves during dust storms have not been studied in depth. Nonetheless, comments have been made in conference proceedings alluding to significant wave variations, e.g., ’The accelerometer data also reveal high- frequency fluctuations in periapsis density that had sizable amplitude during this period’ from Zurek et al., 2018 and ’... the structure of the atmosphere exhibits significantly more turbulence after the onset of the dust event across all longitudes causing high variability in the altitude vs density as much as a factor of 5 -10 within a scale height’ from Elrod et al., 2019. Our study is consistent with these results. Future modelling and further observational studies of local storms may elucidate the connection between wave behaviour and dust.

6.5 Summary

In this chapter, the response of the Martian upper atmosphere to the June 2018 global dust storm has been studied. NGIMS data are exploited in an attempt to gain a fuller understanding of dust storm dynamics are Mars. The main ﬁndings are highlighted below.

• CO2, Ar and N2 density data are utilised to understand atmospheric expansion due to lower atmosphere heating. All species’ densities increase at the onset of the dust storm with a mass

dependence; CO2, Ar and N2 densities increase by factors of ∼1.7, 1.5 and 1.1, respectively. The

stability of N2 densities compared to other species during a dust storm is a new result and poses the question as to what may cause this. Atmospheric expansion is 2-7 km, in agreement with

158 6.5. SUMMARY

previous studies (Bougher et al., 1997; Bougher et al., 1999, Wang and Nielsen, 2003, Qin et al., 2019). Lower atmosphere heating has been predicted to be ∼25-50 K, whereas thermospheric heating is typically less than 10 K.

• A comprehensive comparison with work by Withers and Pratt, 2013 investigating atmospheric recovery timescales after dust storms. For the global storm studied here, storm decay timescales range from ∼30-70° Ls compared to a range of 71-118° found for the Noachis dust storm. Nonetheless, similar local trends are observed with more substantial density enhancements having recovery more quickly. The oﬀset between Noachis and global dust storm values suggest that storms exhibit similar behaviour, as shown by a common gradient in severity versus decay timescales. However, there is not a single relationship between severity and recovery for all storms. This is the ﬁrst time decay timescales in the upper atmosphere have been calculated for a global dust storm using this method. These results allow comparison with previous dust storms.

• The response of upper atmospheric gravity waves to a global dust storm has been studied for the ﬁrst time. Pre-storm waves are compared to those at the peak of the dust storm. Wave amplitudes signiﬁcantly increase during the dust storm (by a factor of ∼1.5); however, the wave spectrum remains similar. The cause of growth is currently unknown; however, increased wind speeds generating larger-scale waves has been proposed.

159 Chapter 7

Results from Trace Gas Orbiter Aerobraking Campaign

7.1 Introduction

For the ﬁrst time, Mars’ thermosphere has been measured in-situ concurrently by multiple orbiting spacecraft. Starting in March 2017, ESA’s Trace Gas Orbiter (TGO) began its year-long aerobraking campaign. During this period MAVEN continued to take measurements of the thermosphere. Although not a dedicated multi-spacecraft mission, much can be learned about the thermosphere from the concurrent datasets. Mars Express is still collecting data but at lower altitudes. The large scale temporal and spatial variations can begin to be decoupled. As shown earlier, MAVEN and TGO sampled a similar region at the same time but diﬀerent altitudes. This opportune occurrence is exploited to understand further density and temperature structures in the upper atmosphere with techniques employed to connect the two sampled regions. The evolution of wave structures is explored using case studies alongside general characteristics. The latter allows wave growth in altitude to be examined using TGO data in conjunction with MAVEN. Questions to answer include what are typical densities and temperatures in this previously unstudied region, and how do values compare to the MCD? We hope to study wave evolution by utilising both the TGO and MAVEN datasets. How do amplitudes behave with increasing height? As postulated, can we observationally show that larger wavelengths dominate with altitude?

160 7.2. SEPARATION OF BACKGROUND AND WAVE PROFILES

7.2 Separation of Background and Wave Proﬁles

The derivation of densities from spacecraft accelerometers was discussed in Chapter 2, and have been performed from TGO accelerometer measurements by Sean Bruinsma and J-C Marty, CNES. This is a new, unique dataset that no one has currently worked on. Figures 7.2.1a-c show three typical density proﬁles from TGO, with periapsis locations show in Table 7.2.1.

Panel Date and Time Latitude LST Ls

a 2017-12-22 20:57:50 62.8°S 16.7 hr 104° b 2018-01-25 15:39:55 68.6°S 7.1 hr 120° c 2018-02-10 01:48:39 46.5°S 2.9 hr 128°

Table 7.2.1: Periapsis locations for proﬁles shown in Figures 7.2.1a-c

Within each panel, there are four density profiles: two for inbound and two for outbound. Inbound and outbound profiles are shown in red and blue, respectively. The two profiles for each leg are derived from TGO density data (solid) and fitted background densities (dotted). Densities are fitted to TGO profiles using a third-order polynomial to the logarithm of the density, as done for MAVEN/NGIMS profiles in Chapter 5. Figure 7.2.1a shows an example of inbound and outbound densities differing by over a factor of two, implying the presence of a strong horizontal density gradient. Figure 7.2.1b exhibits similar behaviour only above around 110 km. Below this, densities converge to a common profile. The opposite is seen in Figure 7.2.1c. Inbound and outbound profiles align above around 112 km, below which densities can differ by a factor of two, again implying horizontal density gradients. The outbound portion in (a) and inbound portion in (c) show stagnation in density near periapsis. For the former (latter) case, densities are constant around 4×10−8 kg/m3 (3×10−8 kg/m3). This is likely due to the offset explained in Chapter 2, whereby closest approach and point of maximum density do not coincide.

Perturbations are observed in TGO density profiles as seen in NGIMS profiles, for example, below 110 km in Figure 7.2.1c, as density oscillate around the background profile. These have been interpreted as gravity waves and are extracted using the same process described in Chapter 5 by subtracting the background profile from the density data. Then, relative perturbations are determined by dividing through by background densities. Figure 7.2.2b shows the extracted perturbations. By inspection, the

161 7.2. SEPARATION OF BACKGROUND AND WAVE PROFILES

Figure 7.2.1: TGO (solid) and fitted (dashed) density profiles for pass (a), (b) and (c). Inbound and outbound legs are signified by red and blue, respectively. I=inbound, O=outbound. Periapsis locations in the format [date-time, latitude, LST, and Ls] are (a) - [2017-12-22 20:57:50, 62.75◦S, 16.7 hr and 104◦], (b) - [2018-01-25 15:39:55, 68.6◦S, 7.1 hr and 120◦], and (c) - [2018-02-10 01:48:39, 46.5◦S, 2.9 hr and 128◦]

inbound wave has an amplitude of 5% relative to the background. Around 114 km, the amplitude reaches 10%. The outbound wave exhibits considerably smaller perturbations with amplitudes around 2.5% below 114 km and about 3-5% above.

Wave characteristics can be calculated following diﬀerent methods starting with an initial wave such as that shown in Figure 7.2.2b. Using MAVEN data, Terada et al., 2017 calculated the root-mean- square of the perturbations, and England et al., 2016 considered sections along each orbit and computed the three most dominant waves using a Lomb-Scargle spectral analysis. Using TGO accelerometer data, Jesch et al., 2019 took the standard deviation of perturbations as the amplitude. The same

162 7.2. SEPARATION OF BACKGROUND AND WAVE PROFILES

Figure 7.2.2: (a) Inbound (red) and outbound (blue) TGO (solid) and ﬁtted (dotted) density proﬁles as shown in Figure 7.2.1a. (b) Extracted inbound and outbound waves from the orbit shown in Figure 7.2.1a. (c) and (d) show inbound and outbound wave spectra, respectively, computed from Fourier transforms of waves shown in (a).

technique used to extract NGIMS waves in Chapter 5 is used here for consistency. Both amplitudes and wavelengths can thus be computed. As noted in the study mentioned above, caution should be taken with this technique; the maximum wavelength that can be extracted with conﬁdence is equal to the altitude range considered. Consequently, the apparent dominant wave may not indeed be the presiding wave. For nearly all orbits periapsis altitudes are below 110 km, this allows a maximum obtainable wavelength of up to 10 km. For comparison, scales heights are ∼5 km in this region, as will be shown in Section 7.4. Figures 7.2.2c and d show the spectra determined by performing a Fourier transform on the inbound and outbound waves, respectively, and coloured accordingly. This is demonstrated in wavelength. For the inbound wave, the dominant wavenumber is approximately 0.19 km−1, equivalent to a wavelength of ∼6 km. The amplitude of this component is 3.3%. For the outbound leg, the

163 7.3. BACKGROUND DENSITY STRUCTURES dominant wavenumber is around 0.21 km−1, equivalent to a wavelength of 4 km. The amplitude of this component is 3%. It should be emphasised that only the most dominant composite waves have been highlighted. However, the spectra reveal other similarly dominant waves at 0.25 km−1 and 0.08 km−1 for inbound and outbound legs, respectively. Spectra are determined as above for all orbits and analysed in Section 7.5. Wavelengths greater than 10 km are likely present but are not captured here.

7.3 Background Density Structures

7.3.1 TGO and MAVEN Densities

In Section 7.2, it was shown that each density proﬁle could be split into two components - background values and waves. In this section, we present the global structure and seasonal variability of Mars’ background thermosphere. The global properties of atmospheric waves are examined in Section 6. While the spacecraft observations provided density measurements at vertical locations which changed from one orbit to another, we have interpolated these onto a common vertical grid. Thereby, we can more easily perform comparisons between orbits and analysis of density variations across the parameter space of solar zenith angle (SZA), longitude, local solar time (LST) and latitude. Red symbols in Figure 7.3.1 show TGO densities at 110 km altitude versus (a) SZA, (b) longitude (c) LST and (d) latitude. Thermosphere densities at 110 km do not show consistent trends with most of these parameters, having −9 −8 −3 typical constant values of 5×10 -5×10 kgm . Assuming a CO2 dominated region, these densities equate to number densities of around 6×1016-6×1017m−3. These values are within an order of magnitude of those derived from EUV solar occultation data by Thiemann et al., 2018. A slight trend of densities decreasing towards the south pole can, however, be seen in Figure 7.3.1d.

Figure 7.3.1 also shows densities at 150 km (green symbols) and 190 km (blue) from MAVEN observations. MAVEN total densities are calculated from CO2, Ar and N2 data. Densities have been calculated using measured count rates obtained from MAVEN NGIMS Level 1 (L1) export, versions 9 and 10, revision 1 data files, data that is available publicly in MAVEN NGIMS Level 1b (L1b) files on the NASA Planetary Data System (PDS). The reader is referred to Stone et al., 2018 and references therein for discussion into data reduction. Possible seasonal effects have been partially mitigated by selecting MAVEN densities collected during similar solar longitudes as the data from TGO’s aerobraking phase. Solar longitude range is taken to be 0-150◦ Ls.

164 7.3. BACKGROUND DENSITY STRUCTURES

Figure 7.3.1: TGO densities at 110 km (red) and MAVEN densities at 150 (km) and 190 (km) in (a) SZA, (b) longitude, (c) LST and (d) latitude.

The expected trend of solar EUV-heating on the dayside is strikingly more evident when looking at densities as a function of SZA (Figure 7.3.1a). Both MAVEN altitudes (150 and 190 km) show densities as being relatively constant on the dayside (0-90◦) and decreasing towards the terminator and into the nightside. Across the SZA range sampled by TGO at 110 km (90-175◦) the densities show no clear trend. As seen from Figure 7.3.1b densities at all altitudes show no trend with longitude, implying that any systematic density structures caused by surface topography can no longer be seen in the thermosphere. Figure 7.3.1c shows densities as a function of LST. At the higher altitudes, densities are larger during daytime hours (10-15 LST). The behaviour observed in the accelerometer dataset at 160 km (Liu et al., 2019) appears inverse at 110 km where daytime densities are at their lowest around 12-15 LST, increasing towards the nightside. The larger dayside densities at higher altitudes are consistent with in-situ solar EUV-driven behaviour, solar heating on the dayside expanding the atmosphere. At 110 km, Mars’ thermosphere is less driven by in-situ solar heating and instead more controlled by atmospheric winds.

165 7.3. BACKGROUND DENSITY STRUCTURES

Figure 7.3.1d shows atmospheric densities as a function of latitude. At 110 km, TGO covers the entire Southern hemisphere from 75◦ S to 0◦, while MAVEN data covers latitudes extending from 75◦ S-75◦ N. MAVEN densities at any particular latitude show variability covering 1-2 orders of magnitude, so it is diﬃcult to extract any latitudinal trends with conﬁdence. Densities at 190 km suggest a weak trend of decrease towards the south pole.

In the upper thermosphere, it is known that solar heating is a strong driver of density; good agreement between Viking 1 and predominantly solar EUV-driven circulation model has been observed Bougher et al., 1990. Solar extreme ultraviolet (EUV) is mainly absorbed in the altitude range 100-200 km (Bougher et al., 2015). Thiemann et al., 2018 used MAVEN solar occultation data to understand thermospheric variability. By considering density profiles at the dawn and dusk terminators, Thiemann et al., 2018 obtained a positive correlation between background temperature and EUV flux; thus, this region is solar EUV-driven. The behaviour at 110 km is different from that of the upper thermosphere. There is a pronounced drop in density across the terminator at MAVEN altitudes, whereas a small increase is seen at TGO altitudes. It can be inferred that dynamics may play a significant role in density structure in this region. One proposed explanation for the higher nightside temperatures is atmospheric downwelling on the nightside. The convergence of global circulation forces a downward wind, leading to the atmosphere ‘collapsing’, increasing the density. Elrod et al., 2017 used MAVEN/NGIMS data to reveal He density bulges on the nightside. They conclude that strong local vertical advection is responsible on the nightside. This is a potential explanation for density behaviour observed here. It can be seen for densities at 140 km that their behaviour is a combination of drivers seen at 190 km and 110 km. A decrease in density is observed across the terminator; however, this is not as rapid as seen at 190 km. Clearly, the driver of density change is dependent on altitude. Additionally, the optical depth at UV wavelengths is above one in the lower thermosphere so the atmosphere can no longer be heated by sunlight.

Although the above findings are not new, they do provide observational evidence which agrees with global-scale modelling of the lower thermosphere being dynamically driven. Some of these modelling studies are discussed now, with comparisons made to our study. Medvedev et al., 2011 used the gravity wave scheme of Yiˇgit et al., 2008 in the GCM described in Hartogh et al., 2005. They found gravity waves impart their dynamical influence on the lower thermosphere (∼100-130 km). Such revealed effects include deceleration of the mean zonal wind. They note that temperature enhancements are complex, with winter polar warming in the upper atmosphere. The introduction of gravity waves can typically alter

166 7.3. BACKGROUND DENSITY STRUCTURES thermospheric temperatures by around ±15 K. Using simulations from the Max Planck Institute Martian General Circulation Model (MPI-MGCM) (Medvedev et al., 2013), Yiğit et al., 2018 demonstrated large temperature ﬂuctuations around 120 km, as induced by gravity waves. By modelling an entire Martian year, they found the global mean temperature to cool by around 9% with the addition of gravity waves. These results highlight the importance and inﬂuence of dynamic processes, such as propagating gravity waves, on the lower thermosphere. Our observations are in good agreement with the predictions of the two aforementioned global-scale modelling studies that the lower thermosphere is dynamically driven.

7.3.2 Comparison with Laboratoire de Météorologie Dynamique Mars Climate Data- base

In the following, TGO density data are compared to those extracted from the Laboratoire de Météoro- logie Dynamique Mars Climate Database v5.3 (LMD MCD). The MCD is a database of atmospheric statistics compiled from state-of-the-art Global Climate Model (GCM) simulations of the Martian atmosphere (Forget et al., 1999; Millour et al., 2015). The solar minimum scenario is employed. It extends from the surface up to 250 km and accounts for physical processes such as the condensation of the CO2 atmosphere during polar nights, the generation and evolution of water ice clouds and the distribution of airborne dust (González-Galindo et al., 2015). The MCD is validated using available measurements across a variety of missions. Atmospheric temperatures are compared to measurements from MGS/TES (Thermal Emission Spectrometer), MRO/MCS (Mars Climate Sounder) and MGS and Mars Express radio occultation experiments. Surface pressures and temperatures are compared to TES, Viking, Pathﬁnder, Phoenix and Mars Science Laboratory (MSL) measurements (Millour et al., 2015). Amongst many other useful outputs, density is used as a comparison parameter between observations and modelling. Densities have been extracted from the MCD and compared to the TGO background proﬁles at 110 km (see above section). Figure 7.3.2a-d shows TGO (red circles) and MCD (blue stars) background densities at 110 km in SZA, longitude, LST and latitude, respectively.

In Figure 7.3.2a, the MCD successfully captures both the order of observed densities and the behaviour in SZA; the MCD correctly identiﬁes the atmosphere not to be solar EUV-driven at this altitude. Orbit-to-orbit variability is visible in the MCD data, though to a lesser degree. This is due to horizontal changes, not in time. Figure 7.3.2b shows densities in longitude. As shown from both TGO and MAVEN data, any inﬂuence of topography on thermospheric densities is not visible in the data, yet the MCD shows a density increase of around 50% near 60◦E when compared to TGO densities. Similarly, a slight

167 7.3. BACKGROUND DENSITY STRUCTURES

Figure 7.3.2: TGO (red circles) and MCD (blue stars) densities interpolated at 110 km shown in (a) SZA, (b) longitude, (c) LST and (d) latitude. Here, only background proﬁles are used.

dip can be seen near 250◦E. These deviations are most likely associated with the Hellas Basin and Tharsis Region, respectively. Figure 7.3.2c shows densities in LST. Orbit-to-orbit variability is observed in the midnight-dusk sector with MCD densities typically larger than TGO densities. Moving towards to the dayside sees well-matched TGO and MCD densities. In the dusk-midnight sector, MCD densities are several factors lower than observed by TGO. Again, the variability is not captured. The ﬁnal panel, Figure 7.3.2d, shows densities in latitude. The general behaviour is captured well with both datasets exhibiting diminishing densities toward the south polar region. There is a smattering of larger-than- expected MCD densities around 30◦S-60◦S which are most likely associated with the topographical regions discussed above.

This next exercise stems from that above. Now, for both inbound and outbound legs on each pass densities have been interpolated to altitudes of 105 km, 110 km, 115 km and 120 km. Densities are

168 7.3. BACKGROUND DENSITY STRUCTURES taken from the background fitted profiles (Figure 7.2.1). Then, for each inbound and outbound profile, the ratio of TGO to MCD densities is computed at the stated altitudes. Data have been binned using a bin size of 0.5 hr × 5◦. A mean value is then computed for each bin. Figure 7.3.3a-d show these ratios in LST and latitude at 105 km, 110 km, 115 km and 120 km, respectively. Here, blue (red) shows an overestimation (underestimation) by the MCD.

Figure 7.3.3: TGO to MCD density ratios in LST and latitude at (a) 105 km, (b) 110 km, (c) 115 km and (d) 120 km. Data have been binned using a bin size of 0.5 hr × 5◦

Evidently, the lowest altitudes are the least sampled. At 105 km, TGO densities are larger by a factor two in the dawn sector, fairly comparable towards noon, and lower by around 0.5 on the nightside. We can infer that day-night variations are larger than predicted by the MCD. As will be shown now, this is not the case at higher altitudes. Inspection of the next altitude level (110 km - Figure 7.3.3b) displays more coverage, extending onward from dusk towards midnight. The strong underestimation in the dusk sector is now weakened with TGO and MCD densities diﬀering by around 50%. In the dusk sector, TGO

169 7.4. TGO TEMPERATURES densities are generally larger, shown by a density ratio of about 1.5. Figure 7.3.3c shows this behaviour is duplicated at 115 km with diﬀerences in densities between dawn and dusk becoming larger. The faint underestimation seen around 6-8 LST at 110 km is no longer visible. MCD densities surpass TGO densities here. This behaviour is repeated at 120 km (Figure 7.3.3d). Again, ratios decrease in the dusk and noon sectors, implying MCD densities are decreasing at a faster rate with altitude. That is to say, the scale heights diﬀer, leading to the conclusion that temperatures observed by TGO are cooler than predicted by the MCD in this region of the atmosphere.

Two main results were presented: TGO densities being a factor two larger than MCD densities in the dusk sector compared to being smaller in the dawn and noon sectors and MCD densities decreasing at a faster rate in altitude, leading to more extreme TGO-MCD ratios. The former indicates a deﬁciency in local time dependencies in the thermosphere. This disparity appears to weaken with altitude suggesting the solar EUV-driven nature of the atmosphere is captured, but the lower thermosphere is not. The latter result can be attributed to TGO gathering data within a cooler atmosphere than expected. Within the thermosphere, the MCD has been validated against MGS accelerometer data, Viking 1 and 2 data, and Pathﬁnder. A full validation document is planned Millour et al., 2019b. MGS sampled altitudes and solar longitudes similar to those in this study. However, MGS did not sample the noon sector. Thus, one recommendation is using TGO observations to constrain the MCD in this region further. Similarly, MGS sampled the dusk sector at latitudes below 50◦, thus further constraints are needed for this region. As explained in Chapter 3, discrepancies between the MCD and observational data are expected given the relatively recent extension of the model into the thermosphere. This work will help to further constrain the model densities, allowing to further understand the physics required to replicate the thermosphere.

7.4 TGO Temperatures

7.4.1 Deriving TGO Temperatures

In the following, TGO densities are used to derive temperatures within the lower thermosphere. For reasons explained now, a different method is implemented to compute temperatures, and as such, only a single temperature is derived per pass. From Chapter 3, it was seen that when integrating densities downwards to attain temperature profiles, a convergence of profiles was observed after several scale heights for a wide range of upper boundary conditions. A 100 K difference in upper boundary conditions at 240 km leads a <10 K difference in temperature profiles at 200 km. And this uncertainty diminishes

170 7.4. TGO TEMPERATURES further will lowering altitude. While this technique is favourable for MAVEN, it is not auspicious for TGO as the latter spacecraft only sampled ∼15 km which is not large enough for profiles to suitably converge. If the upper boundary conditions were known exactly, then profiles could be derived. For these reasons, a new technique is implemented to determine a single temperature is retrieved at periapsis with confidence.

Density structures within an isothermal atmosphere can be described in altitude by ρ = ρ0 exp[−(z− z0)/Hs], where ρ0 is density at a reference altitude z0. Hs is the density scale height. This is derived in Chapter 1. In this idealised situation a spacecraft would measure identical density profiles during inbound and outbound passes. As evidenced in Figure 7.2.1a-c this is not necessarily the case. Zurek et al., 2017 present a modified version of the above equation which allows more complex density structures to be taken into account. Equation 7.1 shows the along-track density as a function of altitude (z) and time from periapsis (t) with fitted constants periapsis density (ρ0), along-track density gradient at periapsis ∂ρ0 ∂Hs ∂t , density scale height at periapsis (Hs) and along-track scale height gradient at periapsis ∂t .

! ∂ρ0 z ρ(z, t) = ρ0 + t exp − (7.1) ∂t ∂Hs Hs + ∂t t Zurek et al., 2017 approximates Equation 7.1 to ﬁrst order by assuming gradient terms are small given time variations are slow,

1 ∂ρ0 z 1 ∂Hs ln ρ(z, t) = ln ρ0 + t − + tz (7.2) ρ0 ∂t Hs Hs ∂t

By ﬁtting Equation 7.2 to TGO density proﬁles, Hs can be determined, and subsequently, temperatures can be derived using Equation 3.2 where a mean molecular mass of 43.03 amu is assumed.

7.4.2 Background TGO Temperatures

Temperatures are computed for each TGO orbit using the technique described above. Figures 7.4.1a-d shows periapsis temperatures in altitude, SZA, LST and latitude, respectively. As periapsis altitude varies throughout TGO’s aerobraking period data points are coloured correspondingly to altitude. Thus, panel (a) serves as a colour bar. To further compare observations with the MCD, temperatures have been extracted and shown as a rolling mean by the black dashed line in each panel. Figure 7.4.1a shows temperature as a function of altitude. Fairly good agreement is observed between TGO and MCD at the higher altitudes where temperatures are predicted by the MCD to asymptote around 120 K above ∼108 km. TGO temperatures are observed to be ∼10 K cooler than this. This temperature gap widens at the lowest sampled altitudes (∼102-105 km) as MCD temperatures increase up to ∼130

171 7.4. TGO TEMPERATURES

K. In contrast, TGO temperatures decrease on average to ∼80-90 K. This veriﬁes the inferences made earlier regarding TGO observing cooler temperatures. Figure 7.4.1b shows temperature as a function of SZA. Here, altitudes variations are well mixed such that any trends in SZA should emerge. Again, MCD temperatures are on average ∼20 K warmer than observed by TGO, nonetheless the same trend is seen with fairly invariant temperatures in zenith angle. Figure 7.4.1c shows temperature as a function of local solar time. The midnight-dawn sector is well captured by the MCD with the rolling mean in good agreement with the average TGO temperature (∼120 K). The results within the noon sector imply TGO temperatures are signiﬁcantly cooler than expected from the MCD, however, on inspection of the night sector, a slight increase in MCD temperatures is observed; the commonality between these sectors is the altitude at which temperatures were calculated. Hence, the discrepancies are due to altitude, not local time dependencies. Finally, Figure 7.4.1d shows temperature in latitude. Closest to the south pole, lower altitudes were sampled, hence the divergence between MCD and TGO temperatures. MCD temperatures are fairly invariant in latitude, however slight warming towards the equator is observed in TGO temperatures.

Jesch et al., 2019 performed a similar exercise and found temperatures of ∼120 K in this region. Pre- vious studies have also determined temperatures in the lower thermosphere. Gröller et al., 2018 exploited MAVEN Imaging UV Spectrograph occultation data and required temperatures of ∼70-170 K to explain deduced densities at 120 km. Stone et al., 2018 derived temperature profiles from MAVEN/NGIMS data during the DD campaigns. These campaigns probed the thermosphere down to 120 km. At these altitudes, temperatures generally span 90-150 K. Overall, temperatures derived in our present study are in broad agreement other studies. Such cool temperatures (below ∼100 K) are not wholly unexpected when considering energy sources in particular regions of the atmosphere. Energy sources were touched upon in Section 5.1. Withers, 2006 utilised MGS and ODY aerobraking data to derive background temperatures at similar altitudes to those in this study. Data from MGS Phase 2 is most comparable, given its similar seasonal sampling. Typical afternoon temperatures at 120 km found by Withers, 2006 are 100-150 K and during this phase, relatively invariant in latitude. The difference in altitude may account for the shift in temperatures observed between the two studies. Further, the trend in this study suggests temperatures increase with altitude, thus converging to those found by Withers, 2006. MGS morning temperatures are slightly cooler by ∼10-20 K than their afternoon counterparts. This is in broad agreement with the findings here. Overall, there is good agreement between these studies. As stated earlier, Vals et al., 2019 explored perturbations in MGS, ODY and MRO density profiles. They

172 7.4. TGO TEMPERATURES

Figure 7.4.1: Derived periapsis temperatures from TGO density data shown in (a) altitude, (b) SZA, (c) LST and (d) latitude. Data are coloured according to altitude. Rolling means from extracted MCD temperatures are shown by the black dashed lines.

investigated the correlation between amplitudes and temperatures; this wealth of temperature data is now compared to those from TGO. ODY temperatures are 125-200 K, which are generally higher than those found here. Seasonal and latitudinal sampling differences most likely account for higher temperatures. Similar temperatures were found during MGS’ Phase 2 aerobraking campaign. Again, the majority of TGO temperatures are below this range. The final measurements discussed are from ODY. As stated earlier, ODY sampled a region alike to that by TGO. The temperatures found by Vals et al., 2019 reflect this; they found a range of ∼125-160 K. This overlaps with the range observed for TGO, but temperatures remain warmer for MRO. One potential cause is that TGO temperatures are derived around periapsis, whereas Vals et al., 2019 found the mean temperature from a profile. As temperatures are known to increase with altitude in the region sampled, the mean value is skewed by higher altitude temperatures (Stone et al., 2018).

173 7.5. WAVES

7.5 Waves

This section aims to further understand waves in the thermosphere, with particular emphasis on wave growth, allowing the posed questions to be answered. Following the process outlined in Section 7.2 whereby waves were separated from background structures, wave amplitudes and wavenumbers are calculated for all passes. Spectra are combined and averaged with wavenumbers being replaced by wavelengths. Figure 7.5.1a shows averaged amplitudes of wavelengths using a bin size of 2 km. These are averaged over all altitudes sampled by TGO accelerometers (around 100-120 km). Peak amplitudes relative to the background are around 6±4%. Also shown is the averaged spectrum derived from waves extracted from MAVEN data in Chapter 5.

As vertical wavelengths may scale with scale height, a normalised wavelength is introduced; this is the vertical wavelength divided by the appropriate scale height. For TGO altitudes, we have determined a mean scale height of 5.4±2.0 km, with the latter value being the standard deviation. This uncertainty corresponds to a temperature of ∼40 K. Scale heights are determined from the gradient of a linear fit to log(ρ)-altitude plots, treating inbound and outbound profiles separately (Figure 7.2.1). And for MAVEN altitudes, the scale height is taken to be 12 km (Zurek et al., 2017). Figure 7.5.1b shows amplitude as a function of normalised vertical wavelength. This figure begins to elucidate how particular waves within the thermosphere behave depending on their relative wavelength. For discussion, 7.5.1b is simplified by taking the ratio of MAVEN amplitudes to TGO amplitudes for each bin. This is shown in Figure 7.5.1c. The horizontal dashed line shows a value of one. These results allow the evolution of waves to be explored due to each characteristic - amplitude and wavelength - shedding light on how waves develop. As density falls exponentially, amplitudes necessarily grow exponentially to conserve momentum. Thereby, understanding amplitudes at distinct altitudes allows these theories to be tested and regions of damping to be identified.

Figure 7.5.1c infers two regimes observable at altitudes studied by TGO and MAVEN. The ﬁrst is for normalised wavelengths less than one; that is, measured wavelengths are less than the scale height at which they were captured. In this regime, the ratio of amplitudes is unity leading to the inference that waves of these scales are saturated by the time they reach the upper atmosphere. At the lowest normalised wavelengths (<0.5), ratios are marginally lower than one, indicating damping is present. The second regime occurs beyond normalised wavelengths of unity. Here, MAVEN amplitudes are larger by

174 7.5. WAVES

Figure 7.5.1: (a) Binned TGO (red) and MAVEN (blue) wave spectrum with width 2 km. Error bars are one standard deviation. (b) Same as (a), but wavelengths have been normalised by scale height. (c) Amplitude ratio between MAVEN and TGO waves using normalised data from (b)

up to a factor of two compared to their TGO counterparts. Given MAVEN’s higher altitude orbits, it can be inferred that longer-wavelength waves, those with a normalised wavelength larger than one, will continue to grow with altitude. An undamped wave is expected to grow by a factor of around nine, assuming an average scale height between 120 km and 160 km of 9 km. We can therefore infer that

175 7.5. WAVES although larger wavelengths continue to grow with altitude, they are still damped but to a lesser degree than smaller waves. This is the ﬁrst study to observationally infer these results at Mars.

From Figure 7.5.1a, the most dominant wavelengths are ∼5-15 km. Given the altitude range studied by TGO is about 15 km, wavelengths of this length can be extracted confidently from the data. Creasey et al., 2006b used MGS occultation profiles to determine wave properties at 0-30 km altitude. Near the surface, a bi-modal distribution of vertical wavelengths with peaks at 8-10 km and 13-15 km were found. The former range is in good agreement with the range found in this current study. Consequently, it is plausible that dominant wavelengths remain sufficiently unchanged through the lower atmosphere with amplitudes increasing with altitude; Creasey et al., 2006b found amplitudes typically less than 5%. The latter range is found to still be relatively dominant at TGO altitude; however, 13-15 km wavelengths are nearing the point of not being confidently extracted from the profiles via the Fourier transform. In Chapter 5, we found vertical wavelengths of 10-30 km above 140 km. It is possible that atmospheric wave filtering is being observed above 100 km as smaller-scale waves are absorbed by background winds (Fritts and Alexander, 2003). These results imply shorter wavelengths (<10 km) are dominant at TGO altitudes, whereas larger wavelengths (>10 km) are dominant at MAVEN altitudes (>140 km).

Jesch et al., 2019 found average wave amplitudes of 6-8% with an altitudinal dependent standard deviation of 1.5-4%. These amplitudes are in a very good agreement with values found in this current study; this validates our technique. Using MGS accelerometer data, Fritts et al., 2006 extracted amplitudes from wave profiles. Fortuitously, during the latter stages of its aerobraking phase, MGS sampled a similar region to TGO. MGS sampled nightside southern latitudes during northern spring/summer. At 105 km, amplitudes are around 5-10% and gradually increase to about 15% at 120 km. Evidently, values are very repeatable under similar atmospheric conditions. They did not differentiate between wavelengths. Similarly, Creasey et al., 2006a extracted perturbations from MGS aerobraking data. During similar seasonal conditions as TGO experienced, Creasey et al., 2006a found amplitudes in the Northern hemisphere rarely reach 5% which is comparable to those found in this present study. During the same phase, MGS sampled southern latitudes also. Here, amplitudes are larger than above the equator and hence larger than TGO amplitudes. MGS sampled higher altitudes than TGO, and this difference may account for the wave growth, as justified above. Vals et al., 2019 determined the RMS perturbation amplitudes from MGS, Odyssey (ODY) and Mars Reconnaissance Orbiter (MRO) density data. ODY sampled Mars in approximately the opposite half of the Martian year (Ls=260-310◦). Amp-

176 7.5. WAVES litudes are 5-20% with an average value above 10%. Seasonal effects are expected to vary amplitudes. MGS values are comparable to those found by Creasey et al., 2006a, expected. MRO sampled the comparable region to TGO; measurements were taken in the southern hemisphere at Ls=30-100◦. RMS amplitudes are typically 5-10% which is in very good agreement with those found in this current study. The two underlying findings from our amplitudes are that they are in agreement with previous spacecraft data and there is clear wave growth in the thermosphere. Studies mentioned in this section have shown slight amplitude growth with altitude within their specific altitude range. Our technique for extracting waves could be applied to smaller altitude sections, as in Siddle et al., 2019, and amplitudes calculated for each segment. It would not be unexpected to see wave growth as in previous studies. A reduction in altitude range limits the extent of extractable wavelengths; thus, dominant waves are likely to be overlooked. Further, Medvedev et al., 2016 used the MPI-MGCM to interpret MAVEN Imaging Ultraviolet Spectrograph (IUVS) observations. By comparing density profiles to zonal mean densities, relative deviations in altitude were determined, and it was demonstrated that density perturbations could grow up to a factor of around two as they propagate from the lower to the upper thermosphere. This is in good agreement with results found in our study where wavelengths typically larger than the background scale height grow by up to a factor three between TGO and MAVEN periapsis altitudes (around 100-140 km). Shorter wavelengths appear saturated at these altitudes. Overall, the finding that waves unquestionably grow with altitude is not unexpected, it has been shown using multiple spacecraft data for the first time, increasing confidence in the results. A case study is now presented that shows the possibility that the same gravity has been observed in both the TGO and MAVEN dataset. Figure 7.5.2a shows an outbound TGO wave (red line) sampled on 28 Jan 2018 at 16:53. Less than an hour later, MAVEN sampled a similar region of the atmosphere during its inbound leg. Geographical locations of each spacecraft are shown in Figure 7.5.2. The remarkable similarity is observed in characteristics between the waves as quantified by Figures 7.5.2b and c, which show the wave spectra of the sampled MAVEN and TGO waves, respectively. Dominant amplitudes are ∼10-20% with wavelengths 5-10 km. Although these are typical wavelengths for TGO, these are short for MAVEN, thus increasing the confidence that the same wave has been sampled. There are less than ten occasions where TGO and MAVEN orbits reside is such similar locations. And of these few occasions, not all exhibit similar wave characteristics across both spacecrafts’ datasets.

177 7.6. COMBINING MAVEN AND TGO DATA FOR CONTINUOUS VERTICAL PROFILES

Figure 7.5.2: (a) Extracted inbound MAVEN wave (blue) from 28 Jan 2018 and outbound TGO wave (red) also from 28 Jan 2018. (b) and (c) are wave spectra of the extracted waves in (a) for MAVEN and TGO, respectively. (c) show the trajectory of each spacecraft’s pass in longitude and latitude. Colours are consistent in all ﬁgures.

7.6 Combining MAVEN and TGO Data for Continuous Vertical Proﬁles

Earlier, TGO and MAVEN waves were compared with one case study presented, which posited the possibility that the same wave had been observed in both datasets. This was achieved due to the proximity of both orbits. This fortuitous closeness is exploited to hydrostatically connect the datasets such that density and temperature behaviour in the ‘unsampled’ region, typically in the range 120-140 km, can be derived.

178 7.6. COMBINING MAVEN AND TGO DATA FOR CONTINUOUS VERTICAL PROFILES

7.6.1 Comparing TGO and MAVEN Densities

A short calibration exercise is undertaken to ensure that TGO and MAVEN densities are comparable. By this, it is meant that an analysis is conducted to test whether both spacecraft would measure the same densities at the same location and remove the possibility of any systematic bias between the instruments. MAVEN did not undertake any DD campaigns during TGO’s aerobraking phase; thus, similar altitudes were not sampled. Consequently, the requirement for data concurrency is lifted, and all DD campaigns are considered. Further, to ensure an altitudinal overlap between the datasets, TGO densities are no longer cut-oﬀ at 120 km; they now extend up to 125 km. Background densities within both datasets are interpolated at 125 km. A total along-track density is constructed for MAVEN using

CO2, Ar and N2. At this altitude CO2 is dominant, so the omission of other species does not pose an issue. For each dataset, densities are then interpolated further in solar zenith angle on a fixed grid with spacing 1°. Where possible, MAVEN densities are divided by TGO densities for each interpolated solar zenith angle. Figure 7.6.1 shows the ratio of MAVEN to TGO densities as a function of solar zenith angle. A least-squares fit is shown by the dashed line. A ratio of unity is signified by a dotted line.

Figure 7.6.1: Ratio between TGO and MAVEN densities at 125 km altitude as a function of solar zenith angle. A linear best line is shown with by the blue dashed line. For ease of comparison, a grey dotted line shows a ratio of one.

179 7.6. COMBINING MAVEN AND TGO DATA FOR CONTINUOUS VERTICAL PROFILES

The underlying result is that MAVEN densities are typically larger than respective TGO densities. There is a great deal of variability in the ratio for the majority of sampled solar zenith angles. As mentioned earlier in the chapter and in Chapter 2, data are not gathered concurrently at similar locations leading to further variability potentially caused by the following factors: atmospheric tides, seasonal variations, and solar activity. The latter two being addressed in Chapter 4. MAVEN sampled during a time of comparatively higher solar activity. Nonetheless, the majority of MAVEN densities are within a factor of two of TGO densities. A good agreement is observed between the datasets due to no clear oﬀset, and as such, they can be ‘synthesised’ for analysis in the next section.

7.6.2 Hydrostatically Connecting TGO and MAVEN Density Proﬁles

From Chapter 2 it was shown that MAVEN concurrently sampled a similar region as TGO during the tail-end of the latter’s aerobraking phase. During this period it is possible to hydrostatically connect these two regions, allowing densities and temperatures within the unsampled altitudes to determined. This has implications on modelling efforts where a continual profile is required, such as within diffusion models. In the following, the process of connecting individual TGO and MAVEN profile is described.

Profiles are selected where similar TGO and MAVEN latitudes and longitudes are sampled and periapses nominally within three hours of each other. In practice, consecutive TGO and MAVEN orbits occur within one hour. The two regions’ densities cannot be connected by a simple function such as a polynomial as this would create a nonphysical atmosphere, whereby the temperature structure would not successfully reproduce the density profile. For the densities to be connected, a physical temperature profile is initially required. As alluded to in Chapter 3 and explained earlier in this chapter, there would be large uncertainty associated with temperature profiles derived from TGO data; thus a rolling mean of 1 km is performed on TGO densities. This removes sharp variations in density which are present. The gradient of the log-density is calculated every 1 km using a window of 2 km. This is identical to computing the upper boundary condition but applied over multiple smaller ranges. A mean molecular mass of 43.03 amu is used, taking into account a CO2 dominated atmosphere. NGIMS temperature profiles are derived via downward integration (Section 3.2). The two derived temperature profiles are now connected hydrostatically to create a continuous profile, and this is achieved by assuming the missing temperature profile takes the form of a fourth-order polynomial shown by Equation 7.3.

180 7.6. COMBINING MAVEN AND TGO DATA FOR CONTINUOUS VERTICAL PROFILES

T (z) = az4 + bz3 + cz2 + dz + e (7.3)

Coefficients are determined using calculable boundary conditions, as shown in Equation 7.4. The first boundary condition is the bottom temperature (T (z1)) of the missing profile must match the temperature at the highest altitude in the TGO region (z1). Similarly, the upper temperature (T (z2) in the missing region must match the temperature at the lowest MAVEN altitude (z2). Thirdly, the temperature 0 gradient (T (z1)) at z1 must match that of the bottom temperature gradient in the missing region. 0 Fourthly, the temperature gradient (T (z2)) at z2 must match that of the top temperature gradient in the missing region. The final boundary condition is an assumption that there is a local minimum or maximum in the missing temperature profile at an altitude of zm located between z1 and z2. By solving Equation 7.4, a hydrostatic temperature profile can be determined.

      4 3 2 z z z z1 1 a T (z1)  1 1 1             z4 z3 z2 z 1 b  T (z )   2 2 2 2     2         3 2     0   4z1 3z1 2z1 1 0 · c = T (z1) (7.4)              4z3 3z2 2z 1 0 d T 0(z )  2 2 2     2   3 2     0  4zm 3zm 2zm 1 0 e T (z3)

zm is the sixth unknown. However, it is constrained between z1 and z2. Values of zm are iterated through in increments of 0.1 km. Each profile is plausible concerning temperature; however, a further condition is required to be met to determine the actual value of zm. The final condition is the density at the highest altitude in the missing region must match the density of the lowest altitude in the MAVEN profile. A new density profile is created in the missing region using Equation 7.5, dz ρ(z) = ρ(z − dz) exp − (7.5) H(z)

where the scale height H(z) is deﬁned as,

1 m(z)g(z) 1 dT (z) = + (7.6) H(z) kT (z) T (z − dz) dz where dz is 0.1 km and ρ(z) and T (z) are the missing region’s density temperature profile. The initial ρ(z − dz) and T (z − dz) values are the top TGO values. All other symbols have been defined previously. For each zm, the temperature profile is input into Equation 7.5 and a density profile is

181 7.6. COMBINING MAVEN AND TGO DATA FOR CONTINUOUS VERTICAL PROFILES derived. The ratio between the density at the highest altitude in the missing region and the density of the lowest altitude in the MAVEN profile is calculated and subtracted from unity. This is defined as the offset. The zm value that derives the density profile with the lowest offset is taken forward as the best fit.

Figures 7.6.2a and b show connected density and temperature profiles, respectively. MAVEN (TGO) data are shown by blue (red) lines. Data are taken on 29 Jan 2018 in the southern hemisphere, as shown in Figure 7.6.2c. For these orbits MAVEN probes down to just below 140 km and TGO samples just above 120 km. As these are typical altitudes, there is a 20 km range which is not sampled. The well- matched density profile confirms that a simple interpolation between regions is not suitable, but rather a more complicated temperature structure is required. The necessity for the temperature profile to have a maximum or minimum does not introduce any dramatic differences compared to derived profiles.

Figure 7.6.2c shows the coverage of MAVEN and TGO in longitude and latitude. Longitude is utilised as geographically similar profiles are required. Results are not expected to differ dramatically if local time comparisons are made. This section aims to show how this technique works and how applicable it could be to future datasets. The connecting density and temperature profiles should not be assumed to be entirely accurate as the boundary conditions create a volatile profile. If the TGO profile were truncated below 120 km, a different temperature profile would be observed. Similarly, if the MAVEN profile were cut-off below ∼160 km, the resultant temperature profile would be significantly different from what has been derived.

Given time constraints, the following proposed exercise has not been undertaken, but would nonetheless be intriguing. As mentioned, the Martian community is fortunate to have upwards of ten spacecraft gather atmospheric data at the Red Planet. The conﬂation of density datasets may reveal some interesting trends which have been missed due to lack of sampling. By luck, MGS may have studied similar regions to MAVEN, allowing seasonal and even yearly trends to be explored using proﬁles extending upwards of 100 km.

182 7.7. SUMMARY

Figure 7.6.2: (a) Connecting TGO and MAVEN density datasets. TGO and MAVEN densities are shown by red markers and blue lines, respectively. The connecting density profile derived from the connecting temperature profile in (b) is shown by the black dashed line. (b) Derived TGO and NGIMS temperature profiles. Connecting temperature profile (black dashed line) is fit according to boundary conditions specified in the text. It takes the form of a fourth-order polynomial. (c) Latitude and local solar time of used TGO (red) and MAVEN (blue) data.

7.7 Summary

This chapter has focused on concurrent density measurements from MAVEN and TGO. Much of this chapter is an expansion of results previously presented in this thesis. The key ﬁndings are outlined below.

• Concurrent TGO and MAVEN data have been utilised to understand the main drivers of density structures within the thermosphere. It is apparent that at TGO altitudes (<120 km) the atmosphere is predominantly driven by dynamics, demonstrated by invariant densities in solar zenith angle. Above this region, the atmosphere is primarily solar-driven as implied by an apparent

183 7.7. SUMMARY

decrease in density with increasing solar zenith angle in MAVEN data (at 150 km and 190 km).

• TGO and MCD densities have been compared in altitude, local solar time and latitude. The MCD is unable to capture the local solar time dependence in density, as demonstrated by larger than expected TGO densities in the dusk sector. By comparing densities in altitude and computing temperatures, it is evident that the MCD predicts warmer temperatures than observed by 10-20 K.

• Waves have been extracted from TGO densities proﬁles following the same procedure outlined in Chapter 5. Typical amplitudes and wavelengths are ∼5-10% and 5-15 km. Using results from Chapter 5, TGO and MAVEN spectra have been compared by scaling wavelengths by respective scale heights. Waves with wavelengths smaller than their scale heights are saturated within the thermosphere as indicated by similar TGO and MAVEN amplitudes. For longer waves, MAVEN amplitudes increase by a factor of two, thus demonstrated wave growth as expected. Damping is evident as growth is not as rapid as expected.

• Lastly, it has been shown that TGO and MAVEN profiles can be hydrostatically connected. Com- plete density and temperature profiles are now available from ∼100 km up to over 200 km. These can be utilised for use within diffusion models. Additionally, this technique has the potential to connect future TGO and MAVEN datasets.

184 Chapter 8

Conclusions and Future Work

8.1 Summary and Conclusions

In this study, Mars’ upper atmosphere has been studied in depth using in-situ density data from NGIMS on board MAVEN and accelerometer data from TGO. Mars’ atmosphere is appreciably dynamic, both temporally and spatially.

Chapter 1 introduced the relevant background knowledge required for this thesis. The history of Martian observation and exploration has been detailed. The planetary and orbital properties of Earth and Mars have been compared, and the consequences of any dissimilarities have been outlined. The underlying physical principles that determine the observed density and temperature structures have been explained regarding spacecraft data. One particular Martian GCM, the LMD-MCD, has been used throughout this study. The capabilities of the model, and thus reasons for its selection, are highlighted. A summary of Martian GCM development has also been presented for completeness. Observations of gravity waves in the Martian thermosphere were discussed in anticipation of later work, with their generation in the lower atmosphere and evolution up to the thermosphere being described. Lastly, our current understanding of dust storms, from their origin and formation to their trajectory and decay, has been described.

Chapter 2 introduced the MAVEN and TGO missions and datasets used in this thesis. The operating principle, collection, and reduction of data from the Neutral Gas and Ion Mass Spectrometer on board MAVEN have been discussed in detail. NGIMS is capable of measuring individual species’ densities, allowing the composition of Mars’ upper atmosphere to be studied in detail. The three primary species

185 8.1. SUMMARY AND CONCLUSIONS

used in this study are CO2, Ar and N2. CO2 is used for its dominance and Ar for its inertness, thus allows the dynamics of the atmosphere to be studied without considering chemistry. Both MAVEN and TGO have on board accelerometers from which densities can be retrieved from raw measurements. The operation of accelerometers and subsequent density retrieval has been discussed in the context of MAVEN. MAVEN accelerometers densities have been compared directly to NGIMS data, with densities typically diﬀering by ∼20% near periapsis. During TGO’s aerobraking phase MAVEN continued to gather data. Fortunately, during the early months of 2018, TGO and MAVEN sampled similar regions concurrently. The potential science achievable with these overlapping events is discussed and undertaken in Chapter 7.

Chapter 3 introduced the data analysis techniques needed throughout this study. In particular, the derivation of temperature profiles by integrating density data downwards has been discussed. Both the advantages and disadvantages of the presented technique were addressed. The Mars Climate Database was used to test this technique by extracting along-track densities, deriving temperature profiles and comparing them with obtained along-track temperature profiles. The most substantial variations between derived and extracted temperature profiles occurred near the terminator. This is posited due to the derivation technique relying on vertical density variations, however spacecraft travel quasi-horizontally near periapsis, thus sampling horizontal rather than vertical variations. This manifests as a divergence between temperature profiles, with derived temperatures ∼20 K warmer than extracted temperatures. A key aim of this chapter was to assess whether there is a systematic difference between NGIMS and

MCD densities. The local time dependence is not captured successfully, with NGIMS CO2 densities larger at the subsolar point up to a factor of ﬁve. This discrepancy reduces towards the terminator.

Beyond a solar zenith angle of ∼90° , MCD CO2 densities surpass NGIMS up to a factor of ten at the antisolar point. Similar behaviour is seen for Ar and N2 species however MCD densities begin to exceed NGIMS densities at zenith angles of ∼30°. In light of these findings, further open questions that need to be addressed are the following. What is explicitly causing this discrepancy? Can refined gravity schemes account for inconsistencies? What further information is required to constrain model densities further? An offset between timings of the closest approach and maximum density are highlighted in the TGO density dataset. It has been suggested that strong latitudinal density gradients are responsible.

Chapter 4 explored density and temperature variations over three timescales: diurnally, monthly and seasonally. The ﬁrst question to answer was what are typical dayside and nightside temperatures at the Red Planet and how do they compare with modelling eﬀorts? Diurnal temperatures variation has

186 8.1. SUMMARY AND CONCLUSIONS been shown in solar zenith angle using background profiles. Dayside temperatures are typically ∼250 K, reducing to ∼150 K towards the nightside. Significant variations are seen across the terminator owing to the atmosphere no longer being directly heated by solar radiation. The MCD most successfully reproduces observed temperatures below ∼150 km on the dayside. Above this, the MCD is too cool by at least 20 K. The MCD is consistently warmer on the nightside by ∼20 K than observed in the data. The inclusion of refined gravity wave thermal effects should account for some of this. The The effect of the 28-day solar rotation on the thermosphere has been identified in density data, further highlighting the strong influence of the Sun on the atmosphere. However, this effect is not continually observed in the data. Other, more influential factors may cause solar rotation effects to be diminished. Seasonal variations in density and temperature were investigated by identifying periods where MAVEN sampled regions multiple times. This would, for the first time, allow the effect of season to be quantified. Each region spanned ∼2° latitude and ∼0.5 hr local time. The criteria led to 27 periods being identified, each of which contained ∼30 orbits. Wave activity was removed by using background profiles. For a fixed altitude, density is enhanced by nearly a factor of 100 during the summer months as the atmosphere expands due to intensified heating in the lower atmosphere, especially during the dust storm season. Likewise, this was performed using temperature profiles. A trend as above was not visible. Throughout a Martian year, temperature appears to vary by no more than 100 K. Still, a more representative upper limit is ∼60 K. The Mars Global Ionosphere-Thermosphere model accurately reproduces these results. In view of work carried in this chapter, there are two main questions going forward. The first is a revision of seasonal temperature trends. Can models reproduce this unexpected result, or is there an issue with the method used? The second is born from the discussion of polar warming. Enhanced circulation by dust near perihelion has been used to explain warming around 120 km, can the same mechanism explain observed southern warming? If so, how far does this effect extend upwards? If not, what could cause such warming

Chapter 5 investigated wave activity within the upper atmosphere using Ar NGIMS data. Perturb- ations were extracted from density and temperature proﬁles and interpreted as vertically propagating gravity waves. Amplitudes are typically 10-20%, and wavelengths vary from 10-30 km. These values are compared to and agree with results derived from other Martian datasets. Waves amplitudes are correlated with temperature with the largest amplitudes arising in the coolest regions. Amplitude continues to grow with altitude on the nightside, yet appear saturated by ∼120 km on the dayside. The deposition of wave momentum and energy have been discussed, and typical values compared to previous results.

187 8.1. SUMMARY AND CONCLUSIONS

Any evidence of the origin of presented gravity waves appear erased by the time they reach the studied altitudes, given there is no correlation between activity and topography. Results have been introduced which indicate that waves rarely appear persistent across consecutive orbits suggesting they can survive several hours. One consequence of such persistence is the potential for CO2 cloud formation due to lasting cold pockets of air. Other factors, such as nucleation rates and density, need to be considered for further analysis. The posed open questions have been successfully answered, as expected. One additional question which is discussed in Further Work, is can complete gravity wave structures (i.e. vertical and horizontal wavelengths) be computed from purely inbound and outbound trajectory data?

Chapter 6 examined the response of the upper atmosphere to the 2018 global dust storm. Dust storm onset is visible around Ls=187°consistent with previous studies. This is slightly later than first detected by rovers (Ls≈185°) most likely caused by sampling bias either spatially and/or altitudinally. For a fixed altitude, densities increased by ∼10-80%, with the most substantial increases associated with more massive species (i.e. CO2). Combined with Elrod et al., 2019, it can be inferred that species lighter than ∼22 amu will have density decrease during a global dust storm event for a given altitude. Upper atmosphere heating is minimal (O(1) K), whereas the lower atmosphere is expected to be warm by 25-50 K. For the first time, gravity waves have been analysed during a dust storm. Average amplitudes are up to 50% larger during storm periods than during immediately preceding intervals. Storm-waves were compared to waves in a comparable region to account for changes in sampled regions and were found to be significantly larger. One potential explanation is localised dust heating, causing more significant perturbations than typically observed. Another factor may be enhanced winds, which induce larger topographically-induced gravity waves. The relationship between heating and gravity waves has been seen on Earth. Following the technique employed in previous studies, the decay of the June 2018 dust storm has been explored, and it appears that each dust storm exhibits similar abatement behaviour; the severity of the dust storm is anti-correlated with the time needed to recover. However, each storm has a unique recovery relationship with severity. Decay timescales are similar to the 2001 and 2007 dust storm; normally around 60°Ls, equivalent to several months. Modelling efforts of dust storms have been discussed and compared to results in this thesis. The response of the upper atmosphere has been compared to the lower atmosphere with more severe heating is observed in the latter. Two new results in this chapter require new open questions to be posed. The first is the interesting finding that

N2 densities appear relatively stable during global dust storms. Why is this? Can a diﬀusion model explain this surprising ﬁnding? A GCM is most certainly required to complete this work. The second

188 8.2. FUTURE WORK question delves into dust storm gravity waves. What causes a signiﬁcant increase in wave amplitude? Are waves generated with larger amplitudes, or does the dust storm allow substantial growth? It is worth considering the use of a low-level wind/topography product to predict gravity wave activity

Chapter 7 exploited concurrent MAVEN and TGO data. Similar geographic locations were sampled with TGO sampling up to ∼120 km and MAVEN down to ∼140 km (120 km during DD campaigns). Initially, densities were interpolated to 125 km and further interpolated in solar zenith angle. Overall, there was good agreement between the two datasets, thus confirming they can be ’synthesised’ for future use. This allows profiles from TGO and MAVEN to be hydrostatically connecting to understand density and temperature structures in the ‘unsampled’ region, typically in the range of 120-140 km. By comparing background densities at 110 km (TGO), 150 km (MAVEN) and 190 km (MAVEN), it can be inferred that atmosphere structure at higher altitudes (above at least 150 km) is solar-driven, as indicated by evident day-night disparities in density. TGO densities imply that the lower portion of the thermosphere is more driven by dynamics. This new dataset enabled further comparisons with the MCD. Two main conclusions have been drawn from this. The first is a deficiency of the MCD to successfully capture the density trend in local solar time, as found for NGIMS. The second inference is the MCD predicting cooler temperatures than observed by TGO; this is implied by the different rates at which densities decrease by with increasing altitude and explicit calculations of scale heights. The work in Chapter 5 has been extended with the addition of extracted TGO waves. By comparing TGO and MAVEN wave amplitudes, it was found that shorter-wavelength waves (typically less than their scale height) are saturated within this region. In contrast, longer waves continue to grow by over a factor of two. For the first time, the same wave has possibly been observed across both datasets. As found with MCD-NGIMS comparisons, TGO-MCD comparisons highlight deficiencies with the MCD in reproducing observations. The most obvious question to ask is why. What physics is missing from the MCD to prevent replication of observations? One key factor is most likely the inclusion of accurate gravity wave schemes, which allow warming/cooling to be included. Will the addition of MY34 atmospheric and solar conditions in the MCD account for some of this difference?

8.2 Future Work

In the following, potential future work in outlined and concludes with pertinent questions currently unanswered in this thesis.

189 8.2. FUTURE WORK

Extension of MAVEN Mission

The MAVEN mission has been granted an extension beyond its initial mission and will act as a communication relay for current and future landers and rovers, including Mars 2020 (Beswick et al., 2020). As such, the new orbit is more circular with a higher periapsis (∼200 km) than during its previous missions (R Yelle 2019, personal communication). NGIMS is still capable of retrieving in-situ density data at this altitude; therefore, there is potential to extend results found in this thesis. As touched upon in Chapter 3, MAVEN sampled the Red Planet primarily during solar minimum and moderate conditions. If MAVEN continues to sample the atmosphere beyond 2025, the possibility of sampling more frequent and extreme coronal mass ejections will likely increase, thus furthering our understanding of their impact on atmospheric loss. By an extended mission, the interannual variability in density and temperature can be considered. It would be beneficial to seasonal variations as well as the variations during the solar cycle. Additional observational will, needless to say, allow validation of all models described in this study. Moreover, further wave profiles will inform our understanding of wave behaviour in currently missing locations, such as at the smallest and largest solar zenith angles during aphelion. The latter location is expected to produce the largest observed gravity waves. With an increased mission length, the probability of another global dust storm event rises, more so for a regional dust storm. The same analyses would be performed in Chapter 6. This additional potential study could confirm several spec- ulations posited. The first is the behaviour of different species; does O still decrease during a global dust storm? Does the atmosphere expand at the same rate? It is hoped that similar decay behaviour is observed, thus allowing predictions of storm decay times to be made.

Gravity Wave Validation

This thesis has presented gravity wave characteristics determined within the upper thermosphere. Given the reliance of observations required to validate the gravity wave scheme, it would be informative to perform a short literature review comparing observational and model wave characteristics. Do known amplitudes compare favourably with model values in the upper thermosphere? Are wavelengths suﬃ- ciently long/short in schemes to match observations? Reﬁning wave inputs will improve model outputs.

Dust Storms

Dust storms have been investigated with emphasis on the response of individual species and gravity waves to such grand events. The former has been explored in previous studies; however, an in-depth analysis of

190 8.2. FUTURE WORK diffusion during a dust storm has not been performed. Diffusion coefficients can be determined by comparing observed and model density profiles for measured species. This will further our understanding of atmospheric responses to dust storms. Also, gravity wave schemes can be tested under dust storm conditions. Do they accurately predict wave activity? If not, which parameters need to tuning to rectify this?

The rarity of global dust storm events made studying the 2018 event a new priority for this thesis. While comparisons have been drawn between global dust storms both in the upper and lower atmosphere results are derived using independent methods outlined in various studies. A more rigorous overview would benefit from implementing the same technique on each dataset to study each storm. Further, as asserted by Cantor, 2007, over 5000 local dust storms were identified in MOC global maps. A worthwhile, yet potentially interminable task, is mining through lower and upper atmosphere data and, where possible, performing the same analyses on each dataset. Decay rates would be studied such that the effects of severity, location, and altitude can be explored. Cantor et al., 2019 identified 93 regional storms within the Mars 2020 landing site within the last ∼6 years. It is probable that, if possible to study these storms, they would reveal interesting traits. This could inform dust storm models. Are the decay rates and postulations presented in Chapter 6 repeatable? Can we get an early indicator of the duration of the global dust storm? And do global and regional dust storms only differ in size and length? Can results from both be combined into one dataset?

Mars Climate Database Version 6.0

A new version (v6.0) of the Mars Climate Database was due for release in October 2019 Millour et al., 2019a. The ﬁrst beneﬁt of this updated model is the best estimate of conditions during MY34, which is currently unavailable. This is the best representation of daily atmospheric dust loading and daily solar EUV input. This scenario spans May 2017-March 2019, which includes ∼80% of TGO’s aerobraking period. The implementation of this scenario should improve the comparisons. Additionally, the dust cycle has been updated. Purely vertically propagating gravity waves initiated in the MCD were utilised in Chapter 5 with the examination of spacecraft trajectory on measured characteristics. v6.0 will include horizontally propagating gravity waves. And with the addition of this feature, this study can be expanded. Can horizontal and vertical wave components be determined with knowledge of apparent wavelengths and spacecraft trajectory? From this, can the propagation of each wave be calculated and potentially reproduced with a gravity wave scheme?

191 8.2. FUTURE WORK

Utilisation of Previous and Upcoming Missions

Throughout this study, where possible, direct comparisons have been made with previous results, e.g. similarities between MAVEN and MGS gravity waves. A proposed extension of this study is to conflate dataset, as suggested in Chapter 7, to understand trends further whether this be temperature, density or gravity wave behaviour. Previous studies have combined the results of MGS, ODY and MRO (e.g. Keating et al., 2003; Bougher et al., 2006; Withers, 2006). These can be further extended with MAVEN data expanding the sampled region in all parameters - latitude, LST, altitude and season amongst others - such that initially entangled trends can be decoupled. Further, future aerobraking missions will only extensively add to the datasets already available. Both similar and new analyses can be performed to fill in gaps in our understanding, such as simply investigating regions currently unsampled. One such mission is Mars Orbiter Mission 2 (launch date unknown; Haider et al., 2018). Can a global overview of density and temperature structure be assembled using data from all thermosphere spacecraft? How does this picture compare to model outputs? Can occultation data from TGO be combined with in-situ MAVEN data to create further hydrostatically connected temperature and density profiles?

As the above shows, there are still myriad topics for the next generation to undertake. Now, more than ever is a fascinating time to be studying the Red Planet. Techniques presented in this thesis do not apply only to Mars, but all studied planetary atmospheres.

192 Appendices

193 Appendix A

Visualisation of Regions Sampled Multiple Times by MAVEN

Figure A.0.1 shows the regions in latitude and local time which have been sampled twice (or more) by MAVEN as listed in Tables 4.6.1-4.6.3 in Chapter 4. Boxes show the minimum and maximum local time and latitude values. Each box contains two colours which relate to the two Ls values Mars was at whilst MAVEN sampled the region.

Figure A.0.1: Graphical representation of coverage overlap detailed in Tables 4.6.1,4.6.2 and 4.6.3. Boxes show the latitude and local time coverage of each overlap scenario. The two colours in each show the two seasons the overlap periods occurred in.

194 Appendix B

Deriving Lower Atmosphere Heating Caused by a Dust Storm

This section outlines the derivation for an estimation of dust storm warming in the lower atmosphere as shown in Chapter 7 and Chaufray et al., 2019. Assume two density distributions - one prior to the dust storm denoted by subscript 1 and one post-onset denoted by subscript 2. These are given by:

∆z ∆z n1 ∝ exp − n2 ∝ exp − hHi1 hHi2

where n1 is the density above the heated region ∆ z prior to the storm, hHi1 is the average scale height prior to the onset within the heated region. Likewise, n2 is the density above the heated region post-onset, hHi2 is the average scale height after the storm onset.

Then,

exp ∆z n2 hHi1 = n1 exp ∆z hHi2

which can be simpliﬁed to,

n ∆z ∆z 2 = exp − n1 hHi1 hHi2

195 Taking the natural logarithm of both sides leads to,

n ∆z ∆z ln 2 = − n1 hHi1 hHi2

hHi1 Multiplying each term by ∆z results in,

hHi n hHi 1 ln 2 = 1 − 1 ∆z n1 hHi2

Rearranging the above equation leads to,

hHi n hHi 1 − 1 ln 2 = 1 ∆z n1 hHi2

And ﬁnally, reciprocating the above equation results in,

hHi 1 2 = hHi hHi1 1 − 1 ln n2 ∆Z n1

196 Appendix C

Software Used

I am indebted to the below communities who have developed wondrous Python packages that have made this PhD possible.

• Python - programming language (https://www.python.org/)

• Matplotlib - a Python library for plotting (https://matplotlib.org/)

• Pandas - a Python library for data science (https://pandas.pydata.org/)

• NumPy - a Python library for array manipulation (https://docs.scipy.org/doc/numpy/)

• SciPy - a Python library for scientiﬁc computing and technical computing (https://docs. scipy.org/doc/scipy/reference/)

• seaborn - a Python library for statistical data visualization (https://seaborn.pydata.org/ index.html)

197 Appendix D

Data Used

The various datasets used in this thesis can be found in the following locations:

• MAVEN Accelerometer Data Level 3 - https://pds-atmospheres.nmsu.edu/data_and_services/ atmospheres_data/MAVEN/maven_acc.html

• MAVEN Neutral Gas and Ion Mass Spectrometer Data Level 3 - https://pds-atmospheres. nmsu.edu/data_and_services/atmospheres_data/MAVEN/ngims.html

– With special thanks to Roger Yelle and Shane Stone from LPL, University of Arizona for providing initial data and helping with the interpretation of results.

• TGO Accelerometer Data - derived from raw accelerometers counts.

– With further thanks to Sean Bruinsma and Jean-Charles Marty from CNES, Toulouse for deriving density data and helping with the interpretation of results.

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