5 Dipartimento di Matematica e Fisica “E. De Giorgi”

Dottorato in Fisica e Nanoscienze

10 XXXII CYCLE

PHD THESIS (SSD: FIS/05)

SIMULATING MARS:

15 GENERAL CIRCULATION MODELS AND SURFACE REFLECTIVITY MAPS

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Supervisors: Prof. Giorgio DE NUNZIO Prof. Vincenzo OROFINO

25 Prof. Giovanni ALOISIO

PhD Student: Alessandro De Lorenzis 30

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To my parents

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3 CONTENTS

INTRODUCTION 7 CHAPTER 1 PRESENT MARS CLIMATE CONDITIONS: LANDERS/ROVERS 90 OBSERVATIONS 9 1.1 Exploring Mars 10 1.2 Landing site climate situations 12 1.3 Viking 1 and Viking 2 12 1.4 Mars Pathfinder 14 95 1.5 Spirit and Opportunity (MER rovers) 15 1.6 Phoenix 17 1.7 Curiosity 18 1.8 InSight 20

CHAPTER 2 REPRODUCING MARS CLIMATE: SOFTWARE SIMULATORS 100 AND GENERAL CIRCULATION MODELS (GCMs) 23 2.1 An excursus on the GCMs applied to simulate present Mars climate conditions 24 2.2 Simulation of the ancient Mars climate: a challenging task 27 2.3 General description of the two GCMs compared 28 105 2.4 GCM-LMD 30 2.5 MarsCAM-NCAR 31 2.6 The MCD database derived from GCM-LMD 32 2.7 MarsCAM-NCAR simulations on the CMCC Athena cluster 33

CHAPTER 3 LANDERS/ROVERS DATA AND GCMs OUTPUT MANIPULATION 34 110 3.1 Scenarios/Runs considered for the comparison 35 3.2 Set of the initial physical parameters used in the simulations 37 3.3 Initial computational settings used to perform simulations 38 3.4 Changing albedo, thermal inertia and dust OD: impact on surface and 115 near-surface temperatures 39 3.5 Data collection: observational and GCMs output data 41 3.5.1 Landers/rovers observations 41 3.5.2 Keeping time on Mars 44 3.5.3 GCMs output 45 120 3.6 Managing of observational data: preparing lander/rover measurements for the comparisons 45 3.7 Managing of MarsCAM-NCAR output: CMCC Ophidia tool 47 3.7.1 Working with Ophidia terminal 51 3.7.2 An example of an Ophidia WF to process GCMs output 53 125 3.8 Import of NetCDF files into Matlab 54

4 CHAPTER 4 TG AND TSA COMPARISONS: SEASONAL/ANNUAL TRENDS (GROUP 1) AND DIURNAL CYCLE (GROUP 2) 57 130 4.1 Comparisons: Group 1, seasonal and annual trends 58 4.2 Group 1 58 4.3 Comparisons criteria 64 4.4 Modified Borda-Count (MBC) method 66 135 4.5 An example of the MBC for Group 1a and Group 1b 68 4.6 Exceptions for Group 1 analysis 71 4.7 Comparisons: Group 2, daily trends 71 4.7.1 Group 2: features 72 4.7.2 Diurnal data processing 76 4.7.3 Statistical approaches applied for Group 2 77 140 4.7.4 Cross-checks performed for Group 2 77

CHAPTER 5 RESULTS OF THE COMPARISONS BETWEEN GCM-LMD AND MARSCAM-NCAR OUTPUT WITH TG/TSA OBSERVATIONAL DATA 79

145 5.1 Discussion of the results obtained 80 5.2 Group 1 results 80 5.2.1 Evidences for Group 1a 80 5.2.2 Evidences for Group 1b 83 5.3 Group 2 results 86 150 5.3.1 Evidences for Group 2a 86 5.3.2 Evidences for Group 2b 89 5.4 Discussion 92

CHAPTER 6 REPRODUCTION OF OTHER CLIMATIC VARIABLES WITH GCMs 95 155 6.1 MarsCAM-NCAR output: further analyses 96 6.2 Running MarsCAM-NCAR with different spatial resolutions 96 6.3 Comparisons with 1-D model output 101 6.4 Surface pressure 102 160 6.5 Air temperature profiles and sub-surface temperatures 107

CHAPTER 7 GLOBAL REFLECTIVITY MAPS OF MARS BY MEANS OF THE MARSIS SIMULATOR 112

165 7.1 Research stay at INAF (Bologna) 113 7.2 The discover of liquid water on Mars 113 7.3 The radar equation 122 7.4 The MARSIS radar: description and data features 124 7.5 Simulating radar echoes: the MARSIS simulator 126

5 170 7.6 Installation of the MARSIS simulator on the CMCC Athena cluster 129 7.7 Reflectivity maps 131 7.7.1 Physical parameters 131 7.7.2 Mars global reflectivity maps 133 7.8 Discussion of the results obtained 134 175 CONCLUSIONS 139 BIBLIOGRAPHY 145 Appendix A 158 Appendix B 161 Appendix C 167 180 Appendix D 176 Appendix E 183 Appendix F 185 Appendix G 191 Appendix H 204 185

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6 INTRODUCTION

205 During the last decades, Mars was visited by many spacecrafts in order to learn more about the composition of its surface and its atmosphere. The goals of each mission were multiple, covering different fields of research (astronomy, chemistry, physics, astrobiology, geology, space engineering, climatology), all to be considered simultaneously in order to reveal the secrets of the Red Planet. One of the main targets of all the principal national and international space agencies is 210 to plan, in the next future, a human exploration able to land on the planet: in order to achieve this ambitious result, it is fundamental to know as much as possible about the present climate of Mars. The chance to perform in situ experiments, already “robotically” performed by some of the landers/ rovers that visited Mars, could be also a turning point to verify the hypothesis according to which Mars in the past could have host conditions to support life. The indications are multiple: the 215 detection of methane in the atmosphere of the planet (Krasnopolsky et al., 2004; Formisano et al., 2004; Mumma et al., 2009; Webster et al., 2015; Giuranna et al., 2019; discussion about the biological provenience of this gas: Atreya et al., 2007; Yung et al., 2018); the numerous geological evidences of the activity of liquid water on the surface of the ancient Mars, in the form of rivers, lakes and maybe oceans (Howard et al., 2005; Irwin et al., 2005; Fasset and Head, 2008; Di Achille 220 and Hynek, 2010; Matsubara et al., 2013); the recent discovery of a lake of salty liquid water in the southern polar cap of Mars (Orosei et al., 2018).

My PhD research activity was mainly focused on the reproduction of present climate situations of Mars by means of numerical simulations, performed with 3-D General Circulation Models 225 (hereinafter, GCMs), in order to analyze the space/time distribution of atmospheric and surface variables. The main topics can be summarized as follows: • installation and configuration of the MarsCAM-NCAR GCM on the Athena cluster of the “Centro Euro-Mediterraneo sui Cambiamenti Climatici” (CMCC) and optimization of the big-data managing CMCC Ophidia tool used for the first time to manipulate output data 230 referred to Mars; • study of the present Mars climate conditions with the MarsCAM-NCAR software by comparing climatic variables with landers/rovers observations; • installation of the Martian Climate Database (MCD) derived from GCM-LMD (Laboratoire de Météorologie Dynamique), validation with spacecraft measurements and comparisons 235 with MarsCAM-NCAR output; • porting of the MARSIS simulator to the Athena cluster (CMCC). Simulation of the echoes expected for some orbits and comparison with the radargrams obtained from MARSIS radar, in search for the presence of subsurface liquid water; • production of simulated surface reflectivity maps and testing with similar maps based on 240 observational data in order to identify the variations of the dielectric constant on the Martian surface. All the demanding computational tasks I performed were achieved thanks to the scientific affiliation I signed with the Advanced Scientific Computing (ASC) Division of the CMCC Foundation, unit of Lecce, covering all the 3 years of my PhD: Prot. n. 1659/CMCC/2016 for 2016/2017; Prot n. 245 268/CMCC/2018 for 2018; Prot. n. 020/CMCC/2018 for 2019.

7 The PhD thesis is structured as follows. In Chapter 1 a global description of the climate conditions of the eight lander/rover landing sites considered in this work is presented, together with the most important features of the missions.

250 Chapter 2 is dedicated to a brief historical excursus on the GCMs introduced in the literature to perform simulations able to reproduce present and past climate conditions of Mars. The two GCMs compared, GCM-LMD and MarsCAM-NCAR, are also introduced. A discussion on the most important features of the two climatic models is presented, together with some technical operations performed to install the MCD database (created by the developers starting from GCM-LMD 255 simulations) and the MarsCAM-NCAR program on the CMCC Athena cluster. In Chapter 3 a deep discussion on the initial physical parameters used by the two GCMs is provided, as well as the explanation of the features of the simulations performed with them and used in the comparing analysis. Moreover, the list of the available observational data compared (surface and near-surface temperatures), collected by the eight probes and considered as reference 260 values for the comparisons, is reported. Also model output features are presented, together with a discussion on how time is marked for Mars. The preliminary managing of both observational and model output data is described, with the procedures necessary for realizing comparisons as homogeneous as possible. In this occasion, the tool applied to manipulate MarsCAM-NCAR output, CMCC Ophidia terminal, is presented. 265 Chapter 4 introduces the two sets of tests performed on model output: Group 1, related to seasonal and annual trends, and Group 2, related to diurnal trend evolution. The statistical approaches used for the comparisons (Modified Borda Count method, Root Mean Square Error (RMSE), Chebyshev distance, Mean Signed Deviation and maximum and minimum residual, with sign) are also shown.

270 In Chapter 5 a detailed list of the findings obtained is reported, both from a global (i.e. by processing together all the observational data available from all the probes) and from a local point of view (i.e. individual analyses for each spacecraft processed).

Chapter 6 is devoted to a brief discussion about other climatic variables evaluated in the thesis: 275 surface pressure, atmospheric air temperature (zonally averaged for the whole planet and 1-D vertical profile) and subsurface temperatures. Also comparisons between MarsCAM-NCAR Runs, performed with different spatial resolutions (4°x5° and 10°x15° lat/lon) are provided, as well as comparisons between 3-D GCM output and 1-D thermal model, checked with observations.

Chapter 7 describes the activities I performed during my research stay at INAF-IRA (Bologna) 280 under the supervision of Prof. Roberto Orosei (INAF-IRA). The MARSIS radar features are presented, as well as the echoes produced by it. Starting from them, the MARSIS simulator (Cantini et al., 2014) was used in order to test the reliability of the output produced by this code to reproduce the real echoes. The software simulator was installed on the CMCC Athena cluster by processing the echoes expected for more than 650 orbits. Reflectivity maps were then produced in each of the 3 285 directions of acquisition of the radar and for all 4 working-frequencies (1.8, 3, 4 and 5 MHz).

Finally, concluding remarks and an outlook on future studies are provided.

8 CHAPTER 1

290 PRESENT MARS CLIMATE CONDITIONS: LANDERS/ROVERS OBSERVATIONS

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9 310 1. 1. Exploring Mars

Modern Mars exploration started in the early 1960s with the Mariner 4 fly-by of the planet and the first images of the Martian surface in 1965 (Martínez et al., 2017). In the late ‘70, the first landers successfully operated on the Martian surface, Viking 1 and Viking 2. Then we have to wait till 1997 315 for the next successfully Mars-landing, with the Mars Pathfinder. In 2004 the Mars Exploration Rover mission explored the planet with two rovers, Spirit (MER-A) and Opportunity (MER-B), then was the turn of Phoenix in 2008 until reaching the two most recent mission still operating (October 2019) on Mars: Curiosity, sent on 2012, and InSight, arrived on 2018. Table 1.1 reports some information about these missions of in-situ exploration, such as the coordinates of the landing 320 sites (see the map of Figure 1.1), the duration of each mission, the start/end dates and the kind of atmospheric data collected during the explorations. Some of these data were used as reference values in this thesis to test the reliability of two software programs to reproduce present Mars climate conditions (see Section 3.1). In-situ measurements made by meteorological instruments onboard of the cited landers/rovers, together with other data coming from past (Mars 2, Mars 3, 325 Mariner 9, Mars 5, Viking 1, Viking 2, Phobos 2, Mars Global Surveyor) and present orbiters (six actually working as of October 2019: 2001 Mars Odyssey, Mars Express, Mars Reconnaissance Orbiter, Mars Orbiter Mission, Mars Atmosphere and Volatile EvolutioN and ExoMars Trace Gas Orbiter), considerably help to study the characteristics of the present and also the past Martian climate. 330

Figure 1.1: Map of Mars with the indication of the landing sites of the eight landers/rovers that successfully operated from the surface of the planet. The topographic map uses data from the Mars Orbiter Laser Altimeter (MOLA) on NASA's Mars Global Surveyor (MGS) spacecraft. The color coding indicates elevation relative to a reference datum: the lowest elevations are presented as dark blue, the highest as white. 335 The difference between green and orange in the color coding is about 4 km vertically. Courtesy NASA/JPL- Caltech.

10 Table 1.1: List of the landers/rovers that reached Mars. The information related to each mission start/end is taken from the dedicated NASA website (https://mars.nasa.gov/mars-exploration/missions/, last visited: December, 2019). The elevation reported is to be intended with respect to the Martian Datum. MY stands for Martian Year (see Section 1.3). The climatic variables reported in the last column are only a subset of all the data collected by each spacecraft: for more 340 information, also concerning the instrumentation onboard of the various probes, see Martínez et al. (2017). Legend: * = still operating, data updated until the end of December, 2019; ** = not a meteorology station; P = pressure; TSA = Air temperature; W = Wind; TG = ground temperature; RH = relative humidity; s = speed; d = direction;

LANDER/ROVER COORDINATE LANDING SITE ELEVATION (KM) START/END MISSION DURATION (SOLS) MY STRUMENTATION VARIABLES VIKING 1 22.7° N CHRYSE -3.6 July 20, 1976 2245 12-15 VMIS P, TSA, W (s, d) 312° E PLANITIA November 13, 1982 (Viking Meteorology Instrument System) VIKING 2 48.3° N UTOPIA -4.5 September 3, 1976 1281 12-13 VMIS P, TSA, W (s, d) 134° E PLANITIA April 11, 1980 (Viking Meteorology Instrument System) MPF 19.3° N ARES -3.7 July 4, 1997 84 23 ASI/MET P, TSA (x3), W (s, d) 327° E VALLIS September 27, 1997 (Atmosphere Structure Instrument) SPIRIT - -14.6° N GUSEV -1.6 January 4, 2004 2208 26-28 Mini-TES** P, TG, TSA MER A 175.5° E CRATER March 22, 2010 (Miniature Thermal Emission Spectrometer) OPPORTUNITY - -1.94° N MERIDIANI -1.5 January 25, 2004 5111 26-34 Mini-TES** P, TG, TSA MER B 355° E PLANUM February 13, 2019 (Miniature Thermal Emission Spectrometer) PHOENIX 68.2° N GREEN -4.1 May 25, 2008 151 29 MET P, TSA, W (s, d) 234.4° E VALLEY November 2, 2008 (Meteorological station) CURIOSITY -4.9° N GALE -4.4 August 6, 2012 2629* 31-35 REMS P, TG, TSA, W (s, d), RH 137.4° E CRATER ???? (Rover Environmental Monitoring Station) INSIGHT 4.5° N ELYSIUM -2.6 November 26, 2018 387* 34-35 HP3 P, TG, TSA, W (s, d) 135.6° E PLANITIA ??? (Heat Flow and Physical Properties Package) APSS - TWINS (Auxiliary Payload Sensor Suite)

345 Table 1.2: Reference values for albedo, thermal inertia and dust OD in the eight landing sites of the landers/rovers examined. The values of the last parameters are derived from Montabone et al. (2015) and processed as discussed in Section 3.2. For the values of these quantities used in the simulations performed with MCD and MarsCAM-NCAR, see Appendix A.

350 LANDER/ROVER ALBEDO THERMAL INERTIA DUST OD VALUES SOURCE VALUES (J m-2 K-1 s-1/2) SOURCE MIN MEAN MAX VIKING 1 0.26 Haberle et al. (1993) 215 Haberle et al. (1993) 0.07 0.17 0.35 VIKING 2 0.23 Haberle et al. (1993) 240 Haberle et al. (1993) 0.04 0.10 0.18 MPF 0.19-0.23 Putzig et al. (2005) 376-396 Putzig et al. (2005) 0.08 0.18 0.38 SPIRIT 0.20-0.25 Golombek et al. (2003) 290 Fergason et al. (2006a) 0.06 0.18 0.44 OPPORTUNITY 0.13 Haberle et al. (1993) 220 Haberle et al. (1993) 0.07 0.18 0.39 355 PHOENIX 0.21 Golombek et al. (2009) 250-283 Banfield et al. (2008) 0.03 0.09 0.16 CURIOSITY 0.20-0.25 Pelkey and Jakosky, (2002) 295-452 Martínez et al. (2014) 0.07 0.18 0.39 INSIGHT 0.24-0.25 Golombek et al. (2017) 219-237 Golombek et al. (2017) 0.07 0.18 0.42 11 During my PhD, I focused my attention on data coming from landers/rovers, as the principal goal was to test the output of the software simulators on near-surface meteorological parameters (essentially, surface temperature and near-surface temperature, i.e. a few meters), among the most important ones when Mars ancient climate conditions must be reproduced (see Section 2.2). 360 1.2. Landing site climate situations

In the following Sections, an overview of the climatic conditions that characterize the landing sites of the eight landers/rovers reported in Table 1.1 is presented. For a global description of the present 365 Mars climatic conditions, together with a complete analysis of the features of the instrumentation onboard the various probes (with the exception of InSight), see Martínez et al. (2017), by which most of the following discussion is inspired. Compared to this work, some information about the composition of the soil of the landing sites are added. In Table 1.2 the values of albedo, thermal inertia and dust optical depth (OD) deduced for these regions are reported, fundamental parameters 370 for present and past Mars climate simulations. In Figure 1.2 (a-f) a representation of the appearance of each lander/rover, together with the mission badge, are shown.

1.3 Viking 1 and Viking 2

375 Landed on Mars in 1976, the Viking landers (Figure 1.2a) were the first to successfully perform meteorological observations from the surface of the Red Planet (Chamberlain et al., 1976; Hess et al., 1977; Tillman et al., 1994), with the aim to collect data to be compared with Earth’s observations for a better understanding of our atmosphere, thanks also to the information coming from the two orbiters included in the mission. Both landers had onboard a meteorological station, 380 the Viking Meteorology Instrument System (VMIS), able to measure atmospheric temperature, wind velocity and direction at 1.61 m above the ground, and pressure at 0.22 m above ground.

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395 Figure 1.2a: Viking lander model (left) and mission badge (right). Images credits: Vikings webpage (2019).

12 400 Among the most discussed results coming from the Vikings mission, already in the history for being the first U.S. mission to land a spacecraft safely on Mars (Vikings webpage, 2019), there were the three biological experiments carried out by the Biology Instruments onboard the two twin landers: the Gas-Exchange (GeX), Pyrolytic Release (PR) and Labeled Release (LR) experiments. The unexpected and enigmatic chemical activity registered by them in the Martian soil was subject of 405 numerous discussions related to the hypothesis, supported by some authors (Levin and Straat, 1977, 1979a, 1979b, 1981, 2016), that these experiments were the proofs of the presence of microbiological activity in martian regoliths. However, as evidenced by Schuerger and Benton (2008), the Viking biology experiments, despite being a robust set of logical explanations, failed to convince the wider scientific community that life existed at the sampled sites. According to these 410 authors, it is not known whether the climatic conditions observed on these locations will inhibit the activity of a putative Mars microbiota. Thus, martian ecological considerations must be included in the design of future life-detection payloads, suggesting that all life-detection experiments should be accompanied by robust soil chemistry experiments in order to gain a concurrent understanding of geochemical conditions of the soil investigated (Schuerger and Benton, 2008). 415 Viking lander 1 (VL1) landed at 22.7° N, 312° E in Chryse Planitia and worked for 2245 sols (Martian Year, MY, 12-15 – the numbering of Martian years follows the calendar proposed by Clancy et al., 2000, starting on April 11, 1955, at solar longitude LS = 0°), while Viking lander 2 (VL2) arrived at 48.3° N, 134° E in Utopia Planitia and worked for 1281 sols (MY 12-13). Haberle 420 et al. (1993) and Golombek et al. (2003) studied accurately the composition of the two landing sites and were able to deduce the values of albedo and thermal inertia reported in Table 1.2. Chryse Planitia is an extensive basin, at a maximum depth of 3.6 km below the Martian Datum, and it is one of the lowest region of Mars, suggesting that it may be an ancient impact basin (Schulz et al., 1982; Craddock et al., 1997; Pan et al., 2019). Utopia instead is a large shallow depression, 425 approximately 3300 km in diameter, where the presence of mesas, partially buried craters and ring features are thought to represent the buried and modified fragments of a basin rings (McGill, 1989; Kerrigan et al., 2012; Pan et al., 2019).

The climatic situation in these locations, during the years when the landers operated, was not so 430 quiet. In fact, a global storm was observed from the surface by both landers in MY 12: the peak atmospheric opacity reached OD greater that 3 (Colburn et al., 1988; Tillman et al., 1993) and occurred shortly after LS = 300°, during northern winter. As evidenced by Martínez et al. (2017), the atmospheric pressure registered increased during this event (up to tens of Pa), while typically, from MY 12 to MY 15, the interannual variability in these sites was generally small (few Pa) near 435 the aphelion. The interannual variability of the near-surface temperatures registered at VL1 and VL2 landing sites, as evidenced by Martínez et al. (2017), was small during the aphelion season (few Kelvin) while during the perihelion season it consistently increased. This is more evident for VL2 between LS = 260° and LS = 300° in MY 12, where the daily mean air temperatures were consistently higher if compared with MY 13 observations, due to the global dust storm occurred in 440 that year. The abnormal diurnal amplitude of near-surface air temperature, from about 42K to about 12K registered at VL1 site around LS = 275° was caused by a rapid increase in atmospheric opacity during the global dust storm occurred in MY 12 even if the contemporaneous decrease at VL2 was evident but less pronounced that at the VL1 (Martínez et al., 2017).

13 No direct ground temperature observations were made by the two landers. However, thanks to the 445 infrared thermal mappers (IRTM) onboard of the Viking Orbiters, Kieffer (1976) estimated the diurnal temperature variation at depth in the soil and modeled the annual behavior of the ground temperatures at the two landing sites. According to these estimations, VL1 site presented small annual variations in temperature, whereas VL2 site had a large annual range. The author used for his calculation a 1-D thermal model, which accounts for daily and seasonal changes of insolation and a 450 weak interaction with the atmosphere (Neugebauer et al., 1971; Kieffer et al., 1973).

1.4 Mars Pathfinder

It has been necessary to wait more than 20 years to have another mission able to collect 455 meteorological data from the surface of Mars. In 1997, Mars Pathfinder (MPF, Figure 1.2b) successfully landed at 19.3° N and 327° E at Ares Vallis, in Chryse Planitia (close to VL1), and operated for only 84 sols during MY 23. The limited duration of this mission (although it lasted more than the 30 sols predicted) was part of a specific plan studied at NASA: in fact, MPF was designed to be a demonstration of the technology necessary to deliver a lander and a robot able to 460 walk on Mars in a low-cost and efficient manner (MPF webpage, 2019). During the mission, in fact, apart from the lander, also the first rover ever sent on Mars, Sojourner, was able to successfully operate on the surface and collect data: 550 images were sent from the rover which helped to increase the explored part of the planet. The scientific goal of MPF was to study the variability of the Martian atmosphere during the midsummer season on diurnal and seasonal scales and compare 465 the data with that of the neighbor VL1 obtained at the same time of the year (Martínez et al., 2017). The meteorological sensors employed by the Atmosphere Structure Instrument/Meteorology package (ASI/MET) were similar to those used by VLs (Seiff et al., 1997; Schofield et al., 1997) and measured atmospheric pressure, atmospheric temperature at three different heights (0.25, 0.5 and 1 m above the lander deck, which was at 0.27 m above the ground) and wind. 470

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Figure 1.2b: 8-image mosaic of Sojourner rover (left), acquired during the late afternoon on Sol 2, the second Martian day on the planet. Mission badge (right). Images credits: MPF webpage (2019).

485 Ares Vallis is one of the greatest outflow channels of Mars, about 1500 km long. Edgett and Christensen (1997) derived, from Viking IRTM observations, information about the surface materials within this region. With respect to the rest of the planet, the site has an intermediate

14 albedo, intermediate-to-high bulk thermal inertia (these quantities were refined by Putzig et al., 2005, when more detailed data were available) and high rock abundance (18-25%). Pacifici et al. 490 (2009) described accurately the geological history of this land, and concluded that it is characterized by catastrophic flood landscapes partially superimposed by ice-related morphologies. Thermal inertia values appear to be compatible with gravel and sand deposits, while the olivine-rich composition detected in a part of the floor of the region could be due to stream sorting processes (Pacifici et al., 2009). 495 As observed by Schofield et al. (1997), the atmospheric structure and the weather record were similar to those observed by the VL1 at the same latitude, altitude and season, but there were differences related to diurnal effects and the surface properties of the landing site. These included atmospheric temperatures 10-12K warmer than VL1 near the surface. As regards pressure data, the 500 same authors evidenced that daily pressure cycles were characterized by a strong semidiurnal oscillation, with two minima and two maxima per sol. The diurnal cycle of temperature, also discussed by Schofield et al. (1997), evidenced, for sol 25 (one of the few for which it was possible to sample data particularly well, due to many problems with sensors, see Martínez et al., 2017 for details), a typical maximum temperature of 263K at 14:15 LTST (local true solar time) and a typical 505 minimum of 197K at 05:15 LTST, shortly before sunrise.

1.5 Spirit and Opportunity (MER rovers)

The Mars Exploration Rovers mission (MER, Figure 1.2c) delivered on Mars in 2004 two “twins” 510 rovers, both exceeding their planned 90-day mission lifetimes by many years (MER webpage, 2019). Spirit (SPI, MER-A) landed at -14.6° N, 175.5° E in Gusev Crater, and operated for 2208 sols (20 times longer than its original design, MY 26-28). Opportunity (OPP, MER-B) landed at - 1.94° N, 355° E in Meridiani Planum and worked for nearly 15 years (5111 sols, MY 26-34), till June 2018, when the rover last communicated with Earth, as a planet-wide dust storm covered the 515 planet. In 2015, OPP broke the record for extraterrestrial travel by driving for a total of 45.16 km.

Unlike the other landers/rovers, SPI and OPP did not have a meteorological station but a Miniature Thermal Emission Spectrometer (Mini-TES – see Martínez et al., 2017 for more details) able to collect thermal infrared spectra of the Martian atmosphere. The spectrometer was used to determine 520 surface temperatures, near-surface air temperature at about 1.1 m above the surface, atmospheric temperatures at high altitudes (from 30 to 2000 m), dust OD and water vapour abundance (Smith et al., 2004, 2006; Spanovich et al., 2006). Another goal of the mission was the study of high vertical resolution temperature profiles in the boundary layer, to measure dust and ice aerosol OD and to determine aerosol properties from imaging (Squyres et al., 2003).

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Figure 1.2c: Mosaic view of the rover OPP obtained combining various images taken by its panoramic 540 camera (PanCam, left). The downward-looking view omits the mast on which the camera is mounted. It shows Opportunity's solar panels to be relatively dust-free. The images were taken through the camera's 600-, 530- and 480-nm filters during OPP's 322nd and 323rd sols. Mission badge (right). Images credits: MER webpage (2019).

545 Gusev crater, Spirit landing site, is a 160 km diameter, flat floored crater of Noachian age (> 3.7 Gys ago), close to the highland-lowland boundary south of Elysium. Finest-grained material was observed in shallow-filled depressions in Gusev crater (Fergason et al., 2006b): these features, named hollows, were interpreted as having been formed by impacts and filled with aeolian material (Grant et al., 2004; Golombek et al., 2006). From PamCam imagery, it was possible to distinguish 550 surfaces made of a combination of fines, pebbles, cm-sized rock fragments and rocks (Fergason et al., 2006b; Herkenhoff et al., 2004a; Squyres et al., 2004a; Bell et al., 2004a). The surface at Meridiani Planum, Opportunity landing site, instead, as reported by Fergason et al. (2006b), is dominated by low ripples and covered by hematite spherules (Herkenhoff et al., 2004b), and a set of aeolian bedforms interpreted as wind ripples (Squyres et al., 2004b; Bell et al., 2004b; Sullivan et 555 al., 2005). The spherules are relatively free of adhering dust, unlike the surface material at Gusev landing site region, implying a different aeolian environment at these two localities (Fergason et al., 2006b): this is the reason for the different values of albedo and thermal inertia obtained for the two sites (see Table 1.2, Golombek et al., 2003 and Fergason et al., 2006b for more details).

560 Near-surface and ground temperature at MERs landing sites, as mentioned before, were not directly measured. By modeling downward-looking spectra of the Martian surface from Mini-TES, it is possible to retrieve surface and near-surface atmospheric temperatures (Spanovich et al., 2006; Smith et al., 2006). The near-surface atmospheric temperatures were consistently 20K cooler than the surface temperatures in the warmest part of each sol, around 13:00-14:00 LTST depending on 565 the location; moreover, seasonal cooling trends were seen in the data by displaying the temperatures as a function of the sol (Spanovich et al., 2006). Surface temperatures retrieved from Mini-TES spectra taken by OPP followed a well-defined diurnal curve with peak temperatures occurring at about 13:00 LTST, while the near-surface atmospheric temperatures peak was at about 14:30 LTST. OPP presented a maximum daily surface temperature of 295K and near-surface atmospheric

16 570 temperature of 265K at the beginning of the mission (Southern Hemisphere, SH, summer). Temperatures deduced by the SPI rover were similar to those at Meridiani, but there were differences caused by the difference in latitude, surface visible albedo and thermal inertia (Spanovich et al., 2006). The surface temperature at Gusev increased more slowly in the morning and early afternoon hours than it did at Meridiani, with peak temperatures occurring at 14:00 LTST. 575 SPI data presented a maximum surface temperature shortly after landing of 280K and a near-surface atmospheric temperature of 260K (Spanovich et al., 2006). As reported by Smith et al. (2006), between one and four observations were taken each sol during the nominal daytime hours of rover operation (9:00–18:00 LTST). Nighttime observations were rare because of the very large energy cost associated with heating the instrument required for nighttime operation (Smith et al., 2006): for 580 this reason, as clarified in Chapters 4-5, for data coming from these two rovers, only a partial discussion and conclusion could be obtained, related strictly to the maximum of surface and near- surface temperatures retrieved.

1.6 Phoenix 585 The goals of the Phoenix (PHO, Figure 1.2d) mission, landed on Mars in 2008 (MY 29), were to study the history of water in the Martian arctic, search for evidence of a habitable zone, investigate the ice-soil boundary in search of potential biological-favorable conditions (Phoenix webpage, 2019), in particular to characterize the past and present water ice cycle on Mars, including the 590 concentrations of salt species in the soil (Smith et al., 2009; Cull et al., 2010). PHO studied the Martian soil with a chemistry lab (Wet Chemistry Laboratory, WCL), a microscope, a conductivity probe and cameras.

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Figure 1.2d: Artist's depiction of the NASA's PHO Mars Lander, fully deployed on the surface of Mars while it monitors the atmosphere overhead and reaches out to the soil below (left). Mission badge (right). Credits: Phoenix webpage (2019). 610 Landed on the Red Planet at 68.2° N, 234.4° E in Green Valley (Vastitas Borealis), PHO operated for 151 sols, exceeding the mission target design life of 90 sols. This site was chosen among the others in order to permit to the Robotic Arm onboard of the lander of excavating trenches in soil

17 deposits and acquiring icy soil samples (Arvidson et al., 2009): Phoenix was in fact the first to 615 “touch and sample” the surface of the planet. For allowing such kind of activities, the site had to present a surface not so thick and covering icy soil, in a region with poligonal ground produced by processes associated with water ice-rich permafrost, with polygon centers, edges and troughs accessible for sampling (Smith et al., 2008; Smith et al., 2009). WCL performed aqueous chemical analyses of martian soil from the polygon-patterned that evidenced a strong signal that was 620 interpreted as resulting from perchlorate (Hecht et al., 2009). Because perchlorates are strongly deliquescent salts, their homogeneous distribution through the soil column was cited as evidence that the Phoenix soils have not interacted extensively with liquid water (Hecht et al., 2009; Cull et al., 2010).

625 The meteorology package (MET) onboard the lander included thermocouple temperature sensors mounted at three levels, 0.25, 0.5 and 1.0 m on a mast mounted on the deck of the lander, itself approximately 1 m above the Martian surface (Davy et al., 2010), sensors to measure air pressure and a “telltale” to measure wind at 2 m above the surface (Martínez et al., 2017). As part of the MET instrument, PHO also included a light detection and ranging (LIDAR) system to probe the 630 vertical structure of the atmospheric boundary layer using pulsed laser light in order to study the composition of the water-ice clouds, dust and aerosols (Whiteway et al., 2008; Whiteway et al., 2009; Daerden et al., 2010; Dickinson et al., 2010; Dickinson et al., 2011; Moores at al., 2011).

As evidenced by Davy et al. (2010), the air temperature data from the lowest level (0.25m) were not 635 reliable and so the authors concentrated their analyses on data measured at the upper level (2 m above the ground). Looking at temperature data from the mission as a whole, Davy et al. (2010) observed a slow increase in mean daily air temperature over the first 70 sols with a decline of about 20 K in daily mean temperature between sols 70 and 150. The temperature range (daily maximum- daily minimum) increased slightly in the period from sols 60-120 and might have played a role in 640 the increased dust devil opacity (Ellehoj et al., 2009). Moreover, Martínez et al. (2017) observed that the daily mean air temperatures were similar to those at the VL2 site between LS = 78° and 125°, and larger than those at the VL1 site. Finally, the diurnal amplitude of the air temperature was similar to that observed at MPF landing site during the aphelion season, when there was an overlap in date from the two missions (Martínez et al., 2017). 645 1.7 Curiosity

Part of NASA's Mars Science Laboratory (MSL) mission, Curiosity (CUR, Figure 1.2e) is the largest and most capable rover ever sent to Mars (Curiosity webpage, 2019). As the previous (and 650 the future) missions sent to Mars, the principal goal is to examine the surface and the surroundings by exploring rock samples that could present chemical and mineral evidences of past habitable conditions (Grotzinger et al., 2012, 2014, 2015), in order to verify if the Red Planet in the past could have host life. CUR landed at Gale Crater in 2012 at coordinates -4.9° N, 137.4° E and, at the time of the writing of this thesis, had worked for more than 2550 sols (MY 31 - MY 35), sending to 655 Earth the most extensive dataset of images from the surface of Mars.

18 660

665

670 Figure 1.2e: Selfie taken by NASA's Curiosity rover on Oct. 11, 2019, the 2553rd sol, of its mission (left): the rover drilled twice in this location, which is nicknamed "Glen Etive". Mission badge (top). Credits: Curiosity webpage (2019). 675

680 The meteorological aims of CUR are, together with the most important climatic parameters (air temperature, ground temperature, wind velocity, air humidity, atmospheric pressure), the study of water and CO2 cycles and the atmospheric processes at local and global scales. The instrument that collects the data is the Rover Environmental Monitoring Station (REMS), with sensors located at a height of 1.6 m on the rover mast with the exception of the pressure ones located at 1 m on the rover 685 deck (Gómez-Elvira et al., 2012, 2014). The Ground Temperature Sensor (GTS) provides measurements of ground temperature and is also used to investigate the thermophysical properties of the surface materials encountered by the rover during its walk on Mars (Vasavada et al., 2017). By comparing the temperature detected by REMS with predictions of a surface-atmosphere thermal model, Vasavada et al. (2017) were able to derive thermal inertia and albedo along the rover’s 690 traverse, taking into account also the radiative effects of atmospheric dust and seasonal water ice clouds/hazes. In this manner, it was possible to distinguish between surfaces dominated by active sand, other loose materials, mudstone, or sandstone based on their thermophysical properties. A lot of studies have been presented about the composition of Gale Crater surface: mudstone (Schieber et al., 2017), sand, (Bennet et al., 2018), fined-grained sedimentary rocks (Mangold et al., 2019), 695 presence of copper (Payré et al., 2019), calcium sulfate (Kah et al., 2018), opal (Rapin et al., 2018) and so on. Many of them are related with the investigations of ancient geological structures that in the past probably hosted liquid water on the surface (Mitrofanov et al., 2014; Mitrofanov et al., 2016; Savijärvi et al., 2016; Rapin et al., 2019) that, together with the detection of methane (Webster et al., 2015; Giuranna et al., 2019; Moores et al., 2019; Pla-Garcia et al., 2019) are the 700 principal detectors of the possible presence of microbiological life on Mars (Grotzinger et al., 2012, 2014, 2015).

19 As regards climate conditions, CUR observed a dust storm during MY 34 (Guzewich et al., 2019). Richardson and Newman (2018) evidenced how the daily variation of surface pressure measured by REMS is significantly larger than that observed at other landing sites on Mars and larger than that 705 simulated for the CUR site by various GCMs (further discussion about the motivations can be found in the paper just cited). Martínez et al. (2017) underlined how the interannual and seasonal variability of the diurnal amplitude of air temperatures is smaller than at the VL1 sites, due to the small seasonal variability in solar insolation in the tropics and to the absence of dust storm events in the sols considered (the first 1526, MY 31 – MY 33). Also Savijärvi et al. (2019) confirmed such 710 observations for these MYs, detecting similar annual cycles that displayed at the same time low values during the cool seasons and high values during the warm seasons. However, from about sol 1800 onward, air temperatures suddenly increased, about 5K above its previous values from the same season (Savijärvi et al., 2019). For ground temperatures, CUR (the only rover among MPF and PHO able to collect full diurnal measurements of these variable), Martínez et al. (2017) 715 observed that, for MY 31-33, the interannual variability of the daily mean ground temperature was small, on the order of few K, and this occurred in contrast with the different locations investigated by the rover during its walk on Mars. Small differences could be caused by changes in albedo, which ranged from 0.1 on sandy terrains to 0.3 on mudstone (Vasavada et al., 2017). Also the seasonal variability of the daily mean ground temperature was small, with annual amplitude of 720 about 20K (Martínez et al., 2017). Finally, as again evidenced by Martínez et al. (2017), the diurnal amplitude of ground temperature at Gale Crater is primarily governed by the type of terrain, in particular by its thermal inertia (I): low thermal inertia means higher daytime maximum temperatures and lower nighttime minimum temperatures with respect to terrains with high thermal inertia. As an example, the sudden decrease in the diurnal maximum ground temperature (and 725 increase in the diurnal minimum temperature) which occurred at LS ∼ 220° in MY 31 coincided with CUR traverse from a terrain with I ∼ 300 J m−2 K−1 s−1/2 to a terrain (Yellowknife Bay) with I ∼ 420 Jm−2 K−1 s−1/2 (Martínez et al., 2014). The differences in terrain traversed by the CUR likely account for the variability of the diurnal amplitude of ground temperature (Martínez et al., 2017).

730 1.8 InSight

On November 2018, NASA announced the successful landing on Mars of the Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight – INS, Figure 1.2f) lander, designed to be the first outer space robotic explorer to study in-depth the “inner space” of Mars: 735 crust, mantle and core (InSight webpage, 2019). The study of the interior structure of the Red Planet aims to learn more about the early formation of rocky planets in our Solar System as well as rocky exoplanets (Banerdt et al. 2018). InSight measures also tectonic activity and meteorite impacts on Mars.

740 Many complex simulations were carried out, based on the images obtained during previous orbital missions, to chose the final landing site of INS (Golombek et al., 2017): the selected area was individuated in Elysium Planitia, on volcanic Hesperian plains, at 4.5° N, 135.6° E. Up to December 2019, the lander has worked for more than 380 sols (MY 34-35). As reported by Golombek et al. (2017), constraints on latitude, elevation and topography more severely limited 745 possible landing areas than any previous landing site selection process: these constraints forced the

20 selection of western Elysium Planitia that, unfortunately, are 150–675 km north of Curiosity, causing communication relay and imaging conflicts and, eventually, data relay conflicts between Curiosity and InSight (for details about the decision process, see Golombek et al., 2017).

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Figure 1.2f: NASA InSight's second full selfie on Mars (left). This selfie is a mosaic made up of 14 images taken on March 15 and April 11 — the 106th and 133rd sols of the mission — by InSight's Instrument 765 Deployment Camera, located on its robotic arm. Mission badge (right). Credits: InSight webpage (2019).

The three primary instruments onboard the lander are (Spiga et al., 2018):

• SEIS (Seismic Experiment for Interior Structure) is a seismometer designed for studying 770 waves created by marsquakes, thumps of meteorite impacts and surface vibrations generated by activity in Mars’ atmosphere and by weather phenomena such as dust storms (for details, see Lognonné et al., 2019); • HP3 (Heat Flow and Physical Properties Package) is collecting Mars’ temperature (surface temperature and also sub-surface), revealing how much heat is still flowing out of the 775 interior of the planet (for details, see Spohn et al. 2018); • RISE (Rotation and Interior Structure Experiment) tracks the location of the lander to determine how much Mars’ North Pole oscillates as it orbits the Sun, in order to recover the size and composition of Mars’ core (for details, see Folkner et al. 2018).

780 The INS lander holds also a highly sensitivity pressure sensors (PS) and the Temperature and Winds for InSight (TWINS) sensors, both of which form, along with the InSight FluxGate (IFG) Magnetometer, the Auxiliary Sensor Payload Suite (APSS) (Spiga et al., 2018). From the latter, composed of two meteorological booms similar to the REMS meteorological package on the CUR rover (Spiga et al., 2018), atmospheric temperature and wind can be evaluated (Banfield et al., 785 2019a). Up to December 2019, only few results, deriving from the first observations collected by INS, were available. Here the most interesting ones are listed, announced by Banerdt et al. (2019) till October 2019 after six months of science operations:

• InSight seems to have landed in a "hollow", a filled, quasi-circular depression, probably a 790 highly-degraded impact crater;

21 • at least one probable marsquake and several additional likely events, all extremely small, have been detected by the seismometer SEIS; • HP3 instrumentation began to be operative from February of 2019, even if penetration activities started very soon after the landing, at a depth of >40 cm: at the moment, the 795 InSight team is employed on recovering much more data and planning a recovery campaign; • the atmospheric sensors have been operating nearly continuously at high acquisition rates since shortly after landing. Detailed observations of atmospheric phenomena at different time scales (from months to seconds) were carried out thanks to the first data collected; • the first magnetic measurements from the surface of Mars have revealed very interesting 800 results, for example a background field many times larger than that observed from orbit and dynamic field variations that have not been previously observable.

In order to validate and improve the atmospheric models actually available, some members of the INS team (Banfield et al., 2019b) have begun to compare the existing models with the in situ 805 observations from INS. The first results obtained are the following:

• Pressure: the pressure signal recorded by INS shows a regular daily variation, controlled by thermal tides which are well predicted by several Mars GCMs; significant seasonal variations are also evident in INS pressure record. 810 • Air Temperatures: the shape and amplitude of the diurnal cycle stored in INS data is well reproduced by atmospheric models, with little offsets likely reflecting differences between the model-specified and surface properties (e.g., albedo, thermal inertia); • Winds: two main large-scale seasonally-varying wind regimes were predicted for the INS landing site. In northern winter (when INS arrived on Mars) the return flow is generally 815 north to south, whereas in northern summer the return flow is the reverse, generally to the north (Newman et al., 2019).

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CHAPTER 2

840 REPRODUCING MARS CLIMATE: SOFTWARE SIMULATORS AND GENERAL CIRCULATION MODELS (GCMs)

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23 860 2.1 An excursus on the GCMs applied to simulate present Mars climate conditions

With the arrival of the data collected by the numerous space missions sent in the last decades to explore our Solar System, it was necessary to investigate more deeply the meaning hidden behind these enormous datasets. One of the best ways to fully understand the physics at the basis of the 865 data was that of creating numerical models able to satisfactorily reproduce the observations. By comparing model output with the observations, trusty simulation software tools able to reproduce the measurements and then study something that cannot be now observed, such as deep- paleoclimate conditions of some planets and exoplanets, could be achieved. A lot of attempts were necessary to reach such a goal, briefly listed below. 870 The first models proposed in the literature, as can be expected, were 1-D and able to reproduce only few climatic characteristics. For example, Kasting et al. (1993) used a 1-D climate model to estimate the width of the habitable zone (HZ) around our Sun and around other main sequence stars in search of Earth-like planets with CO2/H2O/N2 atmospheres, able to host liquid water on the planet 875 surface. By means of a radiative-convective model, they were able to simulate the inner and outer edge of the HZ in our Solar System. Unfortunately, due to the inability of the model to take into account all the physical parameters involved in the process, the authors were not able to fully consider in their estimations the role of the clouds, the latter having a fundamental function in the planetary habitability. In fact, in the reproduction of the atmosphere of the Earth-like planets, 880 planetary habitability strongly depends on atmospheric CO2 and its control by the carbonate-silicate cycle (Kasting et al., 1993), all influenced by the formation of clouds.

A finite-difference procedure was used by Ulrich et al. (2009) to predict regolith temperature profiles from the surface down into the Martian subsurface as a function of time, latitude, thermal 885 inertia, surface albedo, surface emissivity, distance of Mars from the Sun and atmospheric opacity. The authors compared model temperature predictions with data coming from MPF to validate the model and then apply it to reproduce annual surface and subsurface trends in the landing sites of VL1, VL2, MPF, SPI and OPP. The results obtained where used to discuss principally the hypothesis of supporting life condition in the Martian subsurface (Ulrich et al., 2009). Another 890 example of application of a 1-D model for studying Mars is that of Kieffer (1976), already discussed in Section1.3, for the determination of the surface temperature at Vikings landing sites.

James and North (1982) were among the first researchers that applied a 2-D climate model for studying the Martian climate. Starting from a 1-D model that, as already pointed out, was not able 895 to adequately interpret the observational data available at the time, they proposed a 2-D model with new features. By including an adequate energy balance and the effects of dust, they reasonably reproduced the CO2 cycle on Mars as observed by Viking landers (James and North, 1982).

Theoretical 3-D General Circulation models (with simplified forcing) represented the next step in 900 the simulation of the Martian climate: they were used to analyze the possible atmospheric circulation regime (Read, 2011; Kaspi and Showman, 2015). Finally, the latest steps are the full global climate models aiming at building “virtual planets” and simulating their climatic conditions, like those I compared in this thesis work. As evidenced by Way et al. (2017), GCMs are self-

24 consistently able to simulate all the processes that 1D models cannot, although they present their 905 own limitations: uncertainties in parameterizations of small-scale processes, the computational cost required by radiative transfer and chemistry to be represented in less detail than in 1D models.

One characteristic that joins all the Mars GCMs available nowadays (and also the previous simulation programs developed during the last years) is that all of them were adapted to the Red 910 Planet starting from terrestrial GCMs. Created by the terrestrial atmosphere modeling community, models developed in this way include:

• the NASA/Ames GCM (Pollack et al., 1981, 1990, 1993; Haberle et al., 1993, 2003a, 2003b); 915 • the Laboratoire de Météorologie Dynamique (LMD) GCM (Hourdin et al., 1995, Forget et al., 1999); • the planetWRF developed by the Jet Propulsion Laboratory and Caltech (Richardson et al., 2007); • the Community Atmospheric Model (CAM) developed by National Center for Atmospheric 920 Research (NCAR) (Collins et al., 2004, 2006); • others like that of Wilson and Hamilton (1996), Richardson and Wilson (2002), Kuroda et al. (2005) and Moudden and McConnell (2005).

Apart from Mars, for which there are several references in the literature (examples: Forget et al., 925 2013; Urata and Toon, 2013a; Urata and Toon, 2013b; Wordsworth et al., 2013; Wordsworth et al., 2015; Turbet et al., 2017; Daerden et al., 2019; Haberle et al., 2019; Hartwick et al., 2019; Pál et al., 2019), a similar approach, starting from an Earth-based model modified and adapted to the climatic conditions of a planet/satellite, was applied to simulate present and past climate conditions of other celestial bodies. For example: 930 • Venus : Way et al. (2016) used the ROCKE-3D GCM model, derived from the parent Earth climate GCM ModelE2-R (Schmidt et al., 2014) for their paleoclimatic studies; Lebonnois et al. (2016) used LMD Venus GCM (Lebonnis et al., 2010) for analyzing Venus atmospheric circulation, derived by LMD GCM (Forget et al., 1999); Parish et al. (2011) 935 used Venus-CAM, a modified version of NCAR CAM adapted for Venus, to reproduce Venus’ atmosphere; • Saturn: Friedson and Moses (2012) used Outer Planet General Circulation Model (OPGCM), a modified version of NCAR CAM, for their work; Guerlet et al. (2014) and Spiga et al. (2020) a modified version of LMD-GCM terrestrial climate model; 940 • Titan and other satellites: Friedson et al. (2009), Larson et al. (2014, 2015) used a modified version of NCAR CAM terrestrial model; Charnay et al. (2014) a new type of GCM, the Generic LMDZ, from LMD model; • atmosphere of certain exoplanets: Yang et al. (2013, 2014) and Kopparapu et al. (2016) used a modified version of NCAR CAM Earth-model for reproduce the atmosphere of some of 945 them; Wordsworth et al. (2011), Leconte et al. (2013) used instead a modified version of

25 LMD-GCM Earth model; Del Genio et al. (2019) applied ROCKE-3D GCM to reproduce climate conditions of some Habitable planets; • deep-paleoclimate studies: Wolf and Toon (2013, 2014a, 2014b, 2015) used a modified version of NCAR CAM Earth-model; Wordsworth et al. (2013), Forget et al. (2013), 950 Charnay et al. (2013), Turbet et al. (2019) a modified version of LMD-GCM Earth model.

The first concrete attempt to build up a climatic model useful to reproduce Mars weather was that of Leovy and Mintz (1969), who adapted a GCM developed for Earth at University of California, Los Angeles (UCLA). The model was able to well predict the condensation of CO2 and the existence of 955 baroclinic waves. This model was the basis on which at NASA Ames Research Center scientists worked to discover useful information about the Martian climate (Pollack et al., 1981, 1990; Haberle et al., 1993, 2003b) and, thanks to the simulations carried out with this model, also evaluated the meteorological conditions at the VL1 landing site (Haberle et al., 1997). The Ames Mars GCM was extensively applied to reproduce also other features of the Martian weather 960 conditions, for example dust storms (Murphy et al., 1995), the hydrological cycle (Nelli et al., 2009) and water and carbon dioxide clouds (Colaprete et al., 2008).

In Europe, one of the most important research centers involved in the study of climate on Earth and other planets’ atmospheres is the Laboratoire de Météorologie Dynamique (LMD). Hourdin et al. 965 (1995) adapted a terrestrial model to Martian conditions by adding a new radiative transfer code and CO2 condensation, thus obtaining good agreement with pressure variations derived from the Viking landers. Many changes, as in the case of the NASA/Ames GCM, were applied to the model in order to improve the performances (Forget et al., 1999), the most important were the introduction of modern dynamical algorithms and the inclusion in the code of an extensive chemistry package for 970 atmospheric composition studies (Lefevre et al., 2004).

Also the Geophysical Fluid Dynamics Laboratory (GFDL) developed a Mars GCM, based on the terrestrial “Skyhi” model (Wilson and Hamilton, 1996; Richardson and Wilson, 2002). This is a proven, modern model capable of running on multiple processors, with well-developed physics 975 modules, and has the computational advantage of using a “cubed-sphere” grid (Urata, 2012).

Another climatic model, adapted by Richardson et al. (2007) to Mars weather conditions, is the PlanetWRF, based on NCAR’s Weather Research and Forecasting (WRF). PlanetWRF is a regional computationally modern model, capable of simulations from the regional scale to the global scale. 980 These models, and others (Moudden and McConnell, 2005; Hartogh et al., 2005; Kuroda et al., 2005) make up a large community of Mars general circulation models.

Finally, Urata and Toon (2013a, 2013b) proposed a new model based on the NCAR CAM models, the last ones supported by a large group of developers at NCAR (Urata, 2012): in 2019, Hartwick et 985 al. (2019) added to this model the CARMA libraries so to introduce in the calculations the contribution due to aerosols.

26 2.2 Simulation of the ancient Mars climate: a challenging task 990 Reproducing the current climatic conditions of a planet is a hard task, due to the multiple physical processes that must be adequately modeled and processed all together in order to reach a global representation as reliable as possible. At the same time it is “relatively easy” to verify the adequacy of the output of a model applied to present climate situations by comparing it with observations. An 995 even more challenging task is to adapt an atmospheric model to recreate ancient climate conditions of a planet for which direct observations are not available. The only way of testing the results coming from it is to verify what physically acceptable values of the meteorological parameters introduced in the model are able to support some hypotheses related to accepted ancient climate evidences; in the case of early Mars, for example, reaching mean global surface temperature at or 1000 above 273 K so to host liquid water on the surface for an extended period of time (hundred thousands of years or more).

Due to the similarity between the environmental conditions that Mars might have presented in the early stage of its history and those of the early Earth, where life originated, a lot of models were proposed in the literature in order to simulate these ancient climatic conditions for the Red Planet. 1005 Here only a rapid overview of the most used for this topic are reported, as the goal of my study is the reproduction with GCMs of present Mars observations.

As evidenced by Haberle (1998), the easiest way to achieve warmer conditions for early Mars is

through the greenhouse effect of some gases detected on Mars, principally CO2 and water vapor. 1010 During the 1970s and 1980s, three classes of greenhouse models were built up (for details, see also Haberle, 1998):

• global average energy balance models (Sagan and Mullen, 1972; Sagan, 1977).

Very simple model, the code allows to balance the globally averaged absorption of sunlight with infrared emission; the outgoing infrared is calculated in terms of a contribution from the surface and 1015 one from the atmosphere, the latter represented as a single isothermal layer (Haberle, 1998).

• 1-D radiative-convective models (Pollack, 1979; Cess et al., 1980; Pollack et al., 1987).

In these models, atmosphere is divided into a number of vertical layers but still ignore latitudinal variations. The temperature is retrieved by first balancing the solar and infrared fluxes within each layer so that no net heating occurs, and then performing a correction to the temperature profile in 1020 those regions where the lapse rate exceeds some limit value (Haberle, 1998). The lapse-rate adjustment in the 1-D models is performed to simulate the stabilizing effects of a variety of atmospheric phenomena (dry/moist convection, large-scale motions) that cannot be explicitly evaluated in these models. The calculated radiative fluxes depend, among other factors, on the abundance and distribution of absorbers (Haberle, 1998).

1025 • latitudinally resolved energy balance models (Hoffert et al., 1981; Postawko and Kuhn, 1986).

The net radiative loss (gain) at the top of the atmosphere at a given latitude is balanced by heating (cooling) due to atmospheric transport from neighboring latitudes (Haberle, 1998). These models

27 treat the outgoing infrared as a linear function of surface temperature, which is empirically derived 1030 from Earth data, and atmospheric transport is represented as a diffusive process, even if both the representations are not so accurate (Haberle, 1998). This is done in order to allow for latitudinal variations even if in a very simple way.

The results coming from these models were not so satisfactory in terms of surface temperature, the most important output variable that must be investigated in this kind of simulations, as a global and 1035 annually averaged surface temperature at or above 273K is required to stabilize liquid water on the surface of early Mars (Haberle, 1998). It was immediately clear to these earlier climatic model

developers that a pure CO2/H2O atmosphere has great difficulty in producing enough greenhouse warming to sustain warm and wet conditions (Kasting, 1991). The following necessary step in the refinement of a reliable climatic model was the inclusion, in the code (apart from the atmospheric 1040 greenhouse effect) of a series of complicated atmospheric and chemical processes that could better and more completely represent old weather conditions. The most important ones are listed before:

• the low luminosity of the young Sun (known as “the paradox of the young Sun”, - Gough, 1981; Haberle, 1998; Fairén et al., 2012);

• CO2/H2O ice clouds IR scattering, that increases greenhouse effect (Forget and 1045 Pierrehumbert, 1997; Urata and Toon, 2013a; Forget et al., 2013);

• the additional contribution produced by other greenhouse gases like SO2 (Johnson et al., 2008; Mischna et al., 2013), CH4 (Justh and Kasting, 2001; Yung et al., 2018), water vapour (Wordsworth et al., 2013), NH3 (Sagan and Chyba, 1997) and aerosols (Forget et al., 2013);

1050 • the effects due to the tilt of the martian axis (Mischna et al., 2013);

• the albedo of polar caps and of the terrain free from ice (Fairén et al., 2012; Urata and Toon, 2013a).

Only with the most recent 3-D GCMs it has been possible to simultaneously consider all these processes and advance more-likely conclusions related to ancient Mars climate conditions. As 1055 mentioned before, in this thesis this topic is not deepened, limiting only in the indications of some publications in which the two models compared (GCM-LMD and MarsCAM-NCAR) were applied to reproduce the putative early warm and wet Martian climate:

• GCM-LMD : Wordsworth et al. (2013); Forget et al. (2013); Wordsworth et al. (2015); Turbet et al. (2017).

1060 • MarsCAM-NCAR : Urata and Toon, (2013b).

2.3 General description of the two GCMs compared

Among the GCMs listed in Section 2.1, the output (surface and near -surface temperatures) generated by the GCM developed at LMD (Forget et al., 1999) and that of MarsCAM, developed at 1065 NCAR (Urata and Toon, 2013a; Hartwick et al., 2019) were compared. I decided to focus my

28 attention on these two software programs because they are the only 3-D open codes available, for which publications specific to present and past Mars climate simulation existed. Moreover, GCM- LMD and MarsCAM-NCAR were the only ones ready-to-use and not under upgrading: for example, the new features of the NASA/Ames Legacy Mars Global Climate Model were recently 1070 presented by Haberle et al. (2019) and, as declared by the same authors, not yet fully revised and tested; also Lee et al. (2018) were already testing in the MarsWRF the impact of the introduction in the model of a fully-interactive dust and water cycle. Finally, Way et al. (2017) showed an application to modern Mars performed with ROCKE-3D GCM, declaring that experimental simulations are in progress, but no specific publication is available as yet.

1075 The two GCMs under study are able to simulate and reproduce many climatic variables, listed in Table 2.1. In the following, the main features of the two programs considered in this work are briefly described. In Table 2.2 a summary of the principal input/output features of the two GCMs compared is reported, while in Table 2.3 the list of the main packages implemented in the source code is shown.

1080 Table 2.1: List of the most important variables computed by the two GCMs. TOA stands for Top Of Atmosphere, PBL for Planetary Boundary Layer. The “*” reported for LTST is to underline that this output was deduced indirectly, as specified in Section 4.7.2. For the complete list, see Millour and Forget, (2018) for MCD and Collins et al. (2004) for MarsCAM-NCAR.

VARIABLE MCD MARSCAM Solar Longitude (LS) x x 1085 Local True Solar Time (LTST) x x* atmospheric pressure x x surface pressure x x altitude above local surface x atmospheric reference height x x surface temperature (TG) x x daily max mean TG x daily min mean TG x near-surface temperature (TSA) x x daily max mean TSA x 1090 daily min mean TSA x zonal wind x x meridional wind x x vertical wind x thermal IR flux (ground) x x thermal IR flux (TOA) x x solar flux (ground) x x solar flux (TOA) x x

CO2 mixing ratio x x other trace gases mixing ratio x 1095 electron density (up to ~ 200 km) x water vapour content x water ice content x column values of all species x dust mixing ratio x dust optical depth x x surface stress x x PBL height x x relative humidity x convective cloud coverage x subsurface temperature x

29 1100 Table 2.2: Principal input/output features of the two GCMs compared. For GCM-LMD model, here are reported only those related to the MCD database, used for the comparison (see Section 3.1). The details about the characteristics of the full model can be found in Millour and Forget (2018). Legend: * = this is the format coming from the MCD database; ** = time for collecting data from the database with a normal PC working in sequential mode. A simulation of the GCM-LMD model with 64x48 1105 lon-lat grid takes 12 h with 24 cores in parallel configuration to complete the calculation for 1 Martian year (Millour, 2018). The maximum number of cores one can use for a simulation is half the number of grid points in latitude (Millour, 2018); *** = Calculation time here reported are referred to a “standard simulation” (see text) performed with resolution 4°x5° lat/lon. FEATURES MCD MARSCAM

SPATIAL RESOLUTION (LAT/LON) 3.75° x 5.625° 2°x2.5°, 4°x5°, 10°x15° ATMOSPHERE (layers) 49 (up to 300 km) 26 (up to 60 km) SUBSURFACE (levels) NO 10 (down to 3 m)

CLOUDS water water and CO2 n° VARIABLES IN OUTPUT 80 220 TYPE OUTPUT FILES .txt * NetCDF CORES 1 ** 48, 96, 240 TIME CALCULATION (per MY) 1-2 min ** 1h 15m, 3h 40m, 7h 20m *** OUTPUT SIZE (per MY) few MB ** ~ 200 GB

1110 Table 2.3: List of the packages implemented in the source code of the two GCMs compared. For more details about this topic, see Forget et al. (2017), Millour et al. (2017), Millour and Forget (2018), Millour et al. (2018) for GCM-LMD; Collins et al. (2004), Urata and Toon (2013a) and Hartwick et al. (2019) for MarsCAM-NCAR. PHENOMENON MCD MARSCAM dust cycle Madeleine et al. (2012) CARMA (Toon et al., 1988) water cycle Navarro et al. (2014) Collins et al. (2004)

CO2 cycle Forget et al. (1998) Urata and Toon (2013a) Planetary Boundary Layer Coläitis at al. (2013) Collins et al. (2004) ozone Lefèvre et al. (2008) - Upper atmosphere González-Galindo et al. (2015) - electron content in the Ionosphere González-Galindo et al. (2013) - Ar, N and other non-consensable species Forget et al. (2008) - transfer radiative equation Dufresne et al. (2005) Toon et al. (1989) surface energy balance - Oleson et al. (2004) Rayleigh scattering - Hansen and Travis (1974) pressure-induced absorption of water vapour - Wordsworth et al. (2010)

pressure-induced absorption of CO2 - Thomas and Nordstrom (1985) radiative effetcts of clouds Millour and Forget (2018) Collins et al. (2004), Pincus et al. (2003) optical properties of dust Madeleine et al. (2012) Colburn et al. (1989)

1115 2.4 GCM – LMD

The General Circulation Model of the Martian atmosphere developed by LMD was presented by Forget et al. (1999). As reported in the userguide (Millour and Forget, 2018), the GCM computes the atmospheric circulation in 3D taking into account radiative transfer through the gaseous

atmospheres as well as through dust and ice aerosols. It also includes a representation of the CO2 ice 1120 condensation and sublimation on the ground and in the atmosphere, it simulates the water cycle (with modeling of cloud microphysics), the dust multisize particle transport, the atmospheric

30 composition (controlled by photochemistry) and the local non-condensable gas enrichment and

depletion induced by CO2 condensation and sublimation. The model was also extended to reproduce the thermosphere and is able to simulate the ionospheric processes. Since 2001, the physical part is 1125 available, containing the radiative transfer code valid up to 120 km, tracer transport, the water cycle with water vapor and ice, the “double mode” dust transport model, and with optional photochemistry and extension in the thermosphere up to 250 km (Millour and Forget, 2018).

The operation of the model can be divided into two main categories (Millour and Forget, 2018): • the so called “dynamical part”, containing the numerical solution of the general equations 1130 for atmospheric circulation. This part, including the code, is common to the Earth and the Martian model, and in general for all atmospheres of the terrestrial type. It computes the large scale atmospheric motions; • the so called “physical part”, specific to the planet considered, which calculates the forced circulation and the climate details at each point. It is related to radiative heating and cooling 1135 of the atmosphere, surface thermal balance, subgrid scale atmospheric motions (convection,

gravity wave, turbulence in the boundary layer) and CO2 condensation.

The calculations for the dynamical part are made on a 3D grid with horizontal exchanges between the grid boxes, whereas the physical part is like a juxtaposition of atmosphere “columns” that do not 1140 interact with each other. The dynamical and physical parts deal with variables of different natures, and operate on grids that are differently constructed. The temporal integration of the variables is based on different numerical schemes, also timesteps are different. For the explanations of the grids applied and the calculations that the code performs at each step, see the userguide (Millour and Forget, 2018) from which the previous characteristics were obtained. 1145

2.5 MarsCAM – NCAR

A new general circulation model for Mars, adapted from terrestrial NCAR Community Atmosphere Model (CAM) and named MarsCAM, was presented by Urata and Toon (2013a). As GCM-LMD, the model can be executed on parallel processors, making simulations faster than older models that 1150 do not present the same capability, producing output in NetCDF format.

MarsCAM-NCAR is a low top model, meaning that the lowest pressures investigated reach in the atmosphere an height of ~60 km (Hartwick et al., 2019). Potentially, thanks to the extensive expansions that can be added to CAM code, the model can be used also to investigate features in the 1155 upper atmosphere of Mars and in other zones of the planet. Among them, the most important are:

• WACCM (Whole Atmospheric Community Climate Model), which couples a chemistry model, MOZART, Model Of Ozone and Related Tracers, and an upper atmosphere model, TIME, Thermosphere-Ionosphere-Mesosphere-Electrodynamics Processes;

• CLM (Community Land Model), able to simulate a comprehensive hydrological cycle;

1160 • SOM (Slab Ocean Model), for including an ocean, useful for ancient Mars simulations.

31 The most important changes made to adapt the terrestrial model (CAM) to Martian climate conditions (MarsCAM-NCAR) are the introduction of the Martian planetary parameters (gravity, obliquity, eccentricity of the orbit, orbital semi-major axis, length of year and sidereal day, planetary

radius, topography), the modification of the composition of the atmosphere (95% CO2, 3% N, 2% 1165 Ar), the modification of the longwave radiation transfer scheme so to include the effects due to the

predominant presence of CO2 in the atmosphere and the scattering by dust in the infrared (by using a two-stream transfer algorithm developed by Toon et al., 1989). Dust vertical transport and microphysics are calculated thanks to University of Colorado/NASA Community Aerosol and Radiation Model for Atmospheres (CARMA) (Toon et al., 1988), able also to simulate clouds 1170 (Michelangeli et al., 1993; Colaprete et al., 1999; Colaprete and Toon, 2003; Hartwick et al., 2019). Fractional cloud coverage and cloud overlap is considered using the Monte Carlo Independent Column Approximation (McICA) method described by Pincus et al. (2003).

MarsCAM-NCAR reproduces the behavior of the atmosphere dividing it in 26 levels, adopting a vertical grid of hybrid-sigma pressure levels similar to that of MCD but till a height of about 60 km 1175 (Collins et al., 2004), as the program is a low top model (Hartwick et al., 2019). With respect MCD, MarsCAM-NCAR is able also to reproduce subsurface temperatures: the subsoil in the code is reproduced in 10 different levels down to a depth of about 3 m. For more details about the model, see Collins et al. (2004), Urata (2012), Urata and Toon (2013a; 2013b) and Hartwick et al. (2019).

1180 2.6 The MCD database derived from GCM-LMD

In the comparison that will be presented in Chapter 5 I used, as representative data for this climatic model, the output extracted from the scenarios stored in the Mars Climate Database (MCD) v5.3, a database of atmospheric statistics compiled from state-of-the art GCM-LMD simulations of the Martian atmosphere (Forget et al., 2017; Millour et al., 2017; Millour and Forget, 2018; Millour et 1185 al., 2018). I decided to employ the data extracted from the database rather than performing new simulations using the GCM-LMD software because the database aims at representing the current best knowledge of the present Martian climate conditions with the most performing simulations possible with the GCM-LMD (Millour et al., 2018).

The database is freely available upon request, while a simplified web interface for quickly browsing 1190 MCD outputs is available at http://www-mars.lmd.jussieu.fr (last visited: December, 2019). The MCD includes several scripts written in various programming languages (Fortran, Matlab, Python, IDL, C, C++) in order to easily access the database, as well as detailed indications on the libraries necessary to manipulate the output (for more details, see Forget et al., 2017; Millour et al., 2017).

Data available in the database are organized in a 5.625° x 3.75° longitude-latitude regular, 1195 equispaced horizontal grid from the surface up to an approximate altitude of 300 km, organized in a vertical grid of hybrid coordinates composed of 49 levels, divided between lower atmosphere (l = 1, …, 30) and thermospheric (l = 31, …, 49) (Millour and Forget, 2018). All the output variables are averaged and stored 12 times a day, for 12 Martian “months”, each month covers 30° in LS, about 50-70 days long: in other words, each grid point has 12 “typical” days, one for each month, 1200 included the variability of the data within one month and the day oscillations.

32 MCD provides 18 different combinations of dust distributions and solar EUV irradiation scenarios, which both highly change from year to year (Millour and Forget, 2018). Solar conditions control the heating of the atmosphere above 120 km, which typically varies on a 11-year cycle: according to the selected scenario, fixed (i.e. constant in time) solar minimum and/or minimum conditions are 1205 provided, or varying (i.e. changing from day to day, as observed) realistic solar EUV (Millour and Forget, 2018). The amount and distribution of suspended dust in the atmosphere are however the factors that mostly influence Martian climate conditions. Due to their great variability, and since even for a given year the details of the dust distribution and optical properties are not fully known, various model integrations are available, assuming different “dust scenarios”, i.e. prescribing 1210 various amount of airbone dust in the simulated atmosphere (Millour and Forget, 2018).

2.7 MarsCAM-NCAR simulations on the CMCC Athena cluster

For MarsCAM-NCAR, there is not an equivalent database as the MCD of the GCM-LMD, so it was 1215 necessary to compile and install the source code. By using the ability of the model to be run in parallel configuration, I successfully run it on the Athena cluster (https://sccmon.cmcc.it/) of the Supercomputing Center of the Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC). The model can be executed with three different latitude/longitude spatial resolutions (see Table 2.2): in order to make the comparison with MCD output as homogeneous as possible, I performed the 1220 simulations with resolution 4° x 5° lat/lon for this program, very close to the spatial grid adopted by MCD database (see Section 2.6). In this thesis, the term “standard simulation” is used to define a run performed on the Athena cluster with a 4°x5° lat/lon grid, having time-step frequency of about 3 hours (i.e. the values of the output variables are calculated and stored every three hours in the output files), able to simulate 5 MYs, 1225 with evaluable output consisting of the last three years generated. This because the model starts from a rest state with a globally uniform temperature distribution of T = 250K, no soil moisture and only the northern water ice cap as a source, so it is initially very dry (Urata and Toon, 2013a).

Moreover, initially there are no permanent CO2 caps and the total amount of CO2 is only in the atmosphere (Urata and Toon, 2013a). In order to reach convergence and allow the model to exceed 1230 the spin up phase (in which parameters are stabilizing and results are unreliable), the program must be run to simulate at least three MYs, with the output of the first two years not to be considered in the analyses (Urata, 2018). So, for each simulation having different initial input parameters (for details, see Section 3.2), I decided therefore to perform a 5 MYs-long run and to retain and analyze only the last three years. A standard simulation is completed in ~ 20 h on the Athena cluster with 96 1235 cores.

1240

33 1245

1250 CHAPTER 3

LANDERS/ROVERS DATA AND GCMs OUTPUT MANIPULATION

1255

1260

1265

1270

1275

34 3.1 Scenarios/Runs considered for the comparison

In this Chapter I present the principal physical features of the simulations used to test the two GCMs on present Mars surface and near-surface temperatures. I refer to the term “Scenario” for 1280 each Mars climate representation according to the MCD database, and with the term “Run” for those performed with MarsCAM-NCAR with various configurations of the initial parameters.

For GCM-LMD, the Scenarios taken into account for the comparisons were those stored in the MCD database (see Section 2.6). They are divided into five categories (Millour and Forget, 2018):

1285 • Climatology Scenarios (named 1,2,3): derived from the available observations of dust (till 2013) in MY 24, 26, 28, 29, 30, 31 (years without global dust storms), and thus representative of a standard MY (i.e., without dust storms). The dust field and its evolution was carefully reconstructed, and then gridded and interpolated in the model, by Montabone et al. (2015). The scenarios are provided with 3 solar EUV conditions: solar minimum (1), 1290 average (2) and maximum (3); • Warm Scenario (named 7): it corresponds to “dusty atmosphere” conditions, but nonetheless non-global dust storm conditions. The dust opacity at a given location and seasonal date is set to the maximum observed over the seven MYs (MY 24-MY 31), except during the MY 25 and MY 28 global dust storm, further increased by 50%; 1295 • Cold Scenario (named 8): it corresponds to an extremely clear atmosphere (“Low dust Scenario”) where the opacity is set to be the minimum observed over MY 24-31, further decreased by 50%. Moreover, radiative effects of water ice clouds is not taken into account, to prevent warming of the atmosphere; • Dust storm Scenarios (named 4,5,6): they represent Mars during a global dust storm, with 1300 dust opacity equal to 5 at all times and over the whole planet. Moreover, dust optical properties are for this case set to represent “darker dust” than nominal. These Scenarios are only provided for when such storms are likely to happen, during northern fall and winter (LS = 180-360), but with 3 cases of solar EUV inputs: min (4), ave (5) and max (6);

• The Mars Years Scenarios (10, named MY 24, MY 25,.., MY 32, MY 33): they correspond 1305 to the best representation possible with GCM-LMD of these specific years, both in terms of daily atmospheric dust loading (Montabone et al., 2015) and daily solar EUV input.

In the comparisons performed, I did not take into consideration the three dust storm Scenarios because I was interested in comparing surface temperature (TG) and near-surface temperature 1310 (TSA) collected by the various landers/rovers in the whole year, not only when dust storm events happened.

The Runs performed with MarsCAM-NCAR program were in total 7, so defined: • Run 2: with the default physical parameters set by the developers; 1315 • Run 4: applying the reference values of thermal inertia measured at VL1, VL2 and OPP landing sites (see Table 1.2) in the corresponding grid cells of the model. The goal was to

35 test the effect on TG and TSA of the change of only this parameter with respect to the default ones; • Run 5: same as Run 4 but using the reference values of albedo measured at VL1 and VL2 1320 landing sites (see Table 1.2) in the associated grid cells of the model. The goal was to test the effect of the change in albedo and thermal inertia on TG and TSA; • Run 8: same as Run 5 but changing the value of the dust OD with respect to the default case (Run 2). The goal was to test the effect of the simultaneous change of albedo, thermal inertia and dust OD on TG and TSA; 1325 • Run 10: once fixed the default albedo value in VL1 and VL2 locations, the measured thermal inertia (Run 4) was inserted in these cells as well as the same dust OD of Run 8. The goal was to test the effect of the change in thermal inertia and dust OD on TSA and TG; • Run 11 , same as Run 5, but with a different value of dust OD with respect to Run 2. The goal was to test the effect of the change in dust OD on TSA and TG; 1330 • Run 12 , same as Run 5, but with a different value of dust OD with respect to Run 2 and Run 11. The goal was to test the effect of the change in dust OD on TSA and TG.

In Table 3.1 the values of albedo, thermal inertia and dust OD used for each Run of MarsCAM- NCAR now introduced are reported. The values chosen for the dust OD in the various Runs 1335 correspond to the typical values for periods of normal dust activity (Colburn et al., 1989).

Table 3.1: Runs performed with MarsCAM-NCAR GCM. Starting from Run 4, the thermal inertia (expressed in J m-2 K-1 s-1/2) used in the grid cell containing OPP landing site is set to 220 and not at 481 as in Run 2. The values used for albedo and thermal inertia are taken from Table 1.2. 1340 RUN ALBEDO THERMAL INERTIA DUST OD VL1 VL2 VL1 VL2

2 0.22 0.24 290 232 0.30 4 0.22 0.24 215 240 0.30 1345 5 0.26 0.22 215 240 0.30 8 0.26 0.22 215 240 0.30 10 0.22 0.24 215 240 0.10 11 0.26 0.22 215 240 0.25 12 0.26 0.22 215 240 0.20 1350 The numbering of the Runs is not consecutive because some test simulations were later excluded from processing. This happened because I made some testing simulations, in order to evaluate the time-performance calculations on the Athena cluster, and also for developing some comparison of the output between a standard simulation and a Run performed with the same initial parameters but 1355 with the other spatial resolutions available (2°x2.5° and 10°x15°). Moreover, I had to repeat some Runs (i.e. use the same initial input parameters) in order to take into account for the different heights at which data related to the near-surface temperatures were collected by the eight landers/rovers (see Section 3.5.1 for details).

36 3.2 Set of the initial physical parameters used in the simulations 1360 In the GCMs, everything is deduced from physical equations and physical constants, with the former depending on the parameterization adopted to reproduce a specific phenomenon (see Table 2.3). The only parameters that have to be set “manually”, depending on the planet under study, and thus mainly influencing the output of a climatic model, are principally four: the height over the 1365 planetary (Martian) datum (see Section 6.4), albedo, thermal inertia and dust OD. These parameters are included in the climatic models in lat/lon maps, with the related values associated to the various grid cells computed according to the spatial resolution chosen for the simulation. The best way to implement them in the climatic model, adapting the values to the wanted spatial grid box, is to retrieve them from the observations, when available. In Table 3.2 are reported the references from 1370 which the input maps used by the two GCMs were deduced.

Table 3.2: Sources from which input maps used by the two GCMs at the begin of each simulations are deduced. For more details, see Forget et al. (1999) for GCM-LMD and Urata and Toon (2013a) for MarsCAM-NCAR. MAP MCD MARSCAM

TOPOGRAPHY MOLA DATA MOLA DATA (PDS node archive) (Smith et al., 2003) SURFACE ROUGHNESS (Hébrard et al., 2012) ALBEDO MIDDLE LATITUDES TES DATA (Pleskot and Miner, 1982) (Christensen et al., 2001) NORTHERN POLAR REGION (Paige et al., 1994) SOUTHERN POLAR REGION (Paige and Keegan, 1994) THERMAL INERTIA NORTHERN POLAR CAP TES DATA (Paige et al., 1994) (Putzig and Mellon, 2007) FROM 60 °N TO 30 °S (Mellon et al., 2000) FROM 30 °S TO 60 °S (Palluconi and Kieffer, 1981) SOUTHERN POLAR CAP (Paige and Keegan, 1994) DUST VERTICAL DISTRIBUTION AND PARTICLE SIZE VERTICAL TRANSPORT (Madeleine et al., 2012) (Toon et al., 1988) EIGHT-YEARS MEASUREMENTS (Montabone et al., 2015)

I will not discuss over on how these maps were created and adapted to match the features of each GCMs (for details, see Forget et al. (1999) for GCM-LMD and Urata and Toon (2013a) for MarsCAM-NCAR). According to the spatial resolution available for each GCM (see Table 2.2), these maps were adequately modified and loaded at the begin of each simulation in order to define 1380 the starting physical state of the planet.

Apart from the various sources from which these maps were retrieved, the most significant difference between the two GCMs is related to how the two climatic models take into account the parameterization and the contribution due to dust, which, as already mentioned, is the most 1385 important effect that affects the present Martian climate. In fact, while in MCD simulations the total dust column OD, at each location and time, is derived from the available observations taken for

37 MYs 24-31 (Montabone et al., 2015), MarsCAM-NCAR does not consider these variations, assuming a single value of the dust OD for all the planet. This is the reason why, in Table 3.1, only a fixed value of the dust OD for the various Runs of MarsCAM-NCAR is reported. The dust 1390 vertical distribution and the dust particle size in MCD is computed according to Madeleine et al. (2012) (for more details, see Forget et al., 2017), while MarsCAM-NCAR uses the CARMA libraries (Toon et al., 1988) to perform dust transport. However, Urata and Toon (2013a) in their first simulations adopted instead a constant dust background with a single particle size of 2 μm, following a vertical distribution described by Conrath (1975). 1395 In Table 1.2, when the information defining the physical properties of the eight landing sites coming from the observations are reported, I indicated, as reference values for the dust OD in these locations, minima, averages and maxima of this quantity. They were calculated from the climatology maps used as input files for MCD calculations and derived from Montabone et al. 1400 (2015). In detail, for each MCD Scenario, a dust OD map is provided. A similar extraction was made also from the input files of both programs containing albedo and thermal inertia maps. The complete sets of the values of albedo, thermal inertia and dust OD used at the beginning of the various MCD Scenarios and MarsCAM-NCAR Runs compared in this work are reported in Appendix A, Tables A.1-A.8. 1405 3.3 Initial computational settings used to perform simulations

A set of initial parameters must be specified at the beginning of each simulations. As mentioned in the previous Section, albedo, thermal inertia and dust OD maps are created starting from 1410 observations and adapted to the various spatial resolutions available for that GCM. These maps are stored, for both programs, in Network Common Data Form (NetCDF, extension of the file: .nc), as well as other physical parameters and constants. The way in which these files are “called” in the submission script change from program to program. For MCD I used (and partially modified) a subroutine named “call_mcd.F”, provided by the 1415 developers to query the database and retrieve data from it. The subroutine contains the calls to all the files where starting variables are defined (for example, file “mola32.nc” contains a high resolution map of the Martian topography) common to each Scenarios, each of them having a dedicated sub-directory where data simulated with the GCM-LMD are stored. To generate the output, the following information must be specified: 1420 • date (Earth Julian Date or Mars seasonal time); • height at which climatic variables must be computed (in m or Pa); • latitude and longitude of the location in which data must be reproduced; • one of the 18 Scenarios available in the database; • LS start and end values in which data must be computed; 1425 • generation frequency (in steps of LS) of the output data.

and others. The last two points are not provided by the standard “call_mcd.F” subroutine, therefore I slightly modified it so to query the database for generating output in a well specified LS range. In fact, the initial version of the script allows the user to compute climatic variables only for one value of LS and only for a specific local time. As I was interested in annual, seasonal and daily trends of

38 1430 TG and TSA, I need to know and store the values of these quantities with a higher frequency, so I decided to modify the subroutine as just explained. The output generated by the database is in the .txt format.

For MarsCAM-NCAR GCM all the input variables are organized, as the output, into two main categories in .nc files: atmospheric and land variables. For example, in the first the height (given in 1435 form of map) and the starting surface pressure can be found, while in the second there are the albedo and thermal inertia, also stored in terms of lat/lon maps. Apart from the value of the dust OD to be used in the simulation, the initial settings that need to be specified at the beginning of a simulation includes:

• eccentricity of the orbit; 1440 • number of sols to be simulated; • obliquity of the Mars axis; • frequency with which simulated data must be computed and stored in the output files; • flag to turn on Mars radiative transfer; • flag to turn on the generation of a variable where LS values must be stored; 1445 • the starting value of LS from which calculation must be performed; • depending on the spatial resolution chosen, the number of cores to be used for each latitude/longitude grid point.

LS is not directly generated in output. In fact, all the output variables of this program are not 1450 computed in terms of LS values: the latter is considered as an additional variable, stored and simulated as a function of the time passed since the first second of the first simulated day. The operations necessary to match LS values with the time of the year at which climatic variables are computed, are clarified and shown in Section 3.6.2.

1455 3.4 Changing albedo, thermal inertia and dust OD: impact on surface and near-surface temperatures

The ability of a GCM to reproduce the ground and near temperatures of a planet (not only Mars) is strongly influenced by the three mentioned parameters: albedo, thermal inertia and dust OD. 1460 To get an idea of how these physical quantities affect ground temperatures, let us consider the observations made at CUR landing site, Gale Crater. As evidenced in Section 1.7 the interannual variability of the daily mean ground temperature there observed evidences small variations caused by the change in albedo along the journey of the rover. The sudden decrease revealed by Martínez et 1465 al. (2014, 2017) in the diurnal maximum ground temperature (and increase in the diurnal minimum temperature) occurred at LS ~ 220° in MY 31 and coincided with CUR arrival in a terrain (Yellowknife) with higher thermal inertia. Dust opacity values during this traverse barely changed and neither did solar insolation. As a consequence, the observed change in atmospheric opacity was very small in this region compared with that of thermal inertia (Martínez et al., 2017). 1470 The relationship existing among albedo, thermal inertia, dust OD and ground temperature can be explained as follows. The values and variability of ground temperature are mainly influenced by the

39 surface energy balance (SEB), which depends on the time of year, topography of the site, atmospheric opacity and the thermal and physical properties of the soil. The equation that rules the total amount of energy (E) at the surface available for conduction in the soil and the ground

1475 temperature Tg is given by:

4 (3.1) E =QSW (1 – α)+ QLW – σ ε T g – Q H − QE

where QSW is the downwelling shortwave (SW) solar radiation, α is the surface albedo, QLW is the 4 1480 downwelling longwave (LW) radiation flux from the atmosphere, σ ε Tg is the surface upwelling

longwave radiation flux (with ε being the surface emissivity and σ the Boltzmann constant), QH is

the sensible heat flux and QE is the latent heat flux. Upward fluxes have negative signs (cooling effect) while downward fluxes are positive (heating effect). Radiative forcing of the surface is given by the first two terms on the right of Eq. (3.1), whereas the third, fourth, and fifth terms are 1485 considered to be the responses to this forcing. The forcing terms depend on the distance to the Sun, the surface albedo, and the atmospheric opacity, while the response terms depend on the physical properties of the soil, principally thermal inertia (Martínez et al., 2014). Thermal inertia in fact determines the ability of the soil to exchange the radiative energy received at the surface with the shallow subsurface and near-surface air and depends on many factors, such as particle size, rock 1490 abundance, exposure to bedrock and degree of induration (Presley and Christensen, 1997; Mellon et al., 2000; Fergason et al., 2006a; Piquex and Christensen, 2009a, 2009b). It is defined as:

(3.2) I = √λ ρ c p

1495 where λ is the thermal conductivity of the soil, ρ the soil density and cp the soil specific heat. This parameter is important because it regulates thermal excursions of ground and subsurface at diurnal and seasonal timescales (Martínez et al., 2017), as well as controlling the temperature of the near- surface air (Martínez et al., 2014).

1500 Also atmospheric opacity affects the amplitude of variations in ground temperature (for example, see Määttänen and Savijärvi, 2004). For a given type of soil, lower atmospheric opacity leads to higher daytime maximum temperatures and lower nighttime minimum temperatures and vice-versa (like thermal inertia). In fact aerosols (primarily dust), by scattering and absorbing the solar radiation, reduce the insolation reaching the surface: the results is that, during nighttime, downward 1505 infrared emission from aerosols warms ground.

In order to obtain an estimation of how the output produced by the two GCMs is influenced by the change of these parameters, some sensitivity studies were developed. Here only the results related to ground temperature are presented, but a similar approach was performed also for near-surface 1510 temperatures (for more details, see Forget et al., 1999 and Urata and Toon, 2013a). In Figure 3.1 the diurnal trends of ground temperature as simulated by GCM-LMD, for different values of albedo (Figure 3.1a), thermal inertia (Figure 3.1b) and dust OD (Figure 3.1c) are shown. Analogous tests were performed also for MarsCAM-NCAR.

40 1515 Figure 3.1: Sensitivity studies performed on TG to test the response of MCD for a change in albedo (a), thermal inertia (b) and dust OD (c). A similar approach was performed also for TSA daily trends. For MarsCAM-NCAR, equivalent graphs were produced, here not reported for brevity reasons.

As expected by theory, when surface albedo increases, temperatures decrease and vice-versa. 1520 During daytime, the percentage difference between the three curves is more evident with respect to nighttime hours due to the contribution of the solar radiation. A change in thermal inertia value has a much deeper impact on temperatures. Both MCD and MarsCAM-NCAR experience notable modifications in temperature values reducing thermal inertia. As expected, lower thermal inertia values lead to higher daytime maximum temperatures and lower nighttime minimum temperatures 1525 with respect higher thermal inertia. Diurnal temperature trends show a similar behavior when dust OD changes are performed. In fact, also in this case, lower dust OD means higher daily maximum temperatures and lower nighttime minimum temperatures, and vice-versa. However, the percentage difference for the change of this quantity is less accentuated with respect to thermal inertia ones.

1530 3.5 Data collection: observational and GCMs output data

In order to test the reliability of the two GCMs to reproduce surface and near-surface temperatures registered on Mars, I compared the simulation outputs with the measurements collected by the eight landers/rovers (see Figure 1.1 and Table 1.1). Reference data for the spacecrafts are mainly stored in 1535 the Planetary Data System (PDS) Geosciences node (https://pds-geosciences.wustl.edu).

3.5.1 Landers/rovers observations

In Table 3.3 the list of the data available (in terms of LS range) in each landing sites for surface 1540 temperatures is reported and in Table 3.4 that for near-surface temperatures.

41 Table 3.3: Surface temperature (TG) measurements acquired by the various landers/rovers, reported as a function of LS (in degrees). Data here listed are those available in the PDS node till June 30, 2019. In column 2 is indicated the MY in which observations were collected. 1545 Legend: * = for SPI and OPP, only diurnal hours (9:00-18:00 local time) were used (see text); X = complete dataset, covering all the range indicated, is available. When data are incomplete, the interval of the available one is reported; / = data not available.

LAND/ROV MY SPRING SUMMER AUTUMN WINTER YEAR (0-90) (90-180) (180-270) (270-360) (0-360) INS 34/35 / / / 304.5-360 (FOV 1) / INS 34/35 / / / 304.5-360 (FOV 2) / AUTUMN WINTER SPRING SUMMER YEAR (0-90) (90-180) (180-270) (270-360) (0-360) SPI* 26/27/28 X X X X X (near) SPI* 26/27/28 X X X X X (upview) OPP* 26/27/28 X X 238-270 270-275, 289-304, 0-180, 238-275, (near) 336-360 289-304, 336-360 OPP* 26/27/28 X X 238-270 270-275, 289-304, 0-180, 238-275, (upview) 336-360 289-304, 336-360 CUR 31 / 155.1-180 X X 155.1-360 CUR 32 X X X X X CUR 33 X X X X X CUR 34 X X X 270-284.4 0-284.4

1550 Table 3.4: The same as Table 3.3, but for near-surface temperatures (TSA). The only difference is the addition of a column reporting the height at which the measurements were taken. LAND/ROV MY HEIGHT SPRING SUMMER AUTUMN WINTER YEAR (m) (0-90) (90-180) (180-270) (270-360) (0-360) VL1 12 1.6 / 97-154, 163-180 X 270-298.2 97-154, 163-298.2 VL2 12/13 1.6 92.58-93.37 (MY 13), 180-227.46 (MY 13), 270-342 (MY 13), 0-60.61, 0-60.61, 64.22- 95.3-96.1 (MY 13), 227.46-231.33 (MY 12) 342-360 (MY 12) 64.22-67.8, 67.8 (MY 13) 98.05-110.88 (MY 13), 231.33-270 (MY 13) 92.58-93.37, 111.54-164.82 (MY 13), 95.3-96.1, 164.82-176.01 (MY 12) 98.05-110.88, 176.01-180 (MY 13) 111.54-360 MPF 23 1.3 / 142-180 / / / PHO 29 2 76-90 90-148 / / 76-148 INS 34/35 1.4 / / / 304.5-360 / (BOOM +Y) INS 34/35 1.4 / / / 304.5-360 / (BOOM -Y) AUTUMN WINTER SPRING SUMMER YEAR (0-90) (90-180) (180-270) (270-360) (0-360) SPI* 26/27/28 1.1 X X X X X OPP* 26/27/28 1.1 X X 238-270 270-275, 289-302, 0-180, 238-275, 336-360 289-302, 336-360 CUR 31 1.6 / 155.1-180 X X 155.1-360 CUR 32 1.6 X X X X X CUR 33 1.6 X X X X X CUR 34 1.6 X X X 270-284.4 0-284.4

As it is evident by these two tables, not all the landers/rovers that reached Mars were designed to 1555 collect both surface and near-surface temperatures. Moreover, for some of them, more than one set of measurements of the same variable existed, due to multiple acquisitions coming from different instruments. In such cases, I decided to consider in the comparisons all the datasets available.

42 The sources from which the datasets related to the observational data were collected (for the PDS node, till June 30, 2019) are the following:

1560 • for VL1 and VL2, TSA temperatures at 1.6 m were found at PDS node pages for VMIS instrument and at Tillman’s webpage (one of the members of the mission);

• for MPF, data were derived from PDS node pages for ASI/MET experiment and from Tillman’s webpage. The meteorological sensors acquired temperatures at three different heights (see Section 1.4). For TSA the one measured by the upper sensor (~ 1.3 m above the 1565 surface) was considered;

• for SPI and OPP landing sites, the data published in Smith et al. (2006) were used. As already mentioned in Section 1.5, TG and TSA (at 1.1 m) values were derived indirectly from the spectra collected by the Mini-TES instrument and, as evidenced by Smith et al. (2006), only diurnal hours (9:00-18:00 local time) were mainly sampled. This is the reason 1570 why, for these two rovers, only maxima annual/seasonal trends were compared (see Chapter 4) and diurnal daily cycle (see Chapter 4). Moreover, two estimations of TG are available. In fact, for both rovers, there are two completely different retrieval algorithms and sets of observations used to produce them: “near”, from the downward-looking observations, and “upview”, from the upward-looking observations;

1575 • for PHO, data stored in the PDS node pages of the MET instrumentation were used. Three sensors at different heights collected TSA values (see Section 1.5), but in this work only the dataset related to the upper one (2 m above the ground) was considered: in fact, as evidenced by Davy et al. (2010), data coming from the lower sensors were not reliable;

• for CUR, both for TG and TSA (at 1.6 m), the data published in Martínez et al. (2017) for 1580 the first 1869 sols of the mission were used, while for the following ones (till sol 2224) that stored in the PDS node pages for REMS instrumentation was processed. For this rover, observations were available for about 4 MYs (from MY 31 to MY 34): I decided to consider separately the data collected in each MY so to enrich the set of comparisons;

• for INS, TG data were obtained from the PDS node pages for HP3 instrumentation and TSA 1585 data from the PDS node pages for TWINS instrumentation. Also for this mission were available multiple acquisitions of the same variable registered by different instruments. In fact, for TG two datasets existed from the two Radiometer field of view (FOV) of the HP3 instrument (Grott et al., 2018): I named them “FOV1” and “FOV2” (see Table 3.3). For TSA instead TWINS is made of two identical boom temperature sensors, 1.4 m above the ground, 1590 placed on diametrically opposite sides of the lander deck, one pointing in the -Y lander axis direction and the other in the +Y direction (Sotomayor et al., 2019). I labeled with “BOOM -Y” and “BOOM +Y” respectively the data taken by them (see Table 3.4).

In Section 3.6 a discussion is presented on how this observational data were managed, as well as the description of the tools used to prepare it for the comparisons with the GCM output. It must be said 1595 that measurements were available with different time steps, depending on the instruments onboard the various landers/rovers that collected observations. As I clarify below, this led to create dedicated scripts able to manipulate data in a specific format useful for my purposes.

43 3.5.2 Keeping time on Mars

1600 Before describing how the data compared were managed, it is important to specify how time can be measured on the Red Planet. In the previous Section are listed the pages of the PDS node where it is possible to get the observational data. These ones are stored in different way that change from lander/rover to the other, according to the instruments onboard the various missions. In Tables 3.3 and 3.4 the measurements available as a function of LS are indicated. In most cases, this parameter 1605 is not reported in the files containing the time series of the collected data. Very often, to describe the temporal evolution of the physical information, the start and end times of acquisition are provided. Time is sometimes in terrestrial seconds, sometimes in LTST (i.e in Martian seconds). To make comparisons between observational and simulated data, it is advisable to express temporal trends as a function of a variable able to indicate the moment of the year in which the data were acquired, i.e. 1610 the solar longitude LS.

Following the original practice adopted in 1976 during the Viking missions, the daily variation of Mars solar time is measured in terms of a "24-hour" clock, with an “hour” representing a 24-part division of the planet's solar day, along with the traditional sexagesimal subdivisions of 60 minutes 1615 and 60 seconds (Allison and Schmunk, 2019). A Mars solar day has a mean duration of 24 h 39 m 35.244 s, and is referred to as a "sol" in order to distinguish this from the roughly 3% shorter solar day on Earth (Allison, 1997; Allison and McEwen, 2000). The Mars sidereal day, as measured with respect to the fixed stars, is 24h 37m 22.663s, as compared with 23h 56m 04.0905s for Earth (Allison, 1997). A MY has consequently a length of 668.6 sols (687 Earth days). The way to 1620 distinguish the seasons on Mars is to measure in terms of LS the position of the planet on its heliocentric orbit. LS ranges from 0° to 360° over one MY, with LS= 0°, 90°, 180°, and 270° indicate the Mars Northern Hemisphere (NH) vernal equinox, summer solstice, autumnal equinox, and winter solstice, respectively. For a southern observer, obviously, LS = 0° corresponds to autumn season, LS = 90° to winter season, LS = 180° to spring season and LS = 270° to summer season: 1625 this is the reason for why, in Tables 3.3 and 3.4, the landers/rovers were split into two groups, those landed in the NH (VL1, VL2, MPF, PHO, INS) and those in the southern one (SPI, OPP, CUR).

By using the celestial mechanics equations (for example, see the method of Capderou, 2005), it is possible to retrieve the value of the LS starting from the terrestrial date, after converting it in Julian 1630 date, as well as to compute the corresponding LTST. A simple interface able to rapidly make this calculations is available at http://www-mars.lmd.jussieu.fr/mars/time/martian_time.html (last visited: December, 2019). By using this tool, it is possible to obtain LS for the observational data.

As for the output generated by the two GCMs, the value of LS associated to each simulated variable 1635 can be retrieved as follows:

• for MCD, the database reference time is Mars Universal Time (MUT), i.e. the local time at

longitude 0° (LTST0). It is possible to obtain the LTST at a given East Longitude lon (in

degrees) from LTST0 by the following equation:

1640 LTST=LTST 0+lon/15 (3.3)

44 For all the output variables, it is possible to associate the corresponding LS value and the LTST at which it is computed;

• for MarsCAM-NCAR, as evidenced in Section 3.3, it is not possible to directly associate LS values to the simulated climatic variables, because LS is considered as a separate variable by 1645 the code and it is calculated as a function of the time passed since the first second of the first simulated MY. However, as will be shown in Section 3.6.2, it is indeed possible to couple the climatic variable simulated with the corresponding LS value. Moreover, the time reported by the model is the local time at zero longitude (MUT) and must be corrected by considering the longitude of the landing site. 1650 3.5.3 GCMs output

In Section 3.4 the principal input parameters needed to retrieve simulated data from the two GCMs are described. In order to compare the datasets (observations and simulations) in a way as 1655 homogeneous as possible, it must be used a time step able to cover each hour of a sol in the range of LS to be studied. This led me to develop different approaches for testing GCMs predictions, as will be discussed in Chapter 4.

For MCD, as evidenced in Section 3.3, I slightly modified the script “call_mcd.F” so to extract data 1660 from the database by choosing the LS range in which they must be retrieved. I added also the indication of the time step (in terms of LS degrees) to be used to investigate the database: I so extracted data with an hourly frequency for one MY, in each of the eight landing sites considered in the analysis. I generated data in this way in accordance with the features of MCD: in fact, in order to maintain the seasonal behavior of the climatic variables, data coming from the GCM-LMD were 1665 stored in the database along 12 Martian months (Forget et al., 2017). Each month is defined so to cover 30° in LS, so they are “centered” on LS = 15°, 45°.... Due to the eccentricity of the orbit of Mars, martian months vary from 46 to 66 sols long (see Forget et al. 2017 for details). Time evolution of variables on the scale of a sol (88775.245 seconds long) is included in the datafiles where values at 12 times of day are stored. Also in the MarsCAM-NCAR program, at the beginning 1670 of each simulation, the output time step must be specified. As discussed in Section 2.7, for saving calculation time I decided to perform several “standard simulations”, i.e. 5 MYs-long run with a generation frequency of 3 hours. By merging the output of the last three simulated MY (see Chapter 4 for details), I was able to cover all the hours of a sol.

1675 Finally, as reported in Table 3.4, for TSA, the height at which observational data were collected changes from one lander/rover to the other. Therefore, in order to evaluate the output of the models at the same height, I performed different simulations with the same initial conditions but changing the height according to the landing sites investigated.

3.6 Managing of observational data: preparing lander/rover measurements for the 1680 comparisons

Here I briefly describe how I preliminarily prepared spacecraft data for the comparisons with the outputs obtained from the two software simulators.

45 All the datasets stored in the PDS node are not just copied from the instrumentation reports and 1685 loaded online, but a deep manipulation is necessary to remove possible causes of noises that could have altered measurements. Several correction algorithms were created ad-hoc, depending on the features of the instruments, and applied to the raw data registered by each lander/rover. In the case of PHO, for example, three processing levels are available in the associate PDS node webpage (for details, see Dickinson et al., 2008):

1690 • Level 1 : Raw data. Telemetry data stream as received at the ground station, with science and engineering data embedded; • Level 2 : Edited data (EDR). Instrument science data (e.g. raw voltages, counts) at full resolution, time ordered, with duplicates and transmissions errors removed; • Level 3 : Calibrated data (RDR). Level 2 data that have been located in space and may have 1695 been transformed (e.g. calibrated, rearranged) in a reversible manner and packaged with needed ancillary and auxiliary data (e.g., radiances with the calibration equation applied).

In the collection of observational data, I therefore considered the highest available level of correction applied to observations as provided by the various mission teams.

As mentioned before, data recorded during the various missions are not organized in the PDS node 1700 in the same manner. For this reason, I created, for each lander/rover, dedicated Matlab scripts able to download datasets from the PDS webpages and prepare it for the comparisons.

The most important steps performed, in Matlab, to manipulate the observations were:

1705 • LTST : I firstly controlled if, for each dataset regarding a specific sol, the information related to the moment of the sol at which it was acquired is present. For most of the data processed, a specific indication of this quantity is given in terms of LTST, according to the Martian clock. However, for PHO, only start and end time of acquisition of the data associated to a specific sol are available, but no indications are provided for the LTST of each single 1710 measurement. In this case, I needed to retrieve it indirectly;

• FREQUENCY OF ACQUISITION : the second check was related to the frequency at which the data are reported in the PDS files, and this changes from probe to probe. For example, in the case of VL1 and VL2 TSA values stored hourly are available, even if in few cases multiple measurements at the same hour are provided. For PHO, instead, one can choose 1715 among data collected every 2s or averaged every 512s (about 8 m). For CUR and INS, every 1s is provided. Depending on these features, ad-hoc scripts were created for each lander/rover dataset in order to organize measurements with an hourly frequency;

• LS: the comparisons were performed by using, as principal time counter to distinguish among the various seasons, the LS (see Section 4.2). Often, this information is not explicitly 1720 reported, so I needed to retrieve it starting from the Earth date, reported in the description file of each dataset, at which measurements were performed, as discussed in Section 3.5.2;

• SAMPLING : when the temperature sampling rate was too high (even up to one sample per second, for example in the cases of CUR), data were re-sampled at lower rate (preserving

46 only one sample per hour), averaging temperature in a small window around the chosen 1725 values in order to reduce noise;

• INCOMPLETE SOLS : finally, great attention was paid to eliminate, from the calculations, the sols when there was a lack of information for some hours (for example, due to hardware problems related to the instrumentation).

Once these controls concluded, data are ready to be processed. 1730 3.7 Managing of MarsCAM-NCAR output: CMCC Ophidia tool

As evidenced in Section 3.3, the files produced in output by MarsCAM-NCAR are in the NetCDF format. A Network Common Data Format (NetCDF) dataset is stored as a single file (extension .nc) 1735 comprising two parts:

• header : containing all the information about dimensions, attributes and variables except for the variable data; • data part, divided in a fixed-size data section, containing data for variables that do not have 1740 an unlimited dimension, and a variable-size data section, containing data for variables that have an unlimited dimension.

The header, at the beginning of the .nc file, contains more details about dimensions, variables and attributes such as their names, types and so on. In Figure 3.2 a schematic representation of where all 1745 these parameters can be found in a .nc file (in the header part) is shown.

At the end of a Run, a series of different files are included in the output directory:

• files containing land variables (i.e., caseid.clm2.h0.yyyy-mm-dd-ssss.nc), such as ground 1750 temperature, near-surface temperature, sub-soil temperature; • files containing atmospheric variables (i.e., mars.h0.yyyy-mm-dd.nc), such as surface pressure, longwave and shortwave net and clearsky fluxes at surface, atmospheric temperature, zonal and meridional components of wind, wind velocity, relative humidity; • initial condition dataset files (i.e., caseid.cam2.i.yyyy-mm-dd.ssss.nc): history files 1755 containing instantaneous values for only those fields required to begin a new Run;

where caseid is the case name, yyyy, mm, dd and ssss respectively the current year, month, day and number of seconds into the current day of simulation.

47 1760 Figure 3.2: An example of the header of a NetCDF file. The sample is an output of MarsCAM-NCAR program.

Output files are organized, during run time, in many different “frames”, depending on the time-step chosen at the beginning of the simulation. It is in fact not recommended, during time execution, to 1765 store all the information in a single file or in files of big dimension (Collins et al., 2004). Before managing them, it is nonetheless preferable to concatenate them (Urata, 2018). To do so, I used a toolkit called NCO (NetCDF Operator) able to manipulate and analyze data stored in .nc files. By employing the time dimension as reference-guide for assembling the different frames created in output by the GCM, I was able to assemble all the “partial” output files (separating those related to 1770 land variables from those associated to atmospheric ones) into two datasets (one for land and one for atmospheric outputs) containing all the simulated data for the specific Run investigated. The time required to concatenate the frames so produced depends primarily on the spatial resolution and time-step adopted for each Run: generally, for a standard simulations, about 2.5 hours are needed to complete the operation. 1775 Once the concatenation process concluded, I imported the two complete files (land and atmospheric) for a preliminary elaboration in the Ophidia environment. Ophidia is a CMCC Foundation research project addressing big data challenges for eScience, able to manage huge quantities of data (on the order of tens of TB) and perform calculations in very little time (Fiore et 1780 al., 2013). The features of the terminal were exploited to easily manage the big amount of data produced, thanks to specific workflows (WFs) adapted to the output of this GCM (for more details, http://ophidia.cmcc.it/documentation/index.html). Here I shortly introduce the principal features of the terminal.

48 1785 Ophidia provides a framework for parallel I/0 and data analysis, an array-based storage mode and a hierarchical storage organization to separate and distribute multidimensional scientific datasets. Since the storage model does not rely on any scientific dataset file format, it can be exploited in different scientific domains (e.g. climate, astrophysics, engineering) and with very heterogeneous sets of data. One of the goal of the scientific affiliation I signed with the CMCC Foundation was 1790 that of adapting and extending the capabilities of the tool to easily manipulate data referred to astrophysical quantities. The huge amount of WFs and tests performed in order to correctly interpret the output of the climatic simulations of Mars climate certify the goodness of the work carried out in collaboration with the developers of the tool (Dr. Cosimo Palazzo and Dr. Sandro Fiore).

1795 In Figure 3.3 an example of how the Ophidia terminal looks like is reported. In order to better understand the meaning of the information there reported, some clarifications are necessary.

Figure 3.3: A print-screen of the Ophidia terminal.

The physical design of the Ophidia storage model combines a key-value store approach built on top 1800 of a relational data store to manage multidimensional scientific data as data cubes. A data cube allows data to be modeled and viewed in multiple dimensions. It relies on the dimensions and facts concepts:

• dimensions : represent the entities with respect to which it is desired to keep records and 1805 performs analysis. In my case-study, examples of dimensions in the .nc file containing the output of MarsCAM-NCAR program, are latitude, longitude, depth and time; • facts : numerical measures related to a central theme, by which it is desired to analyze relationships between dimensions. In my case study, examples are the air pressure, surface pressure, relative humidity (atmospheric output), surface and near-surface temperatures 1810 (land part) simulated variables.

49 Measure values are organized into arrays. Each array is identified by a key obtained from:

• explicit dimensions : combination of some dimension values. The dimension identifier is explicitly stored or reported in the key part of the key-value row: in my case-study, examples are latitude, longitude and depth. 1815 • implicit dimensions : other dimensions that identify a value through their position. Their identifiers are not stored in the key-value row at all: in my case-study, an example is the time dimension.

From a physical point of view, a data cube is horizontally partitioned into several blocks (called 1820 fragments) that are distributed across multiple I/O nodes. Each I/O node hosts a set of I/O servers optimized to manage n-dimensional arrays. These I/O servers manage a set of databases consisting of one or more data cube fragments. Analytic tasks on data cubes (i.e. on all fragments associated to a data cube) are performed by the Ophidia analytics framework. It is responsible for automatically processing and manipulating data cubes, by providing a common way to run distributive tasks 1825 (operators) on large set of fragments. Some examples of Ophidia operators are:

• datacube sub-setting (slicing and dicing); • datacube aggregation; • datacube duplication; 1830 • NetCDF file import and export.

In addition, Ophidia comes with an extensive set of primitives to operate on n-dimensional arrays (i.e. on the arrays contained in fragments). Currently available array-based functions allow: • data sub-setting; 1835 • data aggregation (i.e. max, min, avg); • array concatenation; • algebraic expressions; • predicate evaluation; • compression routines (i.e. zlib). 1840 As regards the storage of the cubes (see Figure 3.3), Ophidia uses the concept of container. Intuitively, it could be explained with the following associations (Palazzo, 2017): • folder : folder as that of a common OS; • container : the complete NetCDF file; 1845 • cube : the single variable extracted from the NetCDF file. • When data are imported in Ophidia environment, the process starts with a .nc file and from it the variables to be studied are extracted. Data referred to that variable (e.g. surface temperature TG, near-surface temperature TSA, pressure P, air temperature T, etc) form a cube. Another variable of the same .nc file will create another cube etc. The totality of all variables could generate a set of 1850 cubes which could be assembled in the same container. However, Ophidia doesn’t prevent to group cubes arbitrarily (depending on the user’s request). For this reason, the difference between “folder”

50 and “container” is vague and, as a consequence, the concept of container appears to be the same of “folder of cubes” (Palazzo, 2017).

1855 3.7.1 Working with Ophidia terminal

In this Section I show how it is possible to use Ophidia terminal in order to deal with climatic variables as those simulated with MarsCAM-NCAR software. Here only an easy example is reported in order to better explain the meaning of the definitions given in the previous Section. 1860 Suppose that we have to analyze the ground temperature (TG) for a specific place, e.g. MPF landing site for one MY. The necessary steps can be summarized as follows (the instructions to be written in the Ophidia terminal are reported in bold):

1865 1. search the dimensions by which TG is defined: these are lon, lat, time. 2. after concatenating all output files of the same type (see Section 3.7), download the .nc file (for example, named “land-5h routed.nc”) from Athena cluster to Ophidia server by specifying the variable to be studied (TG); 3. in Ophidia, create an appropriate container where to store the variable (for the meaning of 1870 each parameter, see the documentation online http://ophidia.cmcc.it/documentation/): oph_createcontainer container=land;dim=time|lat|lon|levsoi;hierarchy=oph_time| oph_base|oph_base|oph_base;units=d;calendar=no_leap;dim_type=float|float|float| float; One must be careful: when a container is created, it is necessary to include all the 1875 dimensions that characterize the set from which the variable is extracted (land group in this case). TG depends only on (lat, lon, time) but, for example, TSOI (sub-surface temperature, another land variable) depends also on levsoi. Moreover, attention must be paid to correctly indicate the right dimension data type (float, double, etc.), which can be found in the header of a .nc file (see Figure 3.2); 1880 4. import the TG variable into Ophidia in the container just created with the operator “oph_importnc”: oph_importnc src_path=/astro/land-5h routed.nc;measure=TG; imp_concept_level=6;imp_dim=time;container=land;exp_dim=lat|lon; ncores=1;description=TG_variable; 1885 where the “measure” parameter is used to indicate the variable to be imported (TG), “imp_dim” for the implicit dimension (time, see Section 3.7), “container” where to include the cube (here land), “exp_dim” for the explicit dimensions, “ncores” to indicate the number of parallel processes to be used for the calculations and “description” is an additional label that the user can add in order to rapidly distinguish the output cube. 1890 The variable to be processed is in the container. From the next step, all Ophidia algebraic operators can be applied to extract the information useful for the analysis. 5. before going further, as evidenced in Section 2.7, the first two years of the standard simulation must be excluded so to begin the investigation from the third year. To select it, a

51 1895 subset of the cube containing the values of TG must be extracted. Firstly, the cube must be explored: oph_cubeschema cube=http://193.204.199.174/ophidia/541/18944;level=1;dim=time; show_index=yes; The “oph_cubeschema” operator allows to show metadata information about a datacube and 1900 the dimensions related to it. The “cube” parameter is used to indicate the name of the input datacube (in PID format), “level” is used to show only dimension values (if set to 1 as in this example), “dim” serves for indicating the name of dimension to be shown and “show_index”, set to “yes” shows also the dimension id next to the value. After taking these indexes, the operator “oph_subset” is applied to extract only the values 1905 related with the first simulation year: oph_subset subset_dims=time; subset_filter=3:4; cube=http://193.204.199.174/ophidia/ 541/18944; description=TG_one_year; where subset dimension (time, parameter “subset_dims”) and the range on the indexes in which data must be extracted (3:4, parameter “subset_filter”) must be specified; 1910 6. to compute the averaged daily temperature for every 669 sols of one MY, the operator “oph_reduce2” must be applied:

oph_reduce2 dim=time;operation=avg;concept_level=d;cube=...1;description=TG daily_averaged; where the “operation” parameter is used to specify the reduction operation to be performed 1915 (here, an average) and “concept_level” identifies the hierarchy to be used for the operation (in this case, “d” stands for daily, so the operator will calculate a daily average by considering all data available for each sol/day). Note that Ophidia is set to manipulate Earth’s data. So, for my Mars case-study, the daily average is correctly evaluated, but the same instruction can’t be applied if a monthly or yearly Martian average is required. In the 1920 latter case, another operator, “oph_apply” must be used, by declaring the length of a Martian month and year. The list of numbers in the example contains the length of data available in each month of the 3 evaluable years of a standard simulation (see Section 2.7): oph_apply query=oph_reduce3('oph_float','oph_float',measure,'oph_avg',oph_to_bin('','oph_long 1925 ','278,276,276,276,277,276,276,276,277,276,276,262,276,276,276,277,276,276,277,276,27 6,276,277,261,276,277,276,276,276,277,276,276,276,277,276,262'));check_type=no;cube =...;dim_query=oph_get_index_array('','oph_float',1,36);description=TG_monthly_av erage 7. in this example, only TG values at the MPF landing sites must be considered. Again, as in 1930 the case of time dimension (step 5), the operator “oph_subset” is applied to extract only the latitude and longitude cell containing MPF coordinates from the cube created in step 6: oph_subset subset_dims=lat;subset_filter=11;cube=...;description=TG_averaged_lat; oph_subset subset_dims=lon;subset_filter=22;cube=...;description=TG_averaged;

1 In the following code rows in bold, in order not to weigh down the notation, the elipsis stands for the cube PID.

52 8. finally, the .nc file containing TG values, daily averaged in MPF location, according to 1935 MarsCAM-NCAR first evaluable year of simulation can be downloaded from the webpage associated to my personal Ophidia account thanks to the “oph_exportnc2” operator: oph_exportnc2 cube=...;output_name=TG_averaged MPF_landing site

The analysis related to TG at MPF landing site is ready to be carried out. In Section 3.8 I will show 1940 how these .nc files for MarsCAM-NCAR predictions were imported into the Matlab environment for the comparisons. In the next Section, I present an example of how it is possible to create, with Ophidia, dedicated scripts able to simultaneously manage several instructions.

3.7.2 An example of an Ophidia WF to process GCMs output 1945 As evidenced in Section 3.3, for MarsCAM-NCAR, the temporal evolution of the simulated climatic variables is not produced as a function of the LS values, but in terms of the seconds elapsed since the launch of the simulation. At the beginning of the Run, the clock of an observer located at longitude 0° of the “simulated” Mars marks 00:00 of the sol corresponding to LS = 0°. The model 1950 starts to count the seconds passed since this moment and computes the values of the atmospheric parameters as a function of the so defined “internal” time. The sol so individuated is labeled as the first sol (SOL 1) of the first simulated MY (668.6 sols long) for that simulation, and the following ones are numbered consecutively, each lasting 88642.663 seconds, i.e. the length of sidereal day (Urata and Toon, 2013a). Also the position of the planet (i.e. LS) is calculated in terms of the 1955 “internal” time just defined, so there is no direct correspondence between the simulated variables and the moment of the year at which they were computed. To obtain the temporal evolution of a climatic variable as a function of LS, I created an Ophidia WF able to match the two above-mentioned quantities. The operations performed can be summarized as follows (the meaning of the operators adopted is in accordance with Ophidia terminology; its 1960 documentation can be found online at http://ophidia.cmcc.it/documentation/index.html): • starting from the two .nc files containing respectively LS values and climatic variables (e.g. TSA) (interpreted by Ophidia as “cubes”), both previously concatenated in order to store in a single file all the data produced in a Run for the three available MYs (see Section 2.7), extraction of the values related to the cell of the model containing the landing site to be 1965 studied (oph_subset); • indication of LS extremes in which data must be extracted and also that of the related time dimension (the “internal” time), common to the two cubes (oph_apply); • searching in the LS cube the data (values of LS) having the time dimension falling in the LS range chosen (oph_set) after disposing it in the latitude, longitude, LS sequence 1970 (oph_explorecube); so two intermediate cubes were created, one having the LS values in the wanted range and the other with the corresponding time dimension values; • a for-cycle (oph_for) that, receiving in input the LS range, the corresponding time values, the gap in LS and the offset necessary to distinguish among data coming from three MYs, is able to extract, from the TSA cube for each MY, the values of this variable only in the 1975 chosen LS range;

53 • in this manner, six cubes were produced, two for each MY: one containing the LS values in the wanted range and the other with the corresponding TSA; they can be exported in .nc format (oph_exportnc2) for successive manipulations. In Figure 3.4 the related Directed Acyclic Graph (DAG) is reported, while in Appendix B the code 1980 written to build the WF is described. The direct dependence between the climatic variable and the related LS values for MarsCAM- NCAR output is so established: now the moment of the year the simulated variable refers to is known also for this GCM. In Chapter 4 how the datasets of the three MYs were merged for further manipulations will be specified. By importing them into Matlab, together with MCD output and 1985 observations, the behavior of TG and TSA trends during year, seasons and single sols can be finally shown and compared.

3.8 Import of NetCDF files into Matlab

As mentioned before, MarsCAM-NCAR output is organized in .nc files. Thanks to appropriate 1990 Ophidia WFs like that described in Section 3.7.2, the simulated climatic variables available in the NetCDF format are ready to be processed. In order to make the comparisons with MCD output, I imported them into the Matlab environment for further manipulations. A dedicated script was created to easily extract the physical information stored in these files. The code is reported below and rapidly commented (in red). 1995 Note that the manipulation of the files, after concatenation, was made by means of Ophidia and not directly with Matlab because, due to the big size of the output generated (see Table 2.2), the latter was noticeably slower than the CMCC tool in the extraction of the data stored in the .nc files.

**************************************************************************************************** 2000 % The function “extract2DataColumnsAndTime” receives as input parameters the content of two .nc files % storing the simulated variables (in this example, “TSA VKG1 99-101.nc”) and the associated LS values % (“LS VKG1 99-101.nc”). The function returns in output the values of TSA (obs_values), LS (Ls_values) and % the dimension time (time). The latter is used to extract the hour of the sol associated to each datum. function [obs_values, Ls_values, time] = extract2DataColumnsAndTime(fnameObs, fnameLS) 2005 % fnameObs and fnameLS are the variable used to call the .nc files containing the simulated datasets % produced with MarsCAM-NCAR program

resultsObs = extractData(fnameObs); % TSA VKG1 99-101.nc: temperatures 2010 resultsLS = extractData(fnameLS); % LS VKG1 99-101.nc: Ls values obs_values = cell2mat(resultsObs.varvalues); Ls_values = cell2mat(resultsLS.varvalues); time = resultsLS.dimvalues{3}; end 2015

% the “extractData” function is the one that perform the extraction of the simulated variables from the % output files. They are than stored in the “results” structure function results = extractData(filename)

2020 % opening the .nc to be examined ncid1=netcdf.open(filename,'NC_NOWRITE'); % searching for the number of variables and dimensions that characterize the .nc file (see Section 3.7 for % details)

54 [ndim,nvar,natt,unlim]=netcdf.inq(ncid1); 2025 % determining the number of variables stored in the .nc file nvartrue = nvar – ndim;

% creating and initializing cell arrays where to store data dimnames = cell(1, ndim); % cell for dimensions names 2030 varnames = cell(1, nvartrue); % cell for variables names dimlengths = zeros(1, ndim); % cell with size equal to dimension length dimidsTRUE = cell(1, nvartrue); % cell for variable dimvalues = cell(1, ndim); % cell for containing dimension to be extracted varvalues = cell(1, nvartrue); % the same for the variables 2035 % extraction of dimensions values and names for j = 1 : ndim [dimnames{j}, ~, ~, ~] = netcdf.inqVar(ncid1, j - 1); [~,dimlengths(j)]=netcdf.inqDim(ncid1, j - 1); 2040 dimvalues{j} = netcdf.getVar(ncid1, j - 1, 0, dimlengths(j)); end

% extraction of variables values and names for j = 1 : nvartrue 2045 [varnames{j}, ~, dimidsTRUE{j}, ~] = netcdf.inqVar(ncid1, ndim + j - 1); dimids = dimidsTRUE{j}; v1 = zeros(size(dimids)); v2 = zeros(size(dimids)); for k = 1 : length(dimids) 2050 v2(k) = dimlengths(dimids(k)+1); end varvalues{j} = netcdf.getVar(ncid1, ndim + j - 1, v1, v2); end

2055 % filling the “results” structure with the names and the values of dimensions and simulated variables results.dimnames = dimnames; results.varnames = varnames; results.dimvalues = dimvalues; results.varvalues = varvalues; 2060 netcdf.close(ncid1)

end

2065 ****************************************************************************************************

55 2070

2075

2080

2085

2090

2095 Figure 3.4: DAG of the WF used to associate a simulated climatic variable (from MarsCAM-NCAR program) with the corresponding value of LS. DAG created with Ophidia terminal. For the meaning of the various Ophidia operators adopted, see Ophidia terminal documentation. Three branches similar to the one shown are used for the extraction of the three simulated MYs.

56 2100

2105 CHAPTER 4

TG AND TSA COMPARISONS: SEASONAL/ANNUAL TRENDS (GROUP 1) AND DIURNAL CYCLE

2110 (GROUP 2)

2115

2120

57 2125 4.1 Comparisons: Group 1, seasonal and annual trends

Evaluating a climatic model output is a topic highly debated in the literature, resulting in many different approaches concerning the identification of the most appropriate technique, strongly case- dependent (Alexandrov et al., 2011; McIntosh et al., 2011). Bennet et al. (2013) listed the most 2130 widespread techniques applied to test environmental models, consisting in methods for measuring quantitative performance and methods for qualitative evaluation. In this study, I tried to match some of the features of both these strategies so to present a discussion as complete as possible. In particular, the focus was on the quantification of how well the two models reproduce a set of Mars surface and near-surface temperature measurements. 2135 The reliability of the two GCMs to reproduce present Mars temperatures was tested by dividing the observation/model comparisons into two different test groups: seasonal/annual trends (hereafter named “Group 1” analyses) and daily trends (“Group 2” analyses). All the computational work was done in the Matlab environment. 2140 4.2 Group 1

Group 1 was intended to evaluate the behavior of the two simulation software programs in the reproduction of temperature trends for extended intervals of time, in order to assess the quality of 2145 each tool by several measurements, e.g. by quantifying the maximum and minimum deviations in K from the observational data. The analysis was conducted for the four Martian seasons (spring, summer, autumn and winter) plus the complete annual trend, composed by aggregating data derived from all seasons and considered as the fifth one. The idea underneath this choice was to investigate whether one of the proposed models might be more accurate than the other in simulating 2150 temperatures in one or more specific seasons, or by considering a whole Martian year. Hereafter, the generic term “season” is used in abroad sense to indicate both the actual seasons and the whole year period. The list of the observational data available for surface temperature is reported in Table 3.3, while that for near-surface is in Table 3.4.

2155 This typology of comparison is a key point, especially for ancient Mars climate studies, for which long-run simulations must be performed (on the order of decades/centuries) starting from the climatic model adopted for present Mars conditions. In these works, in fact, the principal results processed are the trends of averaged seasonal and/or yearly temperatures, in order to find how long these temperatures can be hold over 273K (depending on the initial parameters chosen at the 2160 beginning of the simulations), so to sustain liquid water on the surface of the planet.

The idea at the basis of the comparisons was to establish how much each model output differed from the observations. I had to identify an approach able to quantify, in terms of differences in K, some kind of distance between the experimental curve, i.e. the one reproducing the observational 2165 data (for TSA or TG, for the eight landers/rovers), and the model curve, obtained with simulated data (MCD and MarsCAM-NCAR). Details on the distance used are given later in this Chapter.

58 Starting from daily data (see Sections 3.6 and 3.7), minima, averages and maxima TSA and TG temperature trends were calculated as a function of the solar longitude LS, selected as the time 2170 variable so to easily distinguish the data belonging to the various seasons. As mentioned in Section 3.6, usually only complete sols were considered in the calculation in order to avoid possible trend distortions due to incomplete daily observations: this is the reason why, sometimes, the trends are not continuous. In the particular case of SPI and OPP, where no observations were available for complete sols because only diurnal temperatures (09:00-18:00 local time) were recorded, only 2175 maximum temperature trends were computed. The model curves were obtained in a similar way so that, for each probe and for each sol considered, I finally had an experimental minimum/average/maximum TSA/TG point (when possible), and a corresponding minimum/average/maximum TSA/TG value calculated for each model Scenario/Run.

2180 Experimental data noise reduction deserved a special treatment. Martian climatic data were acquired with a variety of sensors. As a consequence, it is affected by different extents of noise, which makes it difficult to quantitatively compare the time series with the model outcomes in a homogeneous way. I decided to apply a different amount of denoising to the data, obtained by the Robust Locally-Weighted Scatterplot Smoothing (RLOWESS) algorithm, with a variable window 2185 size. RLOWESS is a robust version of LOWESS algorithm that assigns lower weight to outliers in the regression process (Cleveland and Devlin, 1988). In an effort of standardizing a heuristic method to choose the smoothing parameter, in particularly noisy cases, I applied smoothing in a loop with increasing window sizes, calculating each time the distance between the models and the (smoothed) experimental curves (see later for details on the distance used); I stopped when I 2190 remarked that distance reached a stationary point. I verified that this method gave consistent qualitative denoised curve appearance. For an example of the application of smoothing, see Figure 4.1.

Some probes have more than one sensor for the same variable measurement: I decided to hold these 2195 cases as independent measurements, so in all the subsequent treatment they actually count as multiple measures. The case of CUR is peculiar, in that there are more than three years of measures for TG and TSA (spread out into four Martian years, from MY 31 to MY 34): these time series too were considered as independent measures. As regards VL2, SPI and OPP, also multiple years of observations existed, even if in these cases the datasets available were not complete for each year. 2200 For this reason, for VL2 I decided to aggregate data referred to different MYs in a unique sample in order to cover almost one full year. In this way I avoided analyzing data related only to fractions of year that could be not sufficient to recreate temperature trends. So I chose to analyze, as reference values for this lander, the observations performed during MY 13 (which represent, between the two available, the largest dataset) completing them with data (when available) collected at the same LS 2205 during MY 12. For SPI and OPP, instead, I assembled, together with the complete MY 27 dataset, the very few data available for MY 26 (from LS = 334° to LS = 360°) and MY 28 (from LS = 0° to LS = 5°).

As to model output, also in this case it was necessary to perform some pre-processing tasks to avoid 2210 evident data defects. For MarsCAM-NCAR, I aggregate three simulated years into one (after verifying that the output data were compatible) so to obtain hourly measures. As concerns MCD

59 results, in some cases an artifact was remarked, in the form of evident high-frequency data ripples. Also in this case, some smoothing was applied to repair the signal. Figure 4.2 shows an example, concerning CUR temperature trends (min, mean and max TSA) compared with the model output. 2215 To quantify the accuracy of the simulation software in predicting TSA and TG trends, in terms of ~ the distance between observational ( yi) and model ( yi) curves (where the i index runs on the various values of a time series), several statistics were computed, in detail:

• RMSE (Root Mean Square Error): 2220 n (~y − y )2 RMSE= i i ∑ n (4.1) √ i=1 • CHEBYSHEV DISTANCE (CHEB), the maximum of the absolute value of the residuals:

~ 2225 CHEB=max i {|yi− yi|} (4.2)

• MSD (Mean Signed Deviation), the average residual (with sign):

n y −~y MSD=∑ ( i i ) 2230 i=1 n (4.3)

• ERR , the maximum and minimum residual (with sign).

I chose to calculate different statistics because each has a different meaning and can be useful to appreciate particular aspects of model performance, as concerns average and minimum/maximum 2235 errors, and temperature over- or underestimation. In more detail, RMSE and MSD are both averages, but the latter also informs on the sign of the deviation, i.e. whether the model is over- or underestimating on average the reference temperatures (respectively if the sign is + or -). A valid substitute for RMSE might have been the Mean Absolute Error (MAE) which anyway did not give significant differences in the conclusions I drew. These statistics are helpful because the value of a 2240 model must be assessed “on average”, without too much taking into account the presence of outliers in temperature forecasting. Nonetheless, it is also important to assess the maximum values of the errors that a model is likely to make: for this reason the ERR statistics gives the range of the errors (signed) while its absolute counterpart (CHEB) gives info on the magnitude of residuals. Before computing the mentioned statistics, model data were re-sampled to obtain estimated 2245 temperature values in the same temporal points as those of the observational data. These statistics were calculated for each combination of variable (TSA or TG), each probe, each season, and for all the available model Scenarios/Runs. RMSE has a special place in this analysis because I decided to use it in a voting system (the modified Borda-Count, described in Section 4.4) designed to support the comparison in the effort to decide which model configuration might be considered the best, if 2250 possible, for the reconstruction of particular data. Besides the min/mean/max trends, experimental diurnal temperature amplitudes were also examined and evaluated. A representative comparison is shown in Figure 4.3. A full analysis is not reported for space reasons.

60 Figure 4.1: Example of the smoothing procedure for noise reduction applied to TSA observational data, taken by CUR during all the MY 32.

61 2255 Figure 4.2: Comparisons between observations and model outputs for min, mean and max TSA trends. Measurements were carried out by CUR for the whole MY 32. For MCD, Scenario MY32 data are plotted, while for MarsCAM-NCAR Run 2 simulated data are shown.

62 Figure 4.3: TSA diurnal variations superimposed on the annual trend, present in the data measured by CUR (during MY 32) and in the GCMs simulations. Original (“OR”) and smoothed (“SM”) curves are shown both for observations and simulated datasets.

63 4.3 Comparisons criteria 2260 The criteria I adopted in the comparisons between the observations and the models are reported below: 1. I analyzed separately data related to surface temperature (TG) and that referred to near- surface temperatures (TSA), because the models use different equations to describe the two 2265 variables, so it appeared natural to differentiate;

2. for each variable, I defined nine different data aggregation cases with the aim of studying and describing GCM performance from different points of views: in case A (Table 4.1) all data (for min/mean/max trends in the whole year) were put together: this is useful for a global view of the performance of the two models; in cases B/C/D respectively minima, 2270 means, and maxima temperatures were considered, for the whole year; in cases E to I, data were aggregated per season, in the broad sense introduced in Section 4.2, e.g. by considering the whole year as a supplementary “season”, and according to Table 4.1, collecting together all the min/mean/max temperature trends. The reason of this approach was to be able to reply, if possible, to questions like e.g. which model performed better in spring (case F), or 2275 which model had better forecasting for daily minimum temperature for the whole year (case B). How these data aggregation cases were used is described in detail in Section 4.4.

Table 4.1: Data aggregations. In E to I aggregations, min/mean/max trends were considered together, in the chosen year period. CASE A the whole year , min / mean / max temperatures CASE B the whole year , min temperatures CASE C the whole year , mean temperatures CASE D the whole year , max temperatures CASE E year (LS∈[0°−360°]) CASE F spring (LS∈[0 °−90 °] for the NH , LS∈[180 °−270 °] for the SH) CASE G summer (LS ∈[90 °−180 °] for the NH , LS ∈[270 °− 360 °] for the SH) CASE H autumn (LS∈[180 °−270 °] for the NH , LS ∈[0 °−90 °] for the SH) CASE I winter (LS ∈[270 °− 360 °] for the NH , LS∈[90 °−180 °] for the SH)

2280 In Figure 4.4 I graphically clarify the meaning of the aggregation cases now introduced. Case A (Figure 4.4a) includes all the possible available data regarding all the landers/rovers considered. For the aggregation per type of measure (Figure 4.4b), once selected the trend to be studied (minima, means or maxima), only data related to it are processed, whatever is the season and the lander/rover considered. Aggregation per season (Figure 4.4c) fixes instead the season: once it was selected, only 2285 the three minima, averages or maxima trends related to the chosen season are taken into account, for all the landers/rovers where data are available.

3. The nine aggregation cases introduced at point 2 were employed to assess the behavior of the models in two analysis subgroups, respectively called Group 1a (all the probes were considered together) and Group 1b (where the focus was on the single lander/rover). This 2290 concept is explained in Figure 4.5.

64 With Group 1a (Figure 4.5a) I plan to test the output of the two GCMs by processing simultaneously all the data available for all the probes divided and classified according to the nine aggregation cases defined . With Group 1b (Figure 4.5b) instead I want to focus the attention on the ability of the two GCMs to reproduce the observational data in each of the eight landing sites by 2295 processing them individually.

Figure 4.4: Diagrams explaining the meaning of the nine aggregation cases (see text) created to perform comparisons. An example is shown for the three macro-aggregation cases: (a) all data; (b) aggregation per type of measure, maxima trends, case B; (c) aggregation per season, year, case E. Green rectangles signal the data considered in each case for the analysis. To avoid confusion, not all the seasons available for each 2300 aggregation case are shown in the diagrams, though obviously all of them were processed.

Figure 4.5: Schemes for (a) Group 1a, merge of all data of the same type deriving from all landers/rovers and (b) Group 1b, single estimations with data coming only from a single lander/rover.

65 In Section 4.4 I show the MBC voting procedure, while Section 4.5 clarifies how it was applied to 2305 the various cases. In this example, I describe practically my reasoning by applying all the steps performed to reach results both for Group 1a and Group 1b.

4.4 Modified Borda-Count (MBC) method

2310 The observations available for the comparisons, listed in Tables 3.3 and 3.4, could be interpreted and manipulated in many ways. In this study, a method is needed able to evaluate data coming from different sources (the landers/rovers) and to rank the performances (in terms of distances in K between theoretical and model curves, see Section 4.2) of the two GCMs, by processing the output derived by the several Scenarios/Runs discussed before. At the same time, the method has to take 2315 into account, in the decision process, the numerousness of the data available for each probe by assigning the most appropriate weight to the respective datasets.

With an abuse of terminology, hereafter the word “scenario” is used to refer both to one of the different MCD Scenarios and to a MarsCAM-NCAR Run obtained with a different initial

2320 parameterization. In order to choose the "best" scenario, if possible, an assessment method was applied, based on a voting system inspired by modified Borda-Count methods. The Borda-Count (Verma et al., 2001, Leon et al., 2017) is a (single-winner) election procedure in which candidates are ranked in order of preference. In the pattern recognition domain this system is used to choose among a set of candidate classifiers. The winner is determined by assigning each candidate an 2325 amount of points corresponding to the position in which it is ranked by each voter. The candidate with the most total points wins. In Modified Borda-Count (MBC) methods, each candidate is also given a “confidence value”, which is later used in establishing its overall vote. Moreover, each voter can be assigned a weight, which is also taken into consideration while calculating the final rank of each candidate. 2330 With this premise, the MBC is given by:

MBC=∑ r p w pc p (4.4) p

2335 where p counts the voters, wp is the voter weight, cp is a confidence measure, and rp is the rank (i.e. a score) associated to the placement of each candidate according to the confidence measure. Transposing this idea to the context of this thesis, for each scenario (i.e. Scenario 1, 7, … MY 24 for MCD, Run 2, 4, …, 12 for MarsCAM-NCAR, covering the role of the candidates) I imagined a certain number of voters, in particular the five “seasons” (defined in Section 4.3) times three trends 2340 (min/mean/max temperatures), giving an overall of 15 voters for TSA and 15 voters for TG. The voters assigned a decreasing placement to each model scenario (from best to worst) according to the RMSE distances of model output from the experimental measures (the lower the distance, the better the placement): in Group 1a the median of the set of the RMSE distances of the considered scenario from each probe measure was used (calculated with a weighted approach, where weights were the 2345 numerousness of each probe dataset), while in Group 1b the RMSE of each single probe had this role. The voter weights were proportional to the number of experimental points in the time series involved in the calculation of the distances (on the basis that a voter should have more weight, i.e. it

66 could be considered more reliable, if it had a larger set of measure points). The output of MBC was the global vote given to each candidate scenario, which allowed to build a classification of the 2350 various scenarios for a particular choice of voters. I made the voters express their votes in the aggregation cases detailed in Section 4.3, finally obtaining nine classifications (A to I) for TSA and nine for TG. In the usual Borda-Count, a voter ranks the candidates, and each candidate receives points (a ranking) from each ballot according to his position in the classification. Generally, a score equal to 1 – position/N (where N is the number of places considered, and position starts from 0) is 2355 used as ranking. Equal rankings are usually not permitted. In the case of interest, MBC was slightly modified to allow equal-rank candidates, which is the case when two or more scenarios have the same RMSE distance from the experimental data. Accordingly, I allowed tied candidates to share the score corresponding to the best placement of the group (because they all deserved the corresponding place in the list), and the candidate immediately following them maintained the 2360 points corresponding to its placement.

In Eq. (4.4) the confidence parameter cp is a value expressed as a percentage. I decided to use the median RMSE distance (for Group 1a) or the single probe RMSE distance (Group 1b) to express confidence. In particular, the conversion of the distance d to a value between 0 and 100, to be used as the confidence level c, was heuristically obtained by an exponential function of the form:

2365 c=α−d/ δ (4.5)

where α (the exponential base) and δ (the scaling factor) where chosen by considering that the exponential function should distinguish and consistently give confidence measures to distance values between 0K and about 30K (the typical RMSE values I got from the comparisons) and everything over 30K is to be considered quite rough (so confidence should rapidly go to zero). I 2370 finally opted for α = 2 and δ = 20K (see Figure 4.6) which give confidence equal to 0.5 for a distance value of 20K, with a rapid drop for larger distances, and reasonable confidence values for smaller median distances. In order to test the robustness of my decision, I anyway repeated the MBC calculations, varying on a grid of values both the exponential base (α values were 2, e, and 10) and the scaling factor (δ chosen between 5 and 50) finding that the conclusions taken by MBC 2375 were substantially consistent and robust to base/scale choice, within the indicated ranges.

2380

2385

Figure 4.6: Sensitivity tests performed on exponential base α (on the left) and the scaling factor δ (on the 2390 right) for MBC method.

67 4.5 An example of the MBC for Group 1a and Group 1b

In this Section I discuss an example of analysis by detailing the MBC voting procedure for case B of Group 1a, TSA observable: the same approach was adopted in all the aggregation cases defined 2395 in Section 4.3, for Group 1a and Group 1b, for both TSA and TG. The aim was to test the reliability of the various scenarios of the two GCMs in reproducing TSA minima trends in all the probe locations, in the whole year.

Once the observable (TSA) is fixed, all the RMSE distances (according to Eq. 4.1) were calculated 2400 between the experimental curve and the various model scenarios for each lander/rover in the five “seasons” (the MBC voters). Only minima trends must be considered for case B, and only in the available LS ranges (according to Table 3.4). As an example, one of the voters was the median distance for the time series related to (TSA, min, year); the median was computed by considering the distances calculated for the landers/rovers for which data were available for this season, that is: 2405 CUR, MY 31; CUR, MY 32; CUR, MY 33; CUR, MY 34; PHO; VL1; VL2.

For each of the five voting “seasons”, a classification of scenarios was defined, where all the competitors (the 15 MCD Scenarios plus the 7 Runs of MarsCAM-NCAR) were listed, in terms of 2410 increasing RMSE distance in K, from the closer to the farther with respect to the observational curve. Each voter was assigned a weight proportional to the total number of points used for RMSE calculation. In the example-case, for the voter here considered (TSA, min, year), the number of points for each available probe was:

2415 CUR, MY 31: 197; CUR, MY 32: 435; CUR, MY 33: 505; CUR, MY 34: 469; PHO: 138; 2420 VL1: 333; VL2: 600.

So, the weight to be used in MBC for this voter was proportional to 2677. The same approach was developed for the other voters (the remaining four seasons). 2425 Besides MBC, which is useful to get conclusions about the most performing scenarios, I decided to also adopt a pictorial way of examining the RMSE data for Group 1a, i.e. by box plots, which allow to analyze data dispersion with respect to the median value obtained for each scenario. Moreover, this graphic approach could be used also to individuate in which situations the simulations present 2430 outliers in some specific lander/rover datasets. In the case shown in Figure 4.7, for example, it can be noticed that almost all of MCD Scenarios present outliers referred to VL2 distances; on the other hand, MarsCAM-NCAR shows outliers in all the Runs for PHO observations, and, for the first three Runs, also for VL1 (the lower values).

68 2435

2440

2445

2450

Figure 4.7: Box plots obtained for the example-case discussed in Section 4.5, TSA, minima trends, year. The distance on the y-axis are in K. 2455 When all the voters had voted, providing their particular classification where each candidate was assigned a placement (giving a ranking score) and a confidence measure (calculated from the median RMSE), the MBC method could be applied. In fact, the purpose of MBC is to merge the vote results registered by the five classifications (the votes) according to the weight of each voter. 2460 Remembering the terminology adopted for the MBC method (discussed in Section 4.4), for TSA variable, case B of Group 1a now detailed (i.e., TSA minima trends), made up of all the data provided by all the landers/rovers for which observations were available, it results:

• candidates : Scenarios (Scenario 1, 2, MY 24, …, MY 33 for MCD; Run 2, 4, …, 12 for 2465 MarsCAM-NCAR); • voters : five seasons (year, spring, summer, autumn, winter), only minima trends (available for all of them), thus resulting in five voters; • classifications of candidates : obtained by each candidate on the basis of the median distance calculated from the RMSE statistics of all the probes; 2470 • confidence : defined in Section 4.4 as a negative exponential function of the median distance; • weight : total number of experimental points for the voter; in this example-case, for the whole year, 2677 (the sum of the experimental points coming from the available landers/rovers datasets, see before); • rank : the score of each candidate in each of the single landers/rovers classifications (related 2475 to its placement). The results obtained for this example-case are reported in Table 4.2. The procedure now discussed was applied also to the other eight aggregation cases (see Section 4.3) of Group 1a.

69 Table 4.2: Classification obtained with MBC method for TSA, case B (min voters) in Group 1a. The ranks reported under the MBC column are normalized as discussed in Section 4.4. The values related to CHEB and 2480 RMSE columns (see Eqs. 4.2 and 4.1) are in K.

A similar approach was performed for Group 1b (single analysis per lander/rover). After collecting the RMSE distances between the observational curve and the model outputs, MBC method can be applied. For example, consider CUR rover observation for MY 33. Once the TG variable is fixed, 2485 suppose to test the various scenarios on reproducing spring season temperatures. According to the cases listed in Section 4.3, case F is that evaluated. Three voters can be considered (minima, averages and maxima trends), each with the same number of points compared (133). In the MBC formula (Eq. 4.4), it is enough to insert the distances collected. Summing up, for this case:

2490 • candidates : Scenarios (Scenario 1, 2, MY 24, …, MY 33 for MCD; Run 2, 4, …, 12 for MarsCAM-NCAR); • voters : three trends (minima, averages and maxima); • classifications of candidates : those obtained in each of the three trends, according to RMSE metrics; 2495 • confidence : defined in Section 4.4;

70 • weight : number of points compared, in this example-case, for each of the three trends, 133; • rank : the placement of each candidate in each of the three classifications.

The results obtained for Group 1a and Group 1b, both for TG and TSA, are discussed in Section 2500 5.2. As clarified there, other statistics were considered besides MBC evidences (see Section 4.2) and computed in order to have an overview as complete as possible of the comparisons made. The approach now presented led me to get outcomes concerning the performance of each Scenario/Run considered individually. Moreover, also a global evaluation of the performances of the two GCMs was developed for Group 1a and 1b in each of the aggregation cases proposed. 2505 4.6 Exceptions for Group 1 analysis

Basically, in the tests I performed for seasonal and annual trends, for all the seasons in which observational data were available (see Tables 3.3 and 3.4), the general rules discussed in Section 4.2 2510 were adopted. However, the following exceptions must be pointed out that I have to deal with in the discussion of the results obtained for Group 1a and Group 1b:

• for SPI and OPP rovers, only maxima trends were compared because, as reported in Section 1.5, only diurnal measurements (09:00-18:00 local time) were performed (Smith et al., 2515 2006) which allowed to calculate only the maximum daily temperatures. Consequently, for Group 1b, I could test the behavior of the two GCMs in all cases but cases B and C, respectively related to minima and means temperatures. The conclusions I reached for SPI and OPP are therefore partial and to be considered within these limits; • for CUR rover, more years of observations were available. I decided to treat and study 2520 separately the data collected in each MY, as if the time series were acquired by different probes; • in some cases (TSA for INS, TG for SPI, OPP, INS) multiple measurements were provided of the same observable taken by the same lander but with different instruments. I considered all of them separately, and processed as in the case of the different MYs of 2525 CUR.

4.7. Comparisons: Group 2, daily trends

Together with seasonal and annual trends, I tested the output of the two GCMs in the forecasting of 2530 temperature daily cycles. The purpose was to verify the ability of the two climatic models to reproduce the hours of the sol in which minimum and maximum temperatures are expected to be observed. In the next Sections, the statistical methods applied to Group 2, similar to the analysis performed for Group 1, are described.

2535 4.7.1 Group 2: features

In order to evaluate daily cycles for all the periods of the year, I split a MY into twelve slots, to be used as voters in the MBC scheme. Each slot was centered on a reference LS value, defined so to gather data every 30° in LS, starting from 0° up to 330°. The relation between the duration of a sol

71 2540 and one degree in LS varies according to the season (see Section 3.5.2) but with a good approximation it can stated that, on average, a sol corresponds to about 0.5° in LS. With the chosen time-step, data were approximately collected every 60 sols, which means about every month (the duration of a Martian month varies from 46 to 66 sols, see Section 3.5.3).

2545 In Table 4.3 the available and processed observational data from the eight landers/rovers for TG are reported, while in Table 4.4 an analogous list is provided for TSA. In some cases, due to the lack of data and/or to the short duration of the missions, enough time slots could not be collected, so “extra” LS values were taken into account in order to increase the number of voters. The total number of cases examined could vary accordingly. 2550 Once the LS values for which comparisons must be made were fixed, the sol closer to each reference LS was taken as the central sol of a 21-day-wide time window (ten sols before and ten after, when possible). As it is better explained in Section 4.7.2, I processed many consecutive sols together for each LS slot to reduce disturbances due to exceptional phenomena (e.g. dust storms) or 2555 anomalous measurements caused by instrumentation noise or faults. The chosen number of days was considered adequate to have clean information on temperature cycles, without suffering too much from seasonal variations

For each probe, a report similar to the one shown in Table 4.5 was filled to indicate the sols 2560 (numbered according to the recognition label assigned in that mission) taken into account for the slot, based on the available data, and the interval of LS spanned. For space reasons, I do not report all the prospects created.

Obviously, as it emerges by consulting Tables 4.3 and 4.4, it was not always possible to obtain such 2565 information and datasets for all the landing sites and for all the slots considered. In fact:

• in some cases, some data were lacking for specific LS values (blank rectangles); • in others, the number of sols considered was lower than 21 (orange rectangles): i.e., VL2, TSA, LS = 90°, or OPP, TG, LS = 240°; 2570 • sometimes, the number of available sols was not enough to reproduce a daily trend (red rectangle): i.e. SPI, TG and TSA, LS = 210°; in these cases, the data were excluded from the analysis; • finally, it happens that the value of LS at which data were available w not perfectly centered on the reference LS (blue rectangles). For example, for CUR, TG, LS = 150°, no data were 2575 available, and the closer central LS value was 160°, so 21 days were considered (where possible) within an interval of ± 10 sols from the new reference. The same happened also for PHO, TSA, LS = 75°: in this case, the sol with LS = 81° was taken as central.

72 Table 4.3: List of sols processed for Group 2, in terms of range in LS, in which surface temperature measurements were available. An example of the exact 2580 indications of the sols considered for a probe, OPP, as well as the LS range, is reported in Table 4.5. In the “extra” column, the “out of collection” LS values considered are reported. In the last column, instead, the total number of LS slots evaluated for each lander/rover is shown. Legend: X = complete dataset for this LS value is available (see text); blank space = data not available in that range; * = for SPI and OPP rovers, data refer only to diurnal hours (09:00-18:00 local time), see text; orange = sols considered are less than 15; blue = sols not centered on the LS reference value, but in the nearest neighborhood available; red = few observational data, not enough to allow the reproduction of the daily trend, so not included in the analysis. 2585

LAND/ROV MY LS (°) EXTRA TOT 0 30 60 90 120 150 180 210 240 270 300 330

2590 SPI (near) 26/27/28 X X X X X X X X X X X X 75, 105, 225, 255 15* SPI (upview) 26/27/28 X X X X X X X X X X X X 75, 105, 225, 255 15*

OPP (near) 26/27/28 X X X X X X X X X 75, 105, 164, 255, 348 14* OPP (upview) 26/27/28 X X X X X X X X X 75, 105, 164, 255, 348 14* 2595 CUR 31 X X X X X X X 225, 255 9 CUR 32 X X X X X X X X X X X X 75, 105, 225, 255 16 CUR 33 X X X X X X X X X X X X 75, 105, 225, 255 16 CUR 34 X X X X X X X X X X 75, 105, 225 13

2600 INS (FOV 1) 34/35 X X 314,346 4 INS (FOV 2) 34/35 X X 314,346 4

2605

73 Table 4.4: The same as Table 4.3, but for near-surface temperatures. The height at which measurements were taken is listed in Table 3.4.

2610 LAND/ROV MY LS (°) EXTRA TOT 0 30 60 90 120 150 180 210 240 270 300 330

VL1 12 X X X X X X 105, 225, 255, 291 10 2615 VL2 12/13 X X X X X X X X X X X X 105, 225, 255 15

MPF 23 X / 1

SPI 26/27/28 X X X X X X X X X X X X 75, 105, 225, 255 15* 2620 OPP 26/27/28 X X X X X X X X X 75, 105, 164, 255, 348 14*

PHO 29 X X X 75, 105, 130 6

2625 CUR 31 X X X X X X X 225, 255 9 CUR 32 X X X X X X X X X X X X 75, 105, 225, 255 16 CUR 33 X X X X X X X X X X X X 75, 105, 225, 255 16 CUR 34 X X X X X X X X X X 75, 105, 225 13

2630 INS (BOOM +Y) 34/35 X X 312,343 4 INS (BOOM -Y) 34/35 X X 312,343 4

2635

74 Table 4.5: Example of collection of sols for Group 2. Data are referred to TSA OPP measurements, MY 26/27. The numbering associated to each sols refers to the label assigned to that sol since the first of measurement for the mission. Where data are missing, a “/” sign is inserted. The second column reports the number of the sol in the mission closest to the reference LS value (first columns). The true LS value is in the third column. In the forth, the sols considered in this range are shown, 2640 while in the fifth the range in LS covered with the sols considered is listed. The last column counts the total number of sols processed for that value of LS. Finally, separated rows related to the “extra” LS values considered (see text) are reported outside the main table.

OPPORTUNITY – TSA/TG (near) REF. LS N° CENTRAL SOL TRUE LS (°) OF START/END SOLS LS (°) RANGE TOT CENTRAL SOL COVERED SOLS 0 41 0.26 30-51 354.68 – 5.35 15 30 102 30.19 92-112 25.42 – 34.89 21 60 167 60.05 157-177 55.46 – 64.56 21 75 201 75.22 191-211 70.74 – 79.76 21 90 235 90.60 220-245 83.75 – 95.21 21 105 267 105.18 257-277 100.68 – 109.99 21 120 299 120.28 289-309 115.51 – 125.27 21 150 358 150.02 348-368 144.74 – 155.40 21 180 / / / / / 210 / / / / / 225 / / / / / 240 510 240.77 506-521 238.15 – 247.92 10 255 532 255.13 522-542 248.43 – 261.60 21 270 555 270.02 545-562 263.41 – 274.57 18 300 603 300.22 593-609 294.06 – 304.04 15 330 / / / / /

EXTRA 164 385 164.51 375-395 159.00 – 170.13 19 348 19 348.90 9-27 343.52 – 353.11 15

75 As it was not always possible to collect a complete set of time slots for all the desired central LS 2645 values, with the purpose of enriching the number of LS windows considered and have a more detailed analysis, some “extra” LS slots were included, reported in the columns named “extra” in Tables 4.3 and 4.4.

Finally, for MPF, data were available only for one LS slot, due to the short duration of the mission 2650 and, moreover, not all the available sols in the range were fully covered in terms of measurement hours (see Figure 4.8). Consequently, to make the data for MPF substantial, 28 sols were aggregated instead of 21. Furthermore, even if the mission lasted up to LS=180°, for the remaining sols after mission sol 30, it was not possible to aggregate the few data available so to reproduce a whole daily cycle in a satisfactory way. Moreover, being the remaining sols spread on a long period, the 2655 seasonal variation could have strongly impacted on the distances between experimental and model curves, distorting the results.

Figure 4.8: Available TSA measurements for MPF in all the sols of the mission. In the y-axis, TSA (K) is reported, while in the x-axis, the local time (in hours). At the top of each windows, the number of the mission-sol is signaled. 2660 4.7.2 Diurnal data processing

The basic idea of diurnal cycle comparisons was again that of studying, for the various LS slots, the distances registered between the experimental curves and those deduced by the different scenarios 2665 of the two GCMs. In Section 3.5.1 it was already evidenced how observational data were acquired and stored with different sampling rates. As performed for Group 1 (see Section 3.6), in order to make the analysis more homogeneous, these data were re-sampled at lower rate (after excluding sols for which a complete coverage for all hours was not provided) preserving only one sample per hour and averaging temperature values in small windows around the chosen values in order to 2670 reduce noise. A similar approach was applied also for the two GCMs output. Now, taking into

76 account consecutive sols (as proposed in the preceding Section) led to consider, for each slot, a short LS interval centered on the reference value (see Table 4.5), so multiple values of temperatures for the same hour are available. By these data, plots similar to Figure 4.9 were built as follows. In order to reproduce the diurnal cycle and, at the same time, reducing noise, observational 2675 temperatures contributing to the same hour were therefore averaged over the sols included in each LS interval and error bars were calculated by data standard deviation. The error bars essentially summed up the diurnal fluctuations over this time period and, to a lesser extent, seasonal variation, which was kept as small as possible by appropriately choosing the length of the considered time slots (21 days, as mentioned in Section 4.7.1). A similar approach was performed by Urata and Toon 2680 (2013a) for testing the output of MarsCAM-NCAR over OPP surface and near-surface measurements. Model data were similarly averaged, though with different time sampling.

4.7.3 Statistical approaches applied for Group 2

2685 Also for Group 2 comparisons the same approaches adopted for Group 1 were performed in order to evaluate the ability of the two GCMs to reproduce diurnal temperature cycles. As already explained in Section 4.5, for global comparisons (Group 2a, see Section 4.7.4) box plots representation was used, before applying MBC method, to the medians deduced from the RMSE distances while, for single comparisons (Group 2b, see Section 4.7.4), MBC was directly employed to RMSE distances. 2690 Also CHEB, MSD and ERR statistics were computed for each cases, together with the results registered for each GCM by considering together all the Scenarios/Runs related to that climatic model. The only difference between the two analyses consisted in the nature of the MBC voters. In fact, while for Group 1a and 1b the voters were the combinations between seasons and the min/mean/max trends, for Group 2a and 2b their role was covered by the LS slots. This because, 2695 due to the lack of data, evaluating diurnal trends by means of seasons could lead to consider seasonal effects, falsifying in this way the aim of these kind of comparisons.

4.7.4 Cross-checks performed for Group 2

In the analysis, data aggregations similar to those introduced in Section 4.3 were considered, with 2700 the exclusions of case B (minima), case C (averages), and case D (maxima). So the aggregations taken into consideration for Group 2 were case A (all data), coinciding with case E (year), case F (spring), case G (summer), case H (autumn) and case I (winter).

The following analyses were performed for TG and TSA, the voters for MBC being the LS slots 2705 (see Section 4.7.1) and listed in Tables 4.3 and 4.4:

• global comparisons by considering data from all the landers/rovers (case A, Group 2a); • global comparisons by considering data of all the landers/rovers for each season (cases E-I, Group 2a), with the seasons composed of the corresponding LS slots; 2710 • single comparisons for each landers/rovers with all data (case A, Group 2b); • single comparisons for each landers/rovers in the available seasons (cases E-I, Group 2b).

77 Figure 4.9: Example of comparison performed for Group 2, in the case of CUR, MY 33, for TG at LS = 330°.

78 2715

2720 CHAPTER 5

RESULTS OF THE COMPARISONS BETWEEN GCM-LMD AND MARSCAM-NCAR OUTPUT WITH

2725 TG/TSA OBSERVATIONAL DATA

2730

2735

2740

79 5.1 Discussion of the results obtained

In this Chapter the results for Group 1 (seasonal and annual trends) and Group 2 (daily cycles) 2745 comparisons are presented. A word of caution must be expressed as concerns the discrepancies between experimental and model data. It was impossible, in most cases, to establish the measurement errors which affected the observational data (because the information was usually not available and because smoothing was frequently necessary to be able to treat the data). Moreover, model output uncertainties, due to model parameter accuracy, to the necessary spatial and temporal 2750 sampling and to the approximations introduced in the model formulations, were also very difficult to quantify, so that the efforts to give a trustworthy estimation would be with no doubt weak and questionable. For these reasons, no attempt was made to assign an error value to the quantities examined in the next Sections, and the conclusions can be considered valid only in this limit. Accordingly, I preferred not to impose any hard threshold on the values of the statistics used to 2755 quantify model quality, reporting also under- and overestimation outcomes as small as a few K.

5.2 Group 1 results

For the sake of clarity, the results obtained for Group 1a and Group 1b are presented separately.

2760 5.2.1 Evidences for Group 1a

In Table 5.1 the outcomes of the analysis performed for Group 1a are reported, both for surface temperatures (TG, Table 5.1a) and near-surface temperatures (TSA, Table 5.1b).

2765 A preliminary evidence concerns MCD Scenarios 1 to 3 for both TG and TSA. From the calculation of the distances between the observational data and the output generated within these three Scenarios, it emerges that, in every aggregation cases, whatever the lander/rover, the period of the year and the trend (min/mean/max) considered, the three scenarios produced identical distances. This happened because (see Section 3.1) the principal difference between them is related to the 2770 Solar EUV conditions (min, mean or max for Scenario 1, 2 and 3 respectively) whose influence is evident only for atmospheric variables evaluated in the Thermosphere (Millour and Forget, 2018). Consequently, as surface and near-surface temperature trends are compared, an equal behavior was expected. Accordingly, the rank obtained from MBC method when evaluating the performance of the three Scenarios was the same, in conformity with the approach used to the treatment of tie 2775 candidates (see Section 4.4).

2780

80 Table 5.1: Group 1a results for (a) surface temperatures and (b) near-surface temperatures. For each of the nine aggregation cases, the most voted Scenario/Run of 2785 one of the two GCMs (column 2) is reported. The statistical evidences (columns 4-9) for the best MCD Scenario (column 3) and those (columns 15-20) of the best MarsCAM-NCAR Run (column 14) are also shown. Moreover, for each GCMs, a global overview performed by considering together all the results registered by the related Scenarios (columns 10-13) for MCD and Runs (columns 21-24) for MarsCAM-NCAR are provided. As regards the meaning of the statistical quantities, in columns 4 and 15 the places in the classification for that case for the Scenario/Run considered, according to MBC, are reported, while in columns 5 and 16 MBC rank is indicated. For RMSE, CHEB and MSD, see Eq. 4.1, Eq. 4.2 and Eq. 4.3 respectively, for ERR see Section 4.2. In the MSD columns, when “<~1” is reported, 2790 it means that the deviations “model output - observational data” are in the range [-1, +1] K.

a TG MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 9 40 <~ 1 [-17, +40] 9-13 33-46 [+1, +2] [-29, +46] 4 2 0.880 9 39 <~ 1 [-19, +39] 9-10 39-40 [-1, 0] [-26, +40] B MCD 7 1 1 5 17 -2 [-17, +17] 5-11 16-28 [-10, -2] [-29, +20] 4 2 0.991 6 19 -3 [-19, +15] 6-9 19-24 [-7, -3] [-24, +15] C MARSCAM 7 6 0.695 7 13 -7 [-13, +8] 7-8 13-14 [-8, -6] [-14, +8] 2 1 1 6 13 -4 [-13, +8] 6-8 13-15 [-7, -4] [-15, +10] D MCD 7 1 1 11 40 +6 [-16, +40] 11-15 33-46 [+6, +11] [-18, +46] 10 3 0.732 12 39 +4 [-18, +39] 11-13 39-40 [+1, +4] [-26, +40] E MCD 7 1 1 9 40 <~ 1 [-17, +40] 9-13 33-46 [+1, +2] [-29, +46] 4 2 0.945 9 39 <~ 1 [-19, +39] 9-10 39-40 [-1, 0] [-26, +40] F MCD 7 1 1 12 33 +2 [-10, +33] 12-19 33-46 [+4, +5] [-29, +46] 2 3 0.963 14 39 +5 [-19, +39] 14-15 39-40 [+4, +5] [-24, +40] G MARSCAM MY 28 5 0.770 8 22 <~ 1 [-14, +22] 8-13 22-33 [0, +2] [-17, +33] 2 1 1 8 26 <~ 1 [-10, +26] 8-9 26-28 [+1, +2] [-13, +28] H MCD 7 1 1 8 19 <~ 1 [-13, +19] 8-10 19-22 [0, +1] [-18, +22] 4 7 0.578 7 16 -3 [-16, +14] 7-9 19-22 [-4, -3] [-25, +14] I MCD MY 27 1 1 6 22 <~ 1 [-13, +22] 6-7 18-23 [-2, -1] [-18, +23] 5 5 0.741 7 20 -4 [-20, +17] 7-9 17-26 [-5, -4] [-26, +17]

b TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 3 0.960 7 23 -3 [-18, +23] 7-10 18-24 [-7, -3] [-24, +24] 4 1 1 7 27 <~ 1 [-16, +27] 7-8 26-29 [-4, -1] [-22, +29] B MCD 7 1 1 6 23 <~ 1 [-12, +23] 6-9 17-24 [-5, -1] [-21, +24] 8 2 0.755 8 22 <~ 1 [-15, +22] 8-9 22-23 [-1, +2] [-15, +23] C MCD MY 27 1 1 8 16 -6 [-17, +9] 7-10 14-18 [-7, -5] [-18, +13] 2 3 0.894 7 14 <~ 1 [-11, +14] 7-8 12-15 [-4, -1] [-15, +14] D MARSCAM 7 4 0.878 7 23 -4 [-18, +23] 7-10 18-24 [-8, -4] [-24, +23] 4 1 1 6 28 -2 [-16, +28] 6-9 26-29 [-5, -2] [-22, +29] E MARSCAM 7 3 0.885 7 23 -3 [-18, +23] 7-10 18-24 [-7, -3] [-24, +23] 4 1 1 7 27 <~ 1 [-16, +27] 7-8 26-29 [-4, -1] [-22, +29] F MARSCAM 7 3 0.879 7 22 -3 [-15, +22] 7-11 18-24 [-9, -3] [-24, +24] 2 1 1 7 21 -2 [-16, +21] 7-8 20-22 [-4, -2] [-21, +22] G MCD 7 1 1 7 16 -3 [-16, +12] 7-10 16-20 [-6, -3] [-21, +14] 11 8 0.806 8 23 <~ 1 [-12, +23] 8-9 22-23 [-2, +1] [-17, +23] H MARSCAM 7 6 0.886 6 15 -3 [-12, +15] 6-8 14-20 [-6, -3] [-20, +16] 4 1 1 5 16 <~ 1 [-11, +16] 5-6 14-16 [-4, -1] [-15, +16] I MARSCAM 7 4 0.923 8 23 -3 [-18, +23] 8-10 18-24 [-7, -3] [-24, +24] 4 1 1 8 28 -2 [-18, +23] 8-10 26-28 [-5, -2] [-22, +29]

2795

81 From TG analysis (Table 5.1a), by examining the MSD column, it emerged that:

• according to the overall case A, MCD slightly overestimates of at maximum 2K the 2800 observational data, while MarsCAM-NCAR is in better agreement with them (~ 1K less than the reference data); • focusing on aggregation per type of measure MCD underestimates minima and averages trends (cases B and C) but overestimates maxima trends (case D). MarsCAM-NCAR has a similar behavior even if the differences are slightly lower; 2805 • for aggregations per seasons, MCD presents data very close to the observations, with the exception of spring, for which a global overestimate was registered, on the order of at maximum 5K. MarsCAM-NCAR also similarly overestimates TG in spring, but tends to underestimate TG during winter and autumn, of about 4-5K at maximum; • according to MBC method and RMSE statistics, the two simulations closer to the 2810 observational data in all the aggregation cases evaluated were, respectively, Scenario 7 for MCD and Run 4 for MarsCAM-NCAR.

In the RMSE column, very small differences (few K) were registered in the ranges obtained for the two GCMs: the values are of the same order in all the nine aggregation cases investigated A to I, 2815 with a global average interval of about 9-10K. Analyzing the CHEB column the same conclusions can be derived: the ranges observed for both programs are of the same entity for all the nine cases processed. Finally, the minimum and maximum error registered in the comparisons between observations/model output, according to the ERR column, is of the same order for MCD and MarsCAM-NCAR scenarios in all the cases, with differences of at maximum 8K in some seasons, 2820 e.g. autumn and winter.

For TSA analysis (Table 5.1b), instead, it emerged that:

• generally (case A), MCD underestimates observational data, ranging between -7K and -3K, 2825 as it happens also for MarsCAM-NCAR program, with differences from the reference values fluctuating from -4K (maximum) to -1K (minimum); • as regards measurements trends, also for these categories MCD underestimates temporal trends, minima (case B) of about -5K at most, means (case C) of about -7K and maxima (case D) of about 8K; MarsCAM-NCAR presents a similar behavior for means and maxima 2830 trends, even if with lower discrepancies (about -5K), while for minima trends a slight overestimation is observed, only of a couple of K; • for seasonal trends, both MCD and MarsCAM-NCAR programs tends to underestimates the temporal trends of observational data, with the latter presenting a slight closer behavior (only 2K deviations on average) to the reference trends. Also for MarsCAM-NCAR, a 2835 negligible overestimate (only 1K) was registered in summer; • according to MBC method and RMSE statistics, the two simulations closer to the observational data in all the aggregation cases evaluated were, respectively, Scenario 7 for MCD and Run 4 for MarsCAM-NCAR.

82 2840 RMSE ranges estimated for MCD and MarsCAM-NCAR were very closer in all the aggregation cases A to I, generally of the order of 7-10K. For CHEB distances, instead, higher values, on the order of 8K, were obtained in the lower limit of the range for MarsCAM-NCAR software with respect to MCD. Finally, the ERR intervals observed were similar for the two GCMs, ranging from -24K to +29K, with the upper limit lower than that registered for TG (which was about 40K). 2845 5.2.2 Evidences for Group 1b

In Table 5.2 the results obtained for Group 1b are reported, for TG (Table 5.2a) and TSA (Table 5.2b). In these Tables, only global statistics for all the scenarios of each GCM are reported (i.e. the 2850 15 Scenarios for MCD and the 7 Runs of MarsCAM-NCAR) and not those concerning the most voted scenarios. In Tables C1-C22 of Appendix C the detailed report performed for each lander/rover, both for TG and TSA, is reported. The results shown were obtained with the MBC method described in Section 4.4.

2855 It must be noted that: • for SPI and OPP (Section 1.5), only daily measurements (09:00-18:00 local time) were collected, so only maxima trend (case D) could be analyzed; • the argumentation presented in certain cases is limited by the few data available: this occurs for MPF and PHO, due to the short mission duration (see Table 1.1), and for INS, 2860 due to the few acquisitions performed and published in the referring PDS node page at the time of writing of this thesis;

As regards to MarsCAM-NCAR simulations, it must be pointed out that the output of different Runs for Group 1 is very similar when initial-parameter variations between the Runs are local (see 2865 Table 3.1) and thus have almost no impact on most of the probes. This lead to output differences between the Runs below 1K and to very similar distances from the observational data, apart from computational fluctuations. So, in Table 5.2, when a Run is indicated as the closest to the observations, it must be intended that the “twin” Run(s) is (are) equivalent. In detail (Table 3.1):

2870 • for VL1 and VL2: all the seven Runs performed were different; • for OPP: Run 4 = Run 5 and Run 8 = Run 10; • for MPF, SPI, PHO, CUR, INS: Run 2 = Run 4 = Run 5 and Run 8 = Run 10.

For this software simulator, I decided to reproduce the same Runs as those presented by Urata and 2875 Toon (2013a) in order to test the impact of the change of initial physical parameters (albedo, thermal inertia and dust OD) on TG and TSA trends. By assigning the reference values measured in VL1, VL2 and OPP landing sites for these variables (see Tables 1.2 and 3.1), evident improvements were effectively noticed with respect to the base-dataset maps provided by the authors (those used for Run 2). For example, according to MBC method, Run 8 resulted the best Scenario, for 2880 MarsCAM-NCAR, in the reproduction of VL1 TSA data, as well as Run 10 for VL1 TSA trends and Run 4 for OPP TG and TSA ones.

83 Table 5.2: Group 1b results. The statistical values globally describe all the Scenarios/Runs associated to each GCM. In the SPI and OPP cells, a “*” reminds that only maxima trends are available (see text). a TG 2885 MCD MARSCAM LAND/ROV MY RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K)

SPI (upview)* 27 15-20 26-34 [+11, +17] [-14, +34] 14-15 28-29 [+8, +9] [-18, +29] SPI (near)* 27 18-23 33-43 [+14, +20] [-10, +43] 16-18 38-39 [+11, +12] [-14, +39]

OPP (upview)* 27 6-8 11-17 [-1, +4] [-11, +17] 8-15 14-26 [-13, -3] [-26, +12] 2890 OPP (near)* 27 6-9 11-20 [0, +5] [-11, +20] 8-14 16-26 [-12, -1] [-26, +17]

CUR 31 7-12 12-20 [-2, 0] [-17, +20] 7-8 13-14 [-2, 0] [-13, +14] CUR 32 6-11 13-23 [-2, -1] [-18, +23] 6-8 16-17 [-4, -2] [-13, +17] CUR 33 7-10 13-18 [-4, -3] [-18, +16] 6-8 15-16 [-4, -3] [-16, +9] CUR 34 7-12 30-46 [-2, -1] [-39, +46] 9-11 39-40 [-4, -2] [-24, +40] , 2895 INS (FOV 1) 34/35 5-11 12-20 [-1, 0] [-17, +20] 9-11 17-20 [-2, 0] [-20, +14] INS (FOV 2) 34/35 3-6 7-18 [-3, -1] [-18, +11] 6-7 13-16 [-4, -3] [-16, +5]

b TSA MCD MARSCAM LAND/ROV MY RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K)

2900 VL1 12 6-8 16-21 [+3, +7] [-9, +21] 7-11 26-29 [+4, +10] [-9, +29]

VL2 12/13 4-6 14-18 [-4, -2] [-18, +9] 4-6 13-16 [+1, +4] [-12, +16]

MPF 23 5-6 8-11 [-4, -1] [-11, +6] 6-8 8-13 [+1, +5] [-8, +13]

2905 SPI* 27 4-7 9-14 [-6, 0] [-13, +14] 4-6 9-15 [-5, -2] [-15, +9] OPP* 27 6-9 12-15 [-9, -5] [-15, +3] 6-9 12-16 [-8, -4] [-16, +4]

PHO 29 5-7 11-14 [-3, -1] [-14, +14] 12-13 22-23 [+7, +9] [-11, +23]

CUR 31 9-14 15-19 [-14, -8] [-19, +6] 7-10 11-17 [-10, -7] [-17, +2] CUR 32 8-13 16-21 [-12, -7] [-21, +6] 7-10 12-18 [-9, -6] [-18, +2] CUR 33 7-12 14-18 [-11, -6] [-18, +6] 6-9 10-14 [-8, -5] [-14, +2] CUR 34 7-11 18-24 [-10, -4] [-24, +23] 6-9 19-22 [-7, -4] [-22, +20] 84 INS (BOOM -Y) 34/35 9-13 18-24 [+2, +8] [-21, +24] 10-13 18-22 [+4, +8] [-19, +22] INS (BOOM +Y) 34/35 7-11 12-21 [+1, +7] [-13, +21] 8-10 15-18 [+3, +7] [-12, +18] 2910 From TG analysis (Table 5.2a), it emerged that, according to the various statistics (in parentheses):

• in the case of SPI, the two programs overestimated maxima trends in both sets of measurements, of more than 10K (MSD), with MarsCAM-NCAR output closer to the observational data; 2915 • also for OPP landing site two datasets were available: for both, MCD slightly overestimated the trends (up to 5K, MSD), while MarsCAM-NCAR underestimated, up to 12K, maxima measurements (from MSD). MCD moreover presented narrower ranges in all the statistics considered; • in the case of CUR, data coming from different MYs of observations were released. For all 2920 of them, MCD and MarsCAM-NCAR slightly underestimated the behavior of observational data, of only few K (at most 5K, MSD). The ranges registered in all the statistics were of the same entity for the two GCMs; • finally, for INS, in the limited data available (only the final part of winter) for the two different datasets, both programs slightly underestimated temporal evolution of temperatures 2925 (of few K, MSD). A quite perfect overlapping of the RMSE, CHEB and ERR ranges was obtained.

From TSA trends (Table 5.2b), it emerged that:

2930 • for VL1 data, both GCMs overestimated the observational trends, up to maximum 10K (MSD). The ranges registered in all the statistics were globally similar for the two models, even if CHEB distances for MCD were lower than MarsCAM-NCAR ones; • for VL2, different behaviors were registered for the two simulators, MCD slightly underestimating and MarsCAM-NCAR overestimating (of about 4K, MSD); 2935 • for MPF a similar behavior was evidenced (in summer, the only season available): MCD underestimated up to 4K temperatures trends, while MarsCAM-NCAR overestimated, nearly of the same quantity (from MSD). The other statistics considered showed similar ranges between the models, with the exception of ERR, for which the latter program showed +13K of difference with respect to reference values; 2940 • for SPI rover, both simulators underestimated maxima trends, at most of 5K (MSD). RMSE and CHEB and ERR ranges were quite overlapped, with the exception of the upper limit of ERR range, about 5K greater for MCD; • also for OPP rover similar performances were registered. In fact, both GCMs generally underestimated maxima trend up to 9K (MSD). Auxiliary statistics employed present 2945 equivalent ranges of variations; • PHO measurements were differently approximated by the two programs. MCD slightly underestimated the observational data, while MarsCAM-NCAR underestimated the trends up to 9K (MSD). Also the other statistics reflected the presence of the discrepancies now signaled; 2950 • in the case of CUR, for all the MYs processed, both climatic models underestimated the observations. On average, MarsCAM-NCAR was slight closer to the reference values for few K (MSD) with respect to MCD output, even if the range observed for the statistics are quite equivalent;

85 • finally, for INS observations, both GCMs tended to overestimate, up to 8K (MSD), the two 2955 datasets registered during winter. CHEB and ERR statistics furnished the same information for both simulators.

Further specific details can be retrieved for each lander/rover by checking the findings registered in the nine aggregation cases considered for the comparisons and summarized in reports Tables C1- 2960 C22 of Appendix C.

Finally, a check was performed to evaluate the results obtained by the MCD Scenarios explicitly referring to the same MY of observation for a particular lander/rover. The check was possible for probes landed on Mars after MY24 included. Only for PHO (MY 29) the output calculated for this 2965 MY is closer to the observational trends than the outputs of other Scenarios. In the other cases (OPP, SPI, CUR), the respective MYs do not present good ranks in the MBC classifications, and also statistics are usually not better than those pertaining to other Scenarios. As the focus of a GCM is to perform reliable simulations able to replicate global climatic conditions and not necessarily those of specific locations, the small deviations registered in these cases are not surprising. 2970 5.3 Group 2 results

As in the case of Group 1, also for daily comparisons the analysis was split into two subgroups, Group 2a (analysis for season or whole year, all the probes) and Group 2b (analysis for single 2975 lander/rover).

5.3.1 Evidences for Group 2a

In Table 5.3 the outcomes for Group 2a are reported, for TG (Table 5.3a) and TSA (Table 5.3b). It 2980 must be pointed out that the surface properties stored in the topographic maps at the basis of the climatic models represent averages over large areas of thousands of km2, while the probes measured local values in the surroundings of the landing places. As reported in Chapter 3, the differences between model output and observations recorded for TG and TSA are due principally to variations in albedo, thermal inertia and dust OD, but also to the local surface roughness (Urata and Toon, 2985 2013a). In other words, the possible differences between the specific physical parameters measured at the landing sites and the grid cell average employed by the model, are the most likely cause of the discrepancies between experimental and modeled temperatures for MarsCAM-NCAR software (Urata and Toon, 2013a), especially when daily cycle temperature curves are studied. For this reason, Urata and Toon (2013a) performed a series of sensitivity-tests in order to evaluate the 2990 impact of changes in albedo and thermal inertia values at VL1 and VL2 landing sites. The result they published is that, in dependence of the hour of the sol considered, differences (on the order of 5-15K) were evidenced with respect to reference measurements. The reasoning just reported endorse the choice I took on how to perform diurnal cycle comparisons. In fact, as evidenced in Chapter 4, the discussion proposed for Group 2 must be interpreted as a check about the ability of 2995 the two programs to reproduce the expected temperature variation curves during the day, without overly focusing on the physical reasons that lead to the absolute values simulated in a certain specific moment of the sol.

86 Table 5.3: The same as Table 5.1, but for Group 2a: surface temperatures (a) and near-surface temperatures (b) results are reported.

a TG MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 7 36 <~ 1 [-27, +36] 7-10 29-42 [0, +1] [-33, +42] 4 15 0.496 9 45 +2 [-26, +45] 9-11 44-45 [0, +2] [-30, +45] F MCD 7 1 1 7 36 <~ 1 [-17, +36] 6-12 26-42 [0, +1] [-26, +42] 2 14 0.260 12 45 +3 [-23, +45] 12-14 44-45 [+2, +3] [-26, +45] G MCD MY 28 1 1 7 25 <~ 1 [-30, +25] 7-11 21-33 [-1, +2] [-33, +28] 4 15 0.265 11 28 +2 [-26, +28] 10-12 28-30 [+3, +5] [-30, +29] H MCD 7 1 1 7 27 -2 [-27, +21] 7-9 27-33 [-2, 0] [-33, +28] 4 2 0.682 8 27 <~ 1 [-26, +27] 8-9 27-30 [-2, -1] [-30, +28] I MCD MY 27 1 1 7 25 <~ 1 [-23, +25] 6-7 25-28 [-2, -1] [-27, +28] 5 7 0.732 7 23 <~ 1 [-19, +23] 7-9 23-27 [-1, 0] [-27, +25]

b TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 3 0.873 7 23 -2 [-18, +23] 7-9 18-24 [-5, -2] [-22, +24] 4 1 1 7 31 <~ 1 [-17, +31] 7-8 29-32 [-2, 0] [-19, +32] F MCD 7 1 1 6 22 -3 [-15, +22] 6-10 18-22 [-7, -3] [-22, +22] 2 3 0.765 8 27 <~ 1 [-16, +27] 8-9 21-27 [-3, -1] [-19, +27] G MCD 7 1 1 7 16 -3 [-16, +14] 7-9 16-21 [-5, -3] [-21 , +15] 8 2 0.938 7 19 <~ 1 [-16, +19] 7-8 18-21 [0, +2] [-18, +21] H MARSCAM 7 4-6 0.742 6 17 -4 [-17, +13] 6-7 17-18 [-5, -2] [-17, +15] 4 1 1 6 21 <~ 1 [-13, +21] 6-8 19-21 [-2, 0] [-15, +21] I MARSCAM MY 27 6 0.813 8 19 -3 [-19, +19] 8-9 18-24 [-5, -1] [-21, +24] 4 1 1 7 31 <~ 1 [-14, +31] 7-8 29-32 [-3, 0] [-17, +32]

3005

3010

87 According to the statistics reported in Table 5.3a, for TG, it resulted that:

3015 • taking into account case A, both models were able to well reproduce the daily curves in all the slots of the year processed (MSD); RMSE and ERR statistics were equivalent for the two GCMs, even if MarsCAM-NCAR presented a higher CHEB lower extreme with respect to MCD, moreover the variation range for this statistics is only 1K wide for MarsCAM- NCAR and of about 13K for MCD; 3020 • MCD and MarsCAM-NCAR tend to slightly overestimate, of only at 2-3K maximum (MSD), the daily cycle curve during spring (case F) and of 3-5K (MSD) in summer (case G), while they show the opposite behavior for autumn (case H) and winter (case I), although in these two cases the maximum deviations reach only 2K, according to MSD statistics; • generally, MarsCAM-NCAR evidences a narrower range of variation in CHEB statistics (of 3025 only few K) with respect to MCD output: it mostly depends on the similar performances registered by the Runs in each case, slightly differing from one another due to the few lander/rover data available in that specific comparison. For RMSE and ERR statistics, the amplitude of the range is instead of the same entity for the two GCMs; • looking at the single winner, Scenario 7 for MCD and Run 4 for MarsCAM-NCAR seems to 3030 be the simulations closer to observational data, according to MBC method.

An essential point already mentioned and underlined for a correct interpretation of the discussion just proposed is related to the amount of data processed. In fact, as evident by consulting Table 4.3, the TG measurements are not available for all the landers/rovers considered, so in many LS slots it 3035 happened that the results deduced were strongly influenced by the same “voting” spacecrafts, for which in addition multiple measurements were collected (i.e. SPI, OPP with double estimations, and CUR, with four MYs of observation). Therefore, the given conclusions must be considered into this limit and not be extended to all the planet.

3040 For TSA analysis (Table 5.3b), instead, it emerged that:

• both MCD and MarsCAM-NCAR GCMs tended to underestimate (MSD) daily temperature cycle values on a per-year basis (case A). Even if ERR range was larger for the second model, according to MSD statistics, MarsCAM-NCAR estimations were slightly closer to 3045 the reference values; • focusing on the single seasons, MCD tended to underestimate (on average, of about 5K, MSD) diurnal cycle values in all the cases (F-I), while MarsCAM-NCAR showed the same behavior with the exception of summer, when a little overestimation was registered (MSD); • for CHEB and ERR statistics, the ranges observed were very similar between the two GCMs 3050 in all the cases studied, with few discrepancies only in the extremes; • Scenario 7 for MCD and Run 4 for MarsCAM-NCAR respectively were the simulations closer to observational data for this kind of comparisons. Slight differences in the winner Scenario/Run reported were probably related to calculation fluctuations.

3055 Generally, both for TG and TSA analysis, the comparison plots performed showed agreement to within the error bars between the model and the observational data throughout most of the day.

88 The conclusions reached in each seasons for the various landers/rovers in the discussions just developed for TSA and TG are in accordance to what observed in the analogous cases for Group 1a.

3060 5.3.2 Evidences for Group 2b

In Table 5.4 the results of the comparisons for Group 2b are reported for TG, Table 5.4a, and TSA, Table 5.4b.

3065 For each lander/rover, as already mentioned for Group 1, data were not available in all the seasons, so the evidences here presented must be interpreted according to this limit: the list of the accessible measurements is shown in Table 4.3 for TG and Table 4.4 for TSA. Consequently, in the following comments, the indications provided refer only to the behavior of the two GCMs in these seasons and are not representative of the global ability of the simulators of reproducing data in the 3070 remaining part of the year for which data are missing. Moreover, due to these reasons, the minimal differences registered among the various Scenarios/Runs in these comparisons are only attributable to calculation fluctuations, so definitive conclusions on the performance of the single simulations should be avoided. The discussion proposed is based on the global behavior of each climatic model derived by considering together all the results obtained. 3075 TG comparisons (Table 5.4a) revealed the following situation:

• for SPI rover (only central-hours trend could be reconstructed, see Section 1.5) both simulation programs tended to overestimate the measurements, up to a maximum of about 3080 10K (MSD). CHEB range for MarsCAM-NCAR was narrower than MCD one, due to the very close ranks registered for all the Runs of this model in the various classifications; • in the case of the twin rover, OPP, instead, a quite opposite behavior was registered. While MCD range in MSD statistics varied from -3K to +2K, MarsCAM-NCAR underestimated, of about 5K on average (MSD), the observations. The other statistics were substantially 3085 similar; • CUR diurnal cycle was globally underestimated in all the MYs of observation by the two climatic models, of about 3K on average (MSD). RMSE and CHEB statistics seemed to be slightly higher for MarsCAM-NCAR program; • the two INS datasets (data refer only to the final part of winter) were slightly underestimated 3090 by both models, by only 2K at maximum (MSD).

For TSA (Table 5.4b), the comparison showed that:

• globally, MCD and MarsCAM-NCAR both overestimated temperature daily-cycle for VL1 3095 measurements, on average of more than 5K up to a maximum of 10K (MSD). CHEB statistics presented higher extremes for the second program, as it happened also for ERR range; • for VL2, MCD tended to underestimate the observational data (4K at maximum, MSD), while MarsCAM-NCAR showed the opposite behavior, with similar absolute values;

89 3100 • also for MPF (ending summer), the two GCMs differed; MCD trends were in quite perfect accordance with the observations, while MarsCAM-NCAR tended to underestimate, in the range [+4, +7] K, the diurnal curve (MSD); • similar behavior was obtained for SPI measurements: both programs slightly underestimated the reference values, most 6K (MSD). RMSE, CHEB and ERR statistics were very similar 3105 for the two simulation tools; • also for OPP measurements an underestimation was evidenced by the comparisons, with a maximum difference of about 9K (MSD) with respect to the reference curve; • for PHO, MarsCAM-NCAR tended to overestimate temperatures, 10K at most (MSD), while MCD provided simulations closer to the observational curve; ERR range for the first 3110 program only covers positive values, RMSE and CHEB statistics did not overlap for the two programs, with MarsCAM-NCAR values higher; • in all the 4 MYs of observation, CUR diurnal cycle temperature values were underestimated (MSD) by both simulation tools, approximately of the same quantity. Also in the other statistics the two GCMs presented similar ranges, with little differences due to calculation 3115 fluctuations; • finally, for ending-winter INS measurements, for both datasets, the MSD intervals recorded for the two programs were equivalent: both tended to overestimate the observations, ranging from 3K to at maximum 11K (MSD).

3120 More information about the comparisons developed for Group 2b can be retrieved for each lander/rover by consulting the reports of Tables D1-D22 of Appendix D, created for each of them. The conclusions reached in each season for the various lander/rover in the discussions just performed for TSA and TG were in accordance with what was observed in the analogous cases for Group 1b. 3125

3130

90 Table 5.4: The same as Table 5.2, but for Group 2b, surface temperatures (a) and near-surface temperatures (b). 3135 a TG MCD MARSCAM LAND/ROV MY RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K)

SPI (upview)* 27 8-11 21-27 [+2, +7] [-21, +27] 11-12 27-28 [+7, +9] [-17, +28] SPI (near)* 27 8-12 21-28 [+3, +9] [-16, +28] 12-13 28-29 [+9, +10] [-16, +29]

3140 OPP (upview)* 27 6-7 22-27 [-3, +2] [-27, +22] 8-9 22-29 [-7, -2] [-24, +29] OPP (near)* 27 6-7 22-27 [-3, +2] [-27, +20] 8-9 24-27 [-5, -3] [-27, +26]

CUR 31 6-12 16-21 [-3, -1] [-17, +21] 11-13 26-27 [-1, +1] [-18, +27] CUR 32 5-10 14-24 [-3, -1] [-19, +24] 9-11 27-28 [-2, 0] [-18, +28] CUR 33 6-10 18-20 [-4, -3] [-20, +17] 8-11 17-21 [-4, -2] [-19, +21] 3145 CUR 34 8-13 29-42 [-4, -3] [-33, +42] 12-14 44-45 [-4, -2] [-30, +45]

INS (FOV 1) 34/35 6-10 15-19 [-1, 0] [-16, +19] 8-9 23-25 [-2, 0] [-10, +25] INS (FOV 2) 34/35 3-6 7-17 [-2, 0] [-17, +12] 5-6 11-13 [-2, 0] [-13, +13]

b TSA MCD MARSCAM 3150 LAND/ROV MY RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K)

VL1 12 6-8 14-18 [+5, +7] [-5, +18] 8-11 29-32 [+5, +10] [-8, +32]

VL2 12/13 4-6 11-16 [-4, -2] [-16, +7] 5-6 15-16 [+1, +4] [-11, +16]

3155 MPF 23 4-5 9-11 [-1, +1] [-11, +10] 4-7 7-13 [+4, +7] [-1, +13]

SPI* 27 6-8 15-17 [-6, -4] [-17, +10] 4-5 16-18 [-2, -1] [-17, +10]

OPP* 27 8-10 18-20 [-9, -7] [-20, +6] 5-7 13-17 [-5, -2] [-17, +13]

PHO 29 3-4 7-11 [-2, +1] [-11, +11] 10-11 18-19 [+8, +10] [0, +19] 3160 CUR 31 7-11 14-21 [-10, -5] [-21, +5] 8-9 15-18 [-7, -4] [-18, +12] CUR 32 5-9 14-21 [-8, -4] [-21, +5] 6-8 13-16 [-6, -3] [-16, +9] CUR 33 6-10 15-22 [-9, -5] [-22, +5] 6-8 12-16 [-6, -3] [-16, +8] CUR 34 7-10 17-22 [-8, -4] [-21, +22] 9-10 21-27 [-6, -3] [-19, +27] 91

INS (BOOM -Y) 34/35 9-14 16-24 [+6, +11] [-11, +24] 9-12 18-22 [+8, +11] [-9, +22] INS (BOOM +Y) 34/35 6-11 13-21 [+3, +8] [-9, +21] 7-10 20-25 [+5, +8] [-5, +25] 5.4 Discussion

This part briefly summarizes the findings reported in detail in the preceding Sections. It is important to remind that, when a result is given for a particular seasons, data for minima, averages 3165 and maxima are considered together; on the other hand, when a result is reported, e.g. for maxima, it sums up data from all the seasons (see the various aggregation cases defined in Section 4.3). Furthermore, over- and underestimations in terms of MSD statistics are presented and arbitrarily considered as negligible when their absolute value was lower than 5K, in which case they were not reported and can be found in Tables 5.1-5.4. 3170 For TG comparisons, by matching the results obtained for Group 1a and Group 2a (seasonal and yearly trends, see Section 5.1), it can be conclude that, according to MSD statistics:

• both models well reproduced the yearly trends, with average negligible fluctuations with 3175 respect to the experimental curves; • MCD slightly overestimated, at most 5K, spring temperatures (Tables 5.1a and 5.3a); the model tended to overestimate maxima trends and to underestimate minima and averages (about 10 K at most, Table 5.1a); • MarsCAM-NCAR slightly overestimated spring trends (about 5K) and (negligibly) summer 3180 trends, while it underestimated winter temperatures (about 5K) and (negligibly) autumn trends; similarly to MCD, it slightly underestimated minima and averages (about 7K), while maxima were (negligibly) overestimated. • finally, for MBC method, the two simulations closer to the observational data in all the aggregation cases evaluated were, respectively, Scenario 7 for MCD and Run 4 for 3185 MarsCAM-NCAR.

For TSA:

• MCD and MarsCAM-NCAR presented a good accordance with observational data, both 3190 tending to globally underestimate the reference measurements, of about 7K for the first program and quite negligibly for the second; • in all the seasons and for minima, averages and maxima, MCD tended to slightly underestimate the observations, at most of 9K (see Tables 5.1b and 5.3b); • MarsCAM-NCAR underestimated negligibly the spacecraft data in almost season (with 3195 winter registering a 5K deviation) but for a negligible overestimation in summer; average and maxima trends were underestimated (respectively, in a negligible way and of about 5K) and minima were negligibly overestimated. • Scenario 7 for MCD and Run 4 for MarsCAM-NCAR, according to MBC method, resulted the most voted simulations. 3200 Focusing on each individual lander/rover data, for the sake of brevity, I preferred not to give here the under- and overestimation numeric discrepancies, because the results are of course less homogeneous than those in Groups 1a and 2a, and only general indications are given. The

92 comparisons showed that, according to the results collected from Groups 1b and 2b in MSD 3205 statistics:

• for TG (Tables 5.2a and 5.4a), MCD seemed to negligibly underestimate CUR (in all MYs), INS (for both datasets) observations and to overestimate SPI (at most 20K) and OPP (at most 5K) measurements; MarsCAM-NCAR underestimated negligibly CUR and INS data, 3210 slightly OPP temperatures (at most 13K), while it overestimated SPI ones (at most 12K); • for TSA (Tables 5.2b and 5.4b), MCD tended to negligibly underestimate VL2, MPF and PHO observations and underestimated more significantly OPP (at most 9K), SPI (at most 6K) and CUR (at most 14K) observations; on the other hand, it overestimate VL1 and INS trends of about 8K; MarsCAM-NCAR instead underestimated SPI (at most 5K), OPP (at 3215 most 8K) and CUR (at most 10K) trends, while it negligibly overestimated VL2 observations and, more notably, VL1 (at most 10K), MPF (at most 5K), PHO (at most 9K) and INS (at most 8K) measurements.

As evidenced in the dedicated Sections, the results obtained in some seasons were strongly 3220 influenced by the few data available. For example, it happened frequently, especially for TG comparisons, both for Group 1 (see Table 3.3) and Group 2 (see Table 4.3), that the data mostly belonged to only three rovers (SPI, CUR, OPP), moreover with multiple measurements for each of them (recorded by different instruments, like SPI and OPP, or more MYs, like CUR). Obviously, the various classifications created by MBC can not be considered as representative of the behavior of 3225 the two GCMs for the whole planet. Consequently, these special situations can be interpreted only as general indicators of how the two programs tended to reproduce surface temperature trends.

By consulting Tables 5.1-5.4, in which the statistics computed for Group 1 and Group 2 are reported, the agreement between the indications retrieved for the two approaches, seasonal and 3230 yearly trends for Group 1, and diurnal cycle for Group 2, can be observed. In few cases, the best Scenario/Run (i.e. the most voted according to MBC method) for each GCM is not the same in the two ratings, but by checking the various statistics calculated (RMSE, CHEB, MSD and ERR) it can be seen that this does not necessarily imply that the Scenarios in lower ranking positions performed significantly worse than the winners. The discrepancies observed were only due to negligible 3235 calculation fluctuations.

From the ERR and CHEB statistics in the same Tables, it can be noticed that, in some circumstances, the difference between model and experimental curves was large, even when the average accordance was very good. In fact, a perfect matching simulated data/observational 3240 measurements is hardly to be expected, because the parameters and the atmospheric processes involved in the reproduction of the climate of a planet are numerous and complex, both of computational and physical nature. For example, simulated data are produced in grid cells which, according to the resolution chosen to perform the simulations (approximately 4°x5° lat/lon), extend for thousands of km2 (depending on the planet region). As a consequence, the values adopted for 3245 topography, albedo, thermal inertia and dust OD are averaged in the entire cell and do not exactly represent the precise landing sites. The deviations between simulation output and observational data in temperature evolution are necessarily affected by this factor, which, however, does not strongly

93 compromise the goodness of the final results. A better approximation would be obtained by interpolating the data obtained from the simulations, considering the landing sites in relation to the 3250 cell in which it is located, but also to the surrounding cells. Some tests performed for this purpose demonstrated that interpolation provided no significant simulation accuracy increase. Moreover, GCMs built up for Mars atmospheric studies were generally designed to reproduce climatic conditions for very extended periods of time (Kys, Mys or even Gys), mostly in the attempt to try to find physically reliable climatic parameters so to sustain warm and wet weather conditions allowing 3255 the presence of liquid water on the surface of the ancient Mars. The focus was to create a reliable climatic model able to replicate global climatic conditions and not necessarily those of specific locations: so the small deviations evidenced during the comparisons are not surprising. In order to increase accuracy in specific places, a fine tuning of the initial parameters would be required, but such an approach is not necessary for analyzing long periods of time (months, seasons, years), in 3260 particular when ancient Mars climate estimates must be developed. The previous discussions can be applied also to explain why the dedicated MCD simulations for some MYs do not turn out to be the best Scenarios to reproduce specific measurements collected during the related observation years.

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3295 CHAPTER 6

REPRODUCTION OF OTHER CLIMATIC VARIABLES WITH GCMs 3300

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95 3320 6.1 MarsCAM-NCAR output: further analyses

The principal goal of the comparisons between GCMs made in this work was that of analyzing surface and near-surface temperatures. Nonetheless, a huge number of proofs were performed with MarsCAM-NCAR software in order to become familiar with this program: for this reason, in order to be confident on the reliability of the simulations made, I decided to replicate the graphs presented 3325 in Urata and Toon (2013a). This Chapter shows some of these tests. After importing the pre-processed output files (with Ophidia) into the Matlab environment (Section 3.8), I conducted several preliminary tests in order to evaluate the difference between a Run performed at 4°x5° resolution (the one used for the comparisons with MCD) and the same with a 10°x15° grid cell (Section 6.2). The output of MarsCAM-NCAR was also compared with other 1-D 3330 models (Section 6.3). I also briefly introduced other results obtained with this GCM for reproducing the annual pressure cycle (Section 6.4), air temperature profiles (Section 6.5), up to an height of about 60 km (see Table 2.2), both 1-D vertical profiles and zonally-averaged ones, and latitudinally- averaged global maps of surface (TG) and sub-surface (TSOI) temperatures (Section 6.5).

3335 6.2 Running MarsCAM-NCAR with different spatial resolutions

As already mentioned in Section 3.2, for MarsCAM-NCAR it is possible to apply the model with different spatial resolutions (see Table 2.2). Obviously, according to the size of the chosen grid cell, at the beginning of the simulation, the maps defining the initial parameters that mostly influence the output (see Chapter 3) must be set at the same spatial resolution. In Table 6.1 a comparison between 3340 the two resolutions is reported, regarding running time for performing a “standard simulation” (see Section 2.7) while in Table 6.2 there is the comparison of the values of the initial parameters used to perform the various Runs in this work.

Table 6.1: Comparison between different spatial resolutions of MarsCAM-NCAR software. The values refer to the completion of a “standard simulation”. 3345 RESOLUTION 4°x5° 10°x15°

CORES 96 48 TIME CALCULATION 18.5 h 6.1 h OUTPUT SIZE ~ 1 TB ~ 250 GB

The choice to use a resolution or another depends on the goal. Generally, if long-term estimations must be performed (for example, to simulate ancient Mars climate conditions, in order to evaluate if 3350 it is possible to observe surface temperatures greater than 273K for many years) it is preferable, also to preserve time calculation and space storage, to use a lower spatial resolution (10°x15°, i.e. bigger grid cells). For short-term evaluations and/or studies related to restricted regions (i.e. landers/rovers landing site or specific zones like Amazonis Planitia), larger spatial resolutions are more suitable (i.e. 4°x5° or 2°x2.5°, i.e. smaller grid cells). To have an idea of the size of the cells, in a location 3355 having coordinates (0° N, 0° E), a 2°x2.5° cell grid is about (5x148) km large, i.e. about 782 km 2, a 4°x5° cell grid about (29x294) km, i.e. about 8620 km2, a 10°x15° cell grid about (165x864) km, i.e. about 142794 km2. Spatial resolution strongly influences the values included in the maps

96 defining the initial parameters used to characterize the starter state of the planet at the beginning of the simulations.

3360 Table 6.2: Comparison between different spatial resolutions of MarsCAM-NCAR software for the initial parameters adopted at the beginning of the Runs.

RUN RES. (lat/lon) ALBEDO THERMAL INERTIA DUST OD VL1 VL2 VL1 VL2

1 10°x15° 0.20 0.24 280.1 194 0.30 2 4°x5° 0.22 0.24 290 232 0.30 3365 4 4°x5° 0.22 0.24 215 240 0.30 5 4°x5° 0.26 0.22 215 240 0.30 6 10°x15° 0.26 0.22 215 240 0.30 8 4°x5° 0.26 0.22 215 240 0.30 9 10°x15° 0.26 0.22 215 240 0.10 10 4°x5° 0.22 0.24 215 240 0.10 11 4°x5° 0.26 0.22 215 240 0.25 12 4°x5° 0.26 0.22 215 240 0.20 13 10°x15° 0.26 0.22 215 240 0.20 3370 14 10°x15° 0.26 0.22 215 240 0.25

In order to quantify the impact on simulated variables due to a change of the grid cell, I performed several tests by checking MarsCAM-NCAR output data obtained with resolutions 4°x5° and 10°x15° with observational data taken at VL1 and VL2 landing sites: the Runs compared had obviously the same values of the initial parameters in order to perform a comparison as 3375 homogeneous as possible. In Figure 6.1 and Figure 6.2 the graphs obtained for TSA at LS = 100° for VL1 and LS = 120° for VL2 are reported: in these plots, also Urata and Toon (2013a) published data are shown for comparison. As it is evident, the agreement between observational curves and simulated data increases when the size of the grid cell decreases (i.e. higher spatial resolution). The nearness between the simulated data and the corresponding ones from Urata and Toon (2013a) 3380 certifies the goodness of the simulations performed. Little variations between them is only due to fine tuning processes (Urata, 2018). The error bars shown in the Figures were built up by considering all the data associated to three simulation years, in the same way as discussed in Section 4.7.

In Figure 6.3 instead the complete diurnal trend for about two sols at VL1 landing site is shown, for 3385 Run 11 (4°x5°) and Run 14 (10°x15°), calculated with initial parameters equal as those experimentally observed at the landing site (see Table 1.2).

97 Figure 6.1: MarsCAM-NCAR estimations, with different spatial resolutions, of the near-surface temperature TSA at VL1 landing site for LS = 100°. 3390

Figure 6.2: MarsCAM-NCAR estimations, with different spatial resolutions, of the near-surface temperature TSA at VL2 landing site for LS = 120°.

98 3395 Figure 6.3: MarsCAM-NCAR estimations, with different spatial resolutions, of the near-surface temperature TSA at VL1 landing site for LS = 142.4°-143.6°.

Some tests were conducted for other climatic variables. For example, in Figure 6.4 the results obtained in the reproduction of the annual pressure cycle (PS) at VL1 landing site are shown. The imperfect matching between simulated and experimental curves will be discussed in Section 6.4.

3400 Figure 6.4: MarsCAM-NCAR simulations, with different spatial resolutions, of the annual pressure cycle registered at VL1 landing site. Error bars are calculated as described for TSA and TG plots.

99 Sensitivity tests, similar to those discussed in Section 3.4 were also performed for evidencing the effects of the change, between a Run and another, of albedo, thermal inertia and dust OD were performed. Some example graphs are reported in Figure 6.5 (for TG) and Figure 6.6 (for TSA) 3405 related to a change of thermal inertia (T.I.) in OPP landing site during aphelion season. For a deeper discussion about this topic, see Section 3.4 and Figure 3.1.

Figure 6.5: MarsCAM-NCAR simulated TG temperatures reproducing measurements at OPP landing site. The curves shown refer to the output obtained with Run 2 (T.I., = 481) and Run 4 (T.I. = 220). The error bars were obtained with an approach similar to that discussed in Section 4.7.1 for Group 2 comparisons.

3410 Figure 6.6: The same as Figure 6.5 but for TSA.

100 From the two figures, it can be deduced how the decrease (by more than half in order to match the observed value, see Table 1.2) of thermal inertia in the grid cell containing OPP landing site produced a noticeable improvement in the accuracy of the simulated temperatures, much more evident for TG than for TSA.

3415 6.3 Comparisons with 1-D model output

In Section 2.1 it was evidenced how, in the early attempts proposed in the literature to reproduce some of the climatic features of Mars, 1-D climatic models were developed. For example, as mentioned in Section 1.3, Kieffer (1976) applied a one-dimensional thermal model, which accounts for the daily and seasonal changes of insolation and a weak interaction with the atmosphere, to fit 3420 the observed temperatures at VL1 and VL2 landing site to compute and derive surface temperature, not directly measured by the two landers. The physical properties which mostly affected the model were the albedo A, the emissivity ε of the surface (set to 1) and the thermal inertia I. By using remote observations, Kieffer (1976) used in his model the following values to retrieve minima, average and maxima trends: for VL1, A = 0.26 and I = (9.0±0.5) 10-3 cal cm-2 sec-1 K-1; for VL2, A = 3425 0.225 and I = (8.0±1.5) 10-3 cal cm-2 sec-1 K-1. I decided to compare these estimations with MarsCAM-NCAR output so to verify if there was accordance between them: no direct validation with experimental data was possible because no reliable estimations were available for this variable. As evidenced by Tillman (1985) and reported in the PDS node-sheets related to these landers, the footpads sensors “have served as a simple indicator of the surface, or near-surface, temperature 3430 during the mission”. In Figure 6.7 the results obtained for VL2 are reported (the same check was performed also for VL1, not shown for the sake of space).

Figure 6.7: Qualitative comparisons between Kieffer (1976) evaluations and MarsCAM-NCAR output for TG at VL2 landing site. Modeled curves were obtained in the same way as described in Section 4.2 for Group 1. 3435

101 Another 1-D thermal model, more elaborated than the previous one, was proposed by Ulrich et al. (2009) in order to predict regolith temperature profiles from the surface down into the martian subsurface as a function of time, latitude, thermal inertia, surface albedo, surface emissivity, distance of Mars from the Sun, and atmospheric opacity. The purpose was to evaluate, with a finite- 3440 difference procedure, the surface and subsurface temperature fields at the VL1, VL2, MPF, SPI and OPP landing sites with regard to the conditions conducive for terrestrial life (Ulrich et al., 2009). I decided to qualitatively evaluate the output generated with this model and compare it with MarsCAM-NCAR predictions, and checking the results so acquired with observational data. In Figure 6.8 an example of these studies is reported for MPF TSA temperatures registered at LS = 3445 162° (for space reasons, not all the comparisons are shown). As it is evident by the plots, the accordance between the output of the 3-D climatic model and MPF observational data is better with respect to 1-D evaluations.

Figure 6.8: Comparison of MPF TSA temperature data, with Ulrich et al. (2009) 1-D model and MarsCAM- NCAR predictions, the latter performed with two different spatial resolutions (4°x5°, Run 2, and 10°x15°, 3450 Run 1). The green stripe summarizes the entire temperature variation-range collected by the three sensors (see Section 1.4).

6.4 Surface pressure

MarsCAM-NCAR output was tested also for other climatic variables different from surface and 3455 near-surface temperatures. In this Section, I show some attempts performed to reproduce the annual pressure cycle at VL1 and VL2 landing sites. A comparison with MCD estimations is also presented as an example.

Pressure estimations in MarsCAM-NCAR are not directly available in the output files, but they must be deduced with a specific procedure. In fact, the program adopts, as vertical coordinates, a

102 3460 hybrid sigma-pressure system (Collins et al., 2004). It consists of a system in which the upper regions of the atmosphere (divided in the model in 26 layers up to a height of ~ 60 km, see Table 2.2) are discretized by pressure only, while lower vertical levels use the sigma (i.e. P/PS, see below) vertical coordinate smoothly merged in, with the lowest levels being pure sigma. A schematic representation of the hybrid vertical coordinate and vertical indexing is presented in Figure 6.9.

3465 Figure 6.9: Hybrid vertical coordinate used in MarsCAM-NCAR GCM. For details, see Collins et al. (2004).

According to this representation (both input and output datafiles follow this format, as well as internal model data structures: Collins et al., 2004), pressure is defined as:

P= A+B=(hyam⋅P 0)+(hybm⋅PS) (6.1)

where P is the pressure at a given level and (latitude, longitude) grid point; the coefficients A, B and

3470 P0 are constants; PS is the model current surface pressure. P0 is set in the model code to the

103 reference pressure. The input model initial conditions datasets sets A and B through the variables hyam, hyai, hybm and hybi. The subscript “i” refers to interface levels, while “m” refers to the mid- point levels: so, hyam refers to Hybrid level “A” and coefficient on the interfaces.

Once the pressure values deduced, the annual pressure cycle can be reconstructed. I tried to 3475 replicate the curves presented by Urata and Toon (2013a) and reported in Figure 6.4. As it is evident, the accordance between experimental and modeled curve is not perfect (especially for 10°x15° resolution), moreover also between the curves I calculated and those by Urata and Toon there is a substantial distance, even if the general trend is respected. In order to understand this discrepancy and to reach a better agreement with observational data, on the advice of one of the 3480 developers of the GCM, Dr. Richard Urata, I tried to apply spatial corrections to the output data.

I performed various attempts and the most evident improvements in the results were obtained by applying two corrections: interpolation of the pressure values registered in adjacent grid cells with a preliminary correction for topography (altitude). The rationale behind the corrections is the observation that the PS value reported in the cell containing the VL1 location can not be considered 3485 as a reliable simulation of the pressure values measured by the probe, but it must be corrected to take into account its effective location and the local topography.

The pressure value (PS variable) calculated for each grid cell pertains to the center of the cell, so a more accurate value for the exact landing site can be computed with an interpolation (by means of a 3490 Voronoi tessellation – Aurenhammer and Klein, 2000) between the four PS values associated to the cells whose centers are closest to the VL1 (or VL2) landing site so to match the real location of the lander. In Figure 6.10 a visual explanation to help in the comprehension is shown. For example, VL1 (coordinates: 22.7° N, 312° E) is associated, in the MarsCAM-NCAR calculation grid (res. 4°x5°), with the cell centered in (22° N, 310° E), covering coordinates in the ranges (20° N - 24° N) 3495 in lat and (307.5° E – 312.5 °E) in lon, because the computed pressure values are referred to the center of the cell. In order to give more accurate pressure values and to effectively take into account the real position of the lander, an interpolation is required, by considering the pressures associated with the nearest neighbor cells. The area so considered, evidenced in green in Figure 6.10, is delimited by the grid points named 1, 2, 3 and 4, containing the VL1 position. As a result, PS values 3500 stored in points 1 (lat = 26 °N, lon = 310 °E), 2 (lat = 26° N, lon = 315°), 3 (lat = 22° N, lon = 310°) and 4 (lat = 22° N, lon = 315°) must be considered. Each value will contribute (with an appropriate weight established with the Voronoi tessellation method) to the final PS estimations, according to the distance of these points from the VL1 coordinates.

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Figure 6.10: Interpolation process performed to reproduce the annual pressure cycle measured at VL1 landing site.

3530 Preliminarily to spatial interpolation, the pressure data in the four considered grid nodes should be corrected in order to consider also the real elevation of the landing site. To do so, the hypsometric equation (Eq. 6.2). must be applied:

g⋅PHIS − ( ) RT (6.2) P2 = P 1⋅exp 3535

where P1 is the pressure output value (corrected with the interpolation process); g is the gravitational

acceleration; R = 189 J/(kg ∙ K) is the gas constant value for CO2; T is the ground temperature (TG) in the four cells used for the interpolation; PHIS (in m2/s2) is the geopotential surface, i.e. the surface that takes into account gravity and topography in the investigated region. The relationship 3540 between the real height h of the location and PHIS is given by:

PHIS h= (6.3) g

Generally, the topography of the planet is referred to the Martian Datum, the zero point of elevation 3545 on Mars. The datum is the isobaric surface at which the atmospheric pressure is 6.1 millibars, or 610 Pascals. Atmospheric pressure must be used for elevation definition because Mars has no ocean, and a "sea level" like on Earth does not exist. On the other hand, in the MarsCAM-NCAR program, the topography map used to define the PHIS variable is not referred to the Martian Datum, but to the MOLA aeroid surface (Urata, 2018). As reported in the PDS node page associated to 3550 MGS spacecraft (Smith et al., 2003), MOLA uses an aeroid defined by a gravitational potential model derived from satellite tracking, and an equatorial mean planetary radius. MOLA topography is the difference between planetary radius and aeroid at a given longitude and latitude. The average 6.1 mbar pressure surface (the Martian Datum) lies about 1.6 km below the MOLA aeroid (Smith and Zuber, 1998), but is expected to vary by 1.5 - 2.5 km with season. 3555

105 As the GCM reference is the MOLA aeroid, in order to apply the correction by the hypsometric equation (so reporting the grid nodes to the VL1 height), elevation must be referred to the same aeroid. As a consequence, from the PHIS values associated to each of the four grid cells used for the interpolation, the heights h (with respect to the MOLA aeroid) can first be computed by Eq. 6.3.

3560 Then, to refer the VL1 landing site altitude to the MOLA aeroid, a quantity d1 must be calculated, given by the algebraic sum of the VL1 landing-site height with respect to the Martian Datum (-3.6 km, see Table 1.2), the offset existing between the Martian Datum and the MOLA aeroid, and h. Eq. 6.2 can be rewritten as follows:

d − ( 1 ) h1 P2 = P 1⋅exp (6.4)

where h1 = (RT)/g is the scale height, which increases when pressure must be decreased (in fact, pressure tends to 0 when the altitude increases).

3565 In Figure 6.11 an example of how the introduction of these two corrections positively influences the accuracy of MarsCAM-NCAR output is reported. In Figure 6.12 a qualitative visual comparison between MarsCAM-NCAR output and MCD output (Scenario 7) is shown.

Figure 6.11: Effects of the corrections described in the text (spatial interpolation and altitude correction) applied to MarsCAM-NCAR PS simulated data and comparison with observational data, for about two sols, 3570 at VL1 landing site.

106 Figure 6.12: Comparison between MarsCAM-NCAR (Run 2, after interpolation and altitude correction) and MCD (Scenario 7) output performed in the same LS interval evaluated in Figure 6.11.

3575 The interpolation process adopted allows to reach a better agreement between observational data and MarsCAM-NCAR (on average, of about 20-25 Pa), even if the matching is not satisfactory. Even if the reliability of the estimation is increased (especially if compared with the plots related to the annual pressure cycle of Figure 6.4), together with the evidence that the temporal trend is well reproduced, deeper analysis are needed to fully understand the reason of the discrepancy now 3580 signaled. MCD instead, without any interpolation process, is able to adequately reconstruct the observations. Personal communications from Dr. Richard Urata (Urata, 2018) pointed out that accuracy in MarsCAM-NCAR calculated pressure might be increased by a fine tuning procedure so to reach the same accordance between modeled curves and measurements as that reported in Urata and Toon (2013a). In fact, according to Urata (2018), the possible causes of the discrepancies that 3585 emerge from plots of Figure 6.4 and Figure 6.11 are multiple: for example, the annual pressure cycle is affected by the initial atmospheric mass, by the annual dust cycle, by subsurface ice, by soil thermal inertia, etc., and the model needs to be tuned each time any of these factors are changed.

6.5 Air temperature profiles and sub-surface temperatures

As mentioned at the beginning of this Chapter, I investigated other climatic variables that can be 3590 produced with MarsCAM-NCAR software. For saving space, in this Section I show only a very limited subset of the several studies I performed in order to become familiar with this GCM. For the same reason, the Matlab scripts and Ophidia WFs created to adequately manipulate these data are not reported, and the Figures are only briefly introduced. Urata and Toon (2013a) comparisons with observational data were used as a guideline to build the plots shown.

107 3595 In Figure 6.13 and Figure 6.14 the plots of zonally averaged temperatures I obtained with the MarsCAM-NCAR program (labeled with a) are reported and visually compared with MGS-TES (Thermal Emission Spectrometer) data (b) and Urata and Toon output (c). The plots shown were graphed with the same initial parameters. The accordance between my plots and the observational data, as well as with the maps calculated by the MarsCAM-NCAR software developers, is evident.

3600 a

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Figure 6.13: Zonally averaged air temperatures at the spring equinox (LS = 0°) for (a) MarsCAM-NCAR simulations carried out in this work, (b) MGS-TES and (c) Urata and Toon (2013a) work.

108 3610 a

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Figure 6.14: The same as Figure 6.13 but for summer solstice (LS = 90°).

3635 In Figure 6.15 a comparison is reported between MGS-TES data, Urata and Toon (2013a) simulations and MarsCAM-NCAR Run 2 concerning vertical temperature profiles registered at a location having coordinates 20° N, 0°W during northern summer solstice (LS = 90°). Model profiles are within ±10 K from the MGS-TES data, except for the uppermost levels, where the model can be up to 15 K cooler, and near the surface where the model is up to 25 K warmer during 3640 the day.

109 3645 Figure 6.15: 1-D vertical temperature profile at the norther summer solstice (LS = 90°) between MGS-TES data and MarsCAM-NCAR predictions, from Urata and Toon (2013a) work and from Run 2.

Finally, with MarsCAM-NCAR, it is possible also to estimate the sub-surface temperatures down to a depth of 3 m (see Section 2.5). In Figure 6.16, some examples of the results obtained with Run 2 3650 are reported for the four turning points of the year, the two equinoxes and the solstices. The ability of this GCM to reproduce this climatic variable could be very useful for studies aimed at investigating the first layers of the subsurface in search for the temperatures needed to sustain the presence of ice.

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3670 Figure 6.16: Subsurface temperatures as simulated with MarsCAM-NCAR software (Run 2) for LS = 0°, 90°, 180°, 270°.

111 3675

CHAPTER 7

GLOBAL REFLECTIVITY MAPS OF

3680 MARS BY MEANS OF THE MARSIS SIMULATOR

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112 7.1 Research stay at INAF (Bologna) 3705 In this Chapter I present the results obtained during the research stay I spent in Bologna, from 18/02/2019 to 15/03/2019 at the “Istituto Nazionale di Astrofisica (INAF), Istituto di Radioastronomia” under the supervision of Prof. Roberto Orosei, P.I. of MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) and member of the SHARAD (SHAllow RADar) 3710 experiments on board, respectively, of the ESA Mars Express and NASA Mars Reconnaissance Orbiter. The main research activities I performed included:

• installation and application of a parallel code (the MARSIS simulator, see Section 7.5), able to simulate the echoes expected from the MARSIS radar, on the CMCC Athena cluster; 3715 • validation of the simulations by means of comparisons with collected radar datasets and pre-existing simulations; • production of simulated surface reflectivity maps for comparison with similar maps based on original and verified data with the aim of identifying the variations of the dielectric constant on the surface of Mars. 3720 7.2 The discover of liquid water on Mars

As evidenced in Section 2.2, GCMs able to well reproduce TG and TSA observational trends were applied to simulate ancient Mars weather (Urata and Toon, 2013b for MarsCAM-NCAR; 3725 Wordsworth et al., 2013; Forget et al., 2013 for GCM-LMD) dating back 3.7 Gys ago when, very probably, wet and warm climate conditions allowed the presence of liquid water on the surface on the planet, as suggested by some geological evidences (Di Achille and Hynek, 2010). At this purpose, Orosei et al. (2018) discovered, for the first time, the evidence of the existence of sub- glacial liquid water, in the shape of a salty lake, in the southern polar cap of Mars, at a depth of 3730 about 1.5 km.

The following discussion is deeply extracted and based on Orosei et al. (2018).

The presence of liquid water in the Martian polar caps was first hypothesized more than 30 years 3735 ago (Clifford, 1987) and since then this topic was widely debated. An appropriate technique than can be applied to clarify this point is the Radio Echo Sounding (RES). Low frequency radars were in fact vastly and successfully used in search for liquid water at the bottom of terrestrial polar ice sheets (Cooper and Smith, 2019) due to the fact that an interface between ice and water (or between ice and water-saturated sediments) generates bright radar reflections (Carter et al., 2007; Ashmore 3740 and Bingham, 2014).

On Mars, to perform similar kind of RES detection (Orosei et al., 2018), the MARSIS instrument, onboard the Mars Express spacecraft (Picardi et al., 2005), was used (for details, see Section 7.4). The radar is investigating the subsurface of the Red Planet for more than 12 years in search for 3745 evidence of liquid water (Farrell et al., 2009). In the southern ice cap of Mars, close to the thickest part of the South Polar Layered Deposits (SPLD), strong basal echoes were observed (Plaut et al., 2007). These features were interpreted by Plaut et al. (2007) as due to the propagation of the radar

113 signals through a very cold layer of pure water ice with negligible attenuation. Also in other areas of the SPLD anomalously bright reflections were observed (Cartacci et al. 2008). 3750 On Earth, qualitative (the morphology of the bedrock) and quantitative (the reflected radar peak power) analyses (Carter et al., 2007; Oswald and Gogineni, 2008) are generally coupled and combined to interpret radar data collected above the polar ice sheets. The capability of the MARSIS radar to detect the presence of sub-glacial water bodies from the shape of the basal topography is strongly limited by its low spatial resolution defined primarily by its very large footprint, ~ 3 to 5 3755 km. As a consequence, a quantitative estimation of the relative dielectric permittivity (i.e. the ratio between the electric field within a material and the corresponding electric displacement) of the basal material (which determines the radar echo strength) is necessary for a correct interpretation and detection of liquid water at the base of the polar deposits. A 200-km-wide area of Planum Australe region, centered at 193° E, 81°S (see Figure 7.1), closer to 3760 a previous investigated region (Cartacci et al., 2008), was surveyed by MARSIS between 29/05/12 and 27/12/15. Apparently, this area does not present any peculiar characteristics from a topographic point of view, both analyzing MOLA data (see Figure 7.1A – Smith et al., 2001; Neumann et al., 2003) and available orbital imagery from THEMIS (Thermal Emission Imaging System) camera (see Figure 7.1B - Edwards et al., 2011). This location is flat, composed of water ice mixed with 3765 dust (about 10%-20% - Zuber et al., 2007; Li et al., 2012) and seasonally covered by a very thin

layer of CO2 ice, less than 1m in thickness (Aharonson et al., 2004; Litvak et al., 2007). In the same zone, SHARAD (Seu et al., 2007a), an high-frequency radar, revealed barely any internal layering in the SPLD and did not detect ant basal echo (see Figure 7.2), in remarkable contrast with what was observed for the North Polar Layer Deposits and other regions of the SPLD (Seu et al., 2007b). 3770

Figure 7.1: Maps of the are investigated. In (A), shaded relief map of Planum Australe, Mars, south of 75° S latitude is reported. The map was produced using MOLA topographic dataset (Smith et al., 2011). The black square outlines the analyzed area. In (B), a mosaic produced with infrared observations by the THEMIS camera is reported, corresponding to the black square in (A). South is up in the image. The red line marks the 3775 ground track (the projection of the satellite's orbit onto the surface of the planet) of orbit 10737, corresponding to the radargram (see text) shown in Figure 7.2. The area consist for the most part of featureless plains, except for a few large asymmetric polar scarps near the bottom right of (B), which suggest an outward sliding of the polar deposits (Grima et al., 2011). Source: Orosei et al. (2018).

114 3780 Figure 7.2: Comparison between MARSIS and SHARAD radar data. Radargrams collected in the area with strong basal reflectivity are shown for (A) MARSIS (orbit 10737) and (B) SHARAD (orbit 2666). In (C), the ground tracks corresponding to the two radargrams are projected on the same infrared image as Figure 7.1B. In the SHARAD data, no basal echo is visible, while layering is faintly discernible. Source: Orosei et al. (2018).

3785

115 A total of 29 radar profiles were acquired using the onboard unprocessed data mode (for details, see the Supplementary material of Orosei et al., 2018), by transmitting closely spaced radio pulses centered at either 3 and 4 MHz or 4 and 5 MHz. In order to minimize ionospheric dispersion of the 3790 signal, observations were performed when the spacecraft was on the night side of Mars. An example of a MARSIS radargram collected in the area is shown in Figure 7.3. A radargram is a bidimensional color-coded section made of a sequence of echoes in which the horizontal axis is the distance along the ground track (see Section 7.3) of the spacecraft. The vertical axis represents the two-way travel time of the echo (from a reference altitude of 25 km above the reference datum), and 3795 brightness is a function of echo power.

Figure 7.3: Radar data collected by MARSIS. In (A) the radargram for MARSIS orbit 10737 is shown, whose ground track is shown in Figure 7.1B. The continuous bright line in the upper part of the radargram is 3800 the echo from the surface interface, whereas the bottom reflector at about 160 μs corresponds to the SPLD/basal material interface. Strong basal reflections can be seen at some locations, where the basal interface is also planar and parallel to the surface. The plot of surface and basal echo power for the radargram (A) is reported in (B). Red dots represent surface echo power, while blue dots reproduce subsurface echo power. The horizontal scale is along-track distance (see Section 7.3), as in (A), and the vertical scale is 3805 uncalibrated power in decibels. The basal echo between 45 and 65 km along-track is stronger than the surface echo even after attenuation within the SPLD. Source: Orosei et al. (2018).

Looking at Figure 7.3, it can be noticed that the strong surface reflection is followed by several 3810 secondary reflections produced by the interfaces between layers within the SPLD. The last of these echoes represents the reflection between the ice-rich SPLD and the underlying (basal) material. Generally, the basal reflection is weak and diffuse in the most part of the studied area, even if, in some locations, it appears very sharp with a greater intensity (bright reflections) than the

116 surrounding area and the surface (Figure 7.3B). Where the observations from multiple orbits 3815 overlap, the data acquired at the same frequency present consistent values of both surface and subsurface echo power, as shown in Figure 7.4.

Figure 7.4: Color-coded representation of surface (A) and basal (B) echo power at 4 MHz for MARSIS 3820 orbits 10737, 12840, 12847, 12995, 14948 and 14967. Ground tracks are projected on the same infrared image as Figure 7.1B. The data represent the measured echo power after applying only the correction of geometric power fall-off due to altitude variations. The width of the ground tracks was reduced with respect to the real one to allow the separation of parallel, partially overlapping orbits. Surface echo power fluctuations are limited to a few dB, while there is clustering of strong basal echoes that are consistently 3825 observed in different orbits crossing the study area. This indicates that the physical properties of the surface are spatially constant whereas the ones at the base of the SPLD show some lateral variations. Source: Orosei et al. (2018).

The estimation of the depth of the subsurface reflector can be derived by evaluating two-way pulse 3830 travel time between the surface and basal echoes, as well as to map the basal topography. Considering an average signal velocity of 170 m/μs within the SPLD, close to that of water ice (Pettinelli et al., 2015), the depth of the basal reflector is about 1.5 km below the surface. The large size of the MARSIS footprint and the diffuse nature of basal echoes outside the bright reflectors prevent a detailed reconstruction of the basal topography, but a regional slope from west to east can 3835 be recognized (see Figure 7.5A). The subsurface area where the bright reflections are concentrated is topographically flat and surrounded by higher ground, except on its eastern side, where there is a depression.

Unfortunately, due to the fact that the radiated power of the MARSIS antenna is unknown, the 3840 permittivity cannot be retrieved from the power of the reflected signal at the base of the SPLD. Thus, the intensity of the reflected echoes can only be considered in terms of relative quantities. Usually, the intensity of the subsurface echo is normalized to the surface value (Lauro et al., 2010),

117 i.e. to compute the ratio between basal and surface echo power. The additional advantage of such a procedure is also that of compensating any ionospheric attenuation of the signal. In this way, Orosei 3845 et al. (2018) normalized the subsurface echo power to the median of the surface power computed along each orbit: they found (see Figure 7.6) that all normalized profiles at a given frequency yield consistent values of the basal echo power. In Figure 7.5B the regional map of basal echo power after normalization is shown: bright reflections are localized around 193 °E, 81°S, in all intersecting orbits, evidencing a well-defined 20-km-wide subsurface anomaly.

3850 Figure 7.5: Maps of basal topography an reflected echo power. In (A) a color-coded map of the topography at the base of the SPLD is shown, computed with respect to the reference datum. The black contour outlines the area in which bright basal reflections are concentrated. In (B) a similar map is shown, but referred to a normalized basal echo power at 4 MHz. The large blue area (positive values of the normalized basal echo power) outlined in black corresponds to the main bright area: the map also shows other, smaller bright spots 3855 that have a limited number of overlapping profiles. Both panels are superimposed on the infrared image shown in Figure 7.1B and the value at each point is the median of all radar footprints crossing that point. Source: Orosei et al. (2018).

In order to obtain the basal permittivity, information about the dielectric properties of the SPLD are 3860 needed, the latter depending on the composition and temperature of the deposits. Due to fact that the exact ratio between water ice and dust is unknown (Li et al., 2012), and moreover the thermal gradient between the surface and the base of the SPLD is poorly constrained (Wieczorek, 2008), Orosei et al. (2008) explored the range of plausible values for such parameters and computed the corresponding range of permittivity values. General assumptions were defined:

3865 1. the SPLD is considered as a mixture of water ice and dust in varying proportions (from 2 to 20%); 2. the temperature profile inside the SPLD is linear, starting from a fixed temperature at the surface (160 K) and rising to a variable temperature at the base of the SPLD (in the range 170-270 K).

3870 Different electromagnetic scenarios were discussed (see the Supplementary material of Orosei et al., 2018), by considering a plane wave impinging normally onto a structure with three layers:

1. a semi-infinite layer with the permittivity of the free-space; 2. a homogeneous layer representing the SPLD;

118 3. another semi-infinite layer representing the material beneath the SPLD, with variable 3875 permittivity values.

Figure 7.6: Color-coded map of normalized surface (A, C, E) and basal (B, D, F) echo power superimposed on the infrared image in Figure 7.1B. The mapped value at a given point is the median echo power of all footprints crossing that point. Panels A, C and E show that the surface radar reflectivity is essentially uniform over the area, with only minor, localized and time-varying (seasonal) fluctuations. Panels B, D and F 3880 illustrate that the bright basal reflector at the center of the map is visible at all frequencies. The surface reflectivity in the bright area does not exhibit peculiar characteristics compared to the surrounding terrain, except at 3 MHz which Orosei et al. (2018) interpreted as due to limited coverage and low data quality. Source: Orosei et al. (2018).

119 The result of this calculation is an envelope including a family of curves that relate the normalized 3885 basal echo power to the permittivity of the basal material (see Figure 7.7A). This envelope was used to determine the distribution of the basal permittivity (inside and outside the bright area) by weighting each allowed value of the permittivity with the values of the probability distribution of the normalized basal echo power (see Figure 7.7B).

3890 The procedure now described lead to two distinct distributions of the basal permittivity estimated inside and outside the bright reflection area (see Figure 7.7C), whose median values are reported in Table 7.1:

Table 7.1: Median values of the basal permittivity estimated inside and outside the bright reflection area for 3895 the two distributions created for the 3 radio pulses at which MARSIS transmits. DISTRIBUTION 1 DISTRIBUTION 2 3 MHz 30 ± 3 9.9 ± 0.5 4 MHz 33 ± 1 7.5 ± 0.1 5 MHz 22 ± 1 6.7 ± 0.1 3900

Figure 7.7: Results of the simulation an retrieved permittivities. In (A), the output of the electromagnetic simulations computed at 4 MHz is shown. The blue shaded area is the envelope of all curves incorporating different amount of H20 ice and dust along with various basal temperatures for the SPLD. The blue line is the 3905 curve for a single model (basal temperature of 205 K and 10% dust content), shown for example, and the black horizontal line is the median normalized basal echo power at 4 MHz from the observations. In (B), normalized basal echo power distributions are reported, inside (blue) and outside (brown) the bright reflection area, indicating two distinct populations of values. These distributions, together with the chart in (A) were used to derive the basal permittivity. For example, the intersection between the blue curve and the 3910 black line gives a basal permittivity value of 24. In (C), basal permittivity distributions inside (blue) and outside (brown) the bright reflection area are shown. The nonlinear relationship between the normalized basal echo power and the permittivity produces an asymmetry in the distributions of the values. Source: Orosei et al. (2018).

3915 The basal permittivity outside the bright area is in the range 4-15, typical for dry terrestrial volcanic rocks, also in agreement with previous estimates of 7.5 to 8.5 for the material at the base of SPLD (Zhang et al., 2008) and with the values derived from radar surface echo power for dense dry igneous rocks on the Martian surface at mid-latitudes (Carter et al., 2009; Mouginot et al., 2010). 3920 By contrast, permittivity values as high as those obtained within the bright area were not previously observed on Mars. Looking at the values registered on Earth, values grater than 15 are seldom associated with dry materials (Guéguen and Palciauskas, 1994). RES data collected in Antarctica

120 (Peters et al., 2005) and Greenland (Oswald and Gogineni, 2008) show that a permittivity larger than 15 is indicative of the presence of liquid water below polar deposits. 3925 On the basis of the evident analogy of the physical phenomena on Earth and Mars, Orosei et al. (2008) deduced that the high permittivity values retrieved for the bright area below the SPLD are due to (partially) water-saturated materials and/or layers of liquid water.

3930 Other possible explanations for the bright area below the SPLD were examined and rejected by

Orosei et al. (2018). For example, a CO2 ice layer at the top or the bottom of the SPLD, or a very

low temperature of the H2O ice throughout the SPLD could enhance basal echo power compared with surface reflections. However, these alternative hypotheses are unlike trustworthy because of the very specific and not physically-reliable conditions required, as well as they do not cause 3935 sufficiently strong basal reflections (see Supplementary material of Orosei et al., 2018). Even if the pressure and the temperature at the base of the SPLD would be compatible with the presence of

liquid CO2, its relative dielectric permittivity is much lower (about 1.6 – Maryott and Smith, 1951) than that of liquid water (about 80), so it does not produce bright reflections.

3940 The presence of liquid water at the base of the polar deposits is supported by the evidences related to the presence of substantial amounts of magnesium, calcium and sodium perchlorate in the soil of the northern plains of Mars, as discovered using the PHO lander’s Wet Chemistry Lab (Hecht et al., 2009, see Section 1.6). In fact, perchlorates can form through different physical and/or chemical mechanisms (Catling et al., 2010; Kim et al., 2013) and were detected in different regions of Mars 3945 (for example, CUR landing site - Glavin et al., 2013): it is therefore reasonable to assume that they are also present at the base of the SPLD. As temperature at the base of the polar deposits is estimated to be around 205 K (Fisher et al., 2010) and due to the fact that perchlorates strongly suppress the freezing point of water (to a minimum of 204 K and 198 K for magnesium and calcium perchlorates, respectively – Hecht et al., 2009), Orosei et al. (2018) concluded that it is plausible 3950 that a layer of perchlorate brine could be present at the base of the polar deposits. The brine could be mixed with basal soils to form a sludge or could lie on top of the basal material to form localized brine pools (Fisher et al., 2010).

The lack of previous radar measurements of sub-glacial water was used to support the hypothesis 3955 that the polar caps are too thin for basal melting and has led some authors to state that liquid water may be located deeper than previously thought (e.g., Lasue et al., 2013). The MARSIS data show that liquid water can be stable below the SPLD at relatively shallow depths (about 1.5 km), thus constraining models of Mars’ hydrosphere. The limited raw-data coverage of the SPLD (a few percent of the area of Planum Australe) and the large size required for a meltwater patch to be 3960 detectable by MARSIS (several km in diameter and several tens of cm in thickness) limit the possibility of identifying small bodies of liquid water or the existence of any hydraulic connection between them. Because of this, Orosei et al. (2018) stated that there is no reason to conclude that the presence of subsurface water on Mars is limited to a single location.

3965

121 7.3 The radar equation

Before introducing the features of the MARSIS radar, some preliminary definitions are reported in 3970 order to better define the terminology used in the following description. A Synthetic Aperture Radar (SAR) is an airborne (or space-borne) side-looking radar system, which utilizes the flight path of the platform to simulate an extremely large antenna or aperture electronically, and that generates high-resolution remote sensing imagery. Typically, SAR produces a two-dimensional (2-D) image. One dimension in the image is called range (or cross track, see 3975 Figure 7.8A) and is a measure of the "line-of-sight" distance from the radar to the target. Range measurement and resolution are achieved in SAR in the same manner as most other radars: range is determined by measuring the time from transmission of a pulse to receiving the echo from a target and, in the simplest SAR, range resolution is determined by the transmitted pulse width, i.e. narrow pulses yield fine range resolution. The other dimension is called azimuth (or along track, see Figure 3980 7.8A) and is perpendicular to range. The ability of SAR to produce relatively fine azimuth resolution differentiates it from other radars. As reported by Brown et al. (2005), the spatial resolution is determined by its Instantaneous Field of View (IFOV), the angle of view from which a signal is received by a sensor (Robinson, 1985), represented by the angle subtended by a single detector element of an optical system and the 3985 geometry of the antenna. IFOV is independent of sensor altitude. The geometric projection of the IFOV onto the ground is called the Ground-projected Instantaneous Field of View (GIFOV) and is determined by IFOV and sensor height (Schowengerdt, 1997). GIFOV is the spatial resolution of the sensor. In combination with sampling rate, the GIFOV determine the spatial dimensions of the picture element (i.e. pixel) in an image. Similarly, the angular extent of observations acquired 3990 perpendicular to the satellite’s path is defined as the Field of View (FOV). The dimensions of the projected FOV onto the ground is the Ground Field of View (GFOV) or the swath width (Schowengerdt, 1997).

Figure 7.8: Cross track (A) and along track (B) scanners. In case (A), the observing beam is swept transverse 3995 to the orbital motion, while in case (B) multiple parallel observations are acquired simultaneously along the path of the satellite with detectors oriented orthogonal to the satellite’s motion. Source: Brown et al. (2005).

122 To describe the features of a radar receiver, the radar equation is used (Curlander et al., 1991). Previously, some definitions are needed.

4000 A transmitting antenna accepts input power Pi at some point along the feed line (the cable or other transmission line that connects the antenna with the radio transmitter or receiver). The point is typically taken to be at the antenna (the feed point), thereby not counting power lost due to joule

heating in the feedline and reflections back down the feed line. The efficiency ϵantenna of an antenna is

the total radiated power P0 divided by the input power at the feed point: 4005

P0 ϵantenna= (7.1) Pi

Antennas are invariably directional to a grater or lesser extent, according to how the output power is distributed in the space. By considering spherical coordinates (θ, φ), where θ is the altitude or angle 4010 above a specified reference plane (such as the ground), while φ is the azimuth as the angle between the projection of the given direction onto the reference plane and a specified direction (such as north or east) in that plane with specified sign (either clockwise or counterclockwise). The distribution of the output power as a function of the possible directions (θ, φ) is given by its radiation intensity U(θ,φ) (in W∙sr-1). The output power is obtained from the radiation intensity by integrating the latter 4015 over all solid angles dΩ = sinθ dθ dφ:

−π π/2 −π π/ 2

P0=∫ ∫ U(θ,ϕ)dΩ=∫ ∫ U(θ,ϕ)sinθdθdϕ (7.2) −π −π/2 −π −π/2

The mean radiation intensity U is given by, considering Eq. 7.1: 4020 P ϵ ⋅P U= 0 = antenna i (7.3) 4π 4 π

The directivity D(θ,φ) of an antenna in a given direction is the ratio of its radiation intensity U(θ, φ) in that direction to its mean radiation intensity U , that is: 4025 U (θ,ϕ) D(θ,ϕ)= (7.4) U

An isotropic antenna, meaning one with the same radiation intensity in all directions, therefore has directivity, D = 1, in all directions independent of its efficiency. More generally the maximum, 4030 minimum and mean directivities of any antenna are always at least 1, at most 1, and exactly 1. When the directivity of an antenna is given independently of direction it refers to its maximum directivity in any direction, namely:

D=max D (θ,ϕ) (7.5) (θ,ϕ) 4035

123 The power gain or simply gain G(θ,φ) of an antenna in a given direction takes efficiency into account by being defined as the ratio of its radiation intensity U(θ,φ) in that direction to the mean

radiation intensity of a perfectly efficient antenna. Since the latter equals Pi /4 π , it is therefore given by: 4040 U (θ,ϕ) U (θ,ϕ) G= =ϵantenna⋅( )=ϵantenna⋅D(θ,ϕ) (7.6) Pi/4 π U¯

As with directivity, when the gain G of an antenna is given independently of direction it refers to its maximum gain in any direction. Since the only difference between gain and directivity in any

4045 direction is a constant factor of εantenna independent of θ and φ, it results:

G=ϵantenna⋅D (7.7)

It is possible now to introduce the radar equation: 4050 P G2 λ2σ P = t (7.8) r (4π)3 R4

where Pr is the power received at the antenna, Pt is the power radiated by the antenna, G the antenna gain, R the distance from radar to the target, λ the operating wavelength and σ the radar target cross 4055 section, a measure of how detectable an object is by radar.

7.4 The MARSIS radar: description and data features

MARSIS is a multi-frequency, synthetic-aperture, subsurface radar sounder onboard the ESA Mars 4060 Express orbiter. Data are collected when the elliptical orbit of Mars Express brings the spacecraft to an altitude of 250 to 800-1000 km above the surface: this condition, as reported by Picardi et al. (2005), is obtained during about 26 min of each 6-7 h orbit. It operates best in dark (local night) as echoes suffer far less distortion from the ionosphere. The radar transmits 1 MHz bandwidth pulses centered at 1.8, 3, 4 or 5 MHz, alternating the transmission at two different frequencies. Peak 4065 transmitted power out of the 40-m dipole antenna is ~ 10 W, with a repetition frequency of 127.7 Hz (Jordan et al., 2009). The radar collects echoes reflected by the surface and by any other dielectric discontinuity present in the subsurface. Longer wavelenghts (lower frequencies) have deeper penetration, but pulse frequency must be above the plasma frequency of the Martian ionosphere to reach the surface. 4070 MARSIS vertical resolution is approximately 210 m in free space (Orosei et al., 2018). In the subsurface, vertical resolution is improved by a factor equal to the square root of the soil permittivity. Horizontal resolution depends on surface roughness characteristics, altitude of the satellite and operating frequency, but for most Mars surfaces, the cross-track footprint (lateral 4075 resolution, see Figure 7.8) is 10 to 30 km whereas the along-track footprint (see Figure 7.8), limited by SAR processing (Jordan et al., 2009), is 5 to 10 km. The SAR processing consists of coherent

124 summation of a group of consecutive pulses after correction for the vertical motion of the spacecraft. Due to limitations related with spacecraft data transmission, MARSIS is typically programmed to 4080 perform SAR processing onboard (Jordan et al., 2009). However, Orosei et al. (2018), for their discovery, used raw echo data. In order to achieve this, some instrument software parameters were modified (Cicchetti et al., 2017), so that the raw data bypassed the on-board processing and were stored directly in the instrument memory for the subsequent downlink. This new data collection protocol yielded 3200 consecutive echoes, at two different frequencies, over a continuous ground 4085 track approximately 100 km long. Data processing on Earth was centered on range compression and geometric calibration to compensate for altitude variations. In the analysis presented in Orosei et al. (2018), SAR processing was not performed because of the smoothness of the SPLD in this area, which causes surface echoes to originate solely from the specular direction; in this case, SAR processing would be reduced to a simple moving average of nadir echoes. Moreover, no correction 4090 for ionosphere distortion (Cartacci et al., 2013) was applied to the data. Due to MARSIS antenna large size, the radiation pattern could not be characterized before launching, thus preventing retrieval of geometric power fall-off due to altitude variations. According to Eq. 7.8, radio echo power decreases as the inverse of the fourth power of distance between the antenna ad the target. Because of the surface smoothness in this area, topographic 4095 roughness is well below the MARSIS wavelength (Smith et al., 2001; Neumann et al., 2003) and scattering is almost totally coherent. Under these conditions, the size of the MARSIS footprint is well approximated by the first Fresnel zone (the first of a series of confocal ellipsoidal regions of space between and around a transmitter and a receiver, see Figure 7.9). The radius of this zone ranges between 3 and 5 km, depending on satellite altitude (300-800 km) and frequency (Picardi et 4100 al., 2004a). The power reflected by a flat disk is proportional to the square of its area (LeVine, 1984) and the area of the Fresnel circle increases linearly with altitude. Substituting these quantities in Eq. 7.8, it is found that the decrease of echo power is inversely proportional to the square of distance. To correct geometric power fall-off due to altitude variations, surface echo power was thus normalized by the squared altitude of the spacecraft. 4105

4110

4115

Figure 7.9: A representation of the Fresnel zone. D is the distance between the transmitter and the receiver; r 4120 is the radius of the first Fresnel zone (n=1) at point P. P is d1 away from the transmitter, and d2 away from the receiver.

125 7.5 Simulating radar echoes: the MARSIS simulator

4125 Radar sounding is the only remote sensing technique allowing the study of the subsurface of a planet from orbit, by detecting dielectric discontinuities associated with compositional and/or structural discontinuities. To map the stratigraphy can be of fundamental importance to better understand the dynamics and the history of the first meters to kilometers of the subsurface. This technique, known as Ground Penetrating Radar (GPR), was extensively used to investigate the 4130 terrestrial subsurface. It is based on the transmission of radar pulses at frequencies in the Medium Frequency (MF, frequency range 0.3-3 MHz), High Frequency (HF, 3-30 MHz) and Very High Frequency (VHF, 30-300 MHz) portions of the electromagnetic spectrum into the surface, to detect reflected signals from subsurface structures (see e.g. Bogorodsky et al., 1985). Orbiting GPR were successfully employed in planetary exploration (Phillips et al., 1973; Picardi et al., 2004b; Seu et 4135 al., 2007a; Ono et al., 2009) and are often called subsurface radar sounders. As mentioned in Section 7.4, MARSIS is optimized for deep penetration, having detected echoes down to a depth of 3.7 km over the SPLD, working at four different bands, from 1.8 MHz to 5 MHz with a 1 MHz bandwidth. It transmits through a dipole, which has negligible directivity, with the consequence that the radar pulse illuminates the entire surface beneath the spacecraft and not only 4140 the near-nadir portion from which subsurface echoes are expected. The electromagnetic wave can then be scattered by any roughness of the surface. This surface backscattering from off-nadir directions is called clutter. Clutter can produce in radar data the impression of subsurface structures where there are in fact none. Thanks to NASA Mars Global Surveyor mission, and more specifically, to the MOLA altimeter, a 500-meter resolution elevation map of nearly the entire Mars 4145 surface is available. This topography map can be used to simulate MARSIS radar echoes from the surface and compare with the actual MARSIS echoes during the interpretation.

A code for the simulation of radar wave surface scattering was developed by Cantini et al. (2014) using the MOLA-MEGDR topographic dataset (http://geo.pds.nasa.gov/missions/mgs/megdr.html), 4150 to represent the Mars surface as a collection of flat plates called facets. The radar echo is computed as the coherent sum of reflections from all facets illuminated by the radar, for all frequencies within the broad-band radar pulse (Nouvel et al., 2004). The code was developed using the Matlab computing language and it was tested also under OCTAVE (http://www.gnu.org/software/octave/), a free, GNU General Public License software (GPL’d, http://www.gnu.org/copyleft/gpl.html) that is 4155 mostly compatible with Matlab. The computational burden of every simulation is very high, requiring more than two weeks on a common desktop PC. In Figure 7.10 a simple flowchart of the program is reported, showing the steps performed to simulate the echoes expected for a orbit.

Because MARSIS accumulated several thousands observations, a drastically different approach was 4160 developed to simulate the entire existing dataset. Federico Cantini rewrote the code in order to use the computational resources available at CINECA (http://www.hpc.cineca.it/). The steps performed can be summarized in the following list:

• rewrite the code using C language; 4165 • parallelizing the code using MPI libraries (http://www.mcs.anl.gov/research/projects/mpi/);

126 • introducing a further parallelization step using Open MP (http://openmp.org/wp/), obtaining an hybrid parallel program.

The serial C code was compared by Cantini and Orosei to the MATLAB/OCTAVE version both 4170 running on a single core of the CINECA PLX cluster. The pure MPI code has been compared to the C serial code running on the PLX cluster and, finally, the hybrid (MPI+OpenMP) code was compared to the serial one on PLX and tested for scalability on FERMI. The simulation of each orbital point involves calculations on different size 2D matrixes. By design, the algorithm is linear with the number of matrix elements. 4175 The performances of the MARSIS simulator depend on computational resources available. The time required for the calculation of few points (up to 10), and the corresponding number of matrix elements, of the testing orbit using GNU-OCTAVE on a single core of the CINECA PLX cluster, together with the same data for the first 100 points of the testing orbit using the C serial program is 4180 shown in Table 7.2.

Table 7.2: Time required to compute the specific numbers of matrix elements running the original version of the MARSIS simulator using GNU-OCTAVE (top) and the serial C version (bottom) on a single core of the CINECA PLX cluster. The linear trend of the compute time as a function of the number of matrix elements is 4185 confirmed by the results shown. GNU-OCTAVE n° matrix elements n° orbital points Time (h)

196128 1 0.90 4190 979776 5 6.05 1962120 10 12.14

C-VERSION n° matrix elements n° orbital points Time (h) 4195 196128 1 0.11 9934184 50 6.04 20234901 100 12.46

The time required for the calculation of the whole testing orbit was estimated on the base of these 4200 data: for Octave/Matlab, 263.71 days, for C version, 25.57 days (Source: Cantini, 2013).

127 Figure 7.10: A simple flowchart showing the principal features of the MARSIS simulator.

128 The noticeable improvements in time calculation was registered after introducing parallellization in 4205 the code, as evident by consulting Table 7.3 (Source: Cantini, 2013).

Table 7.3: Time required to compute the whole testing orbit as a function of the number of cores on the CINECA PLX cluster for pure MPI version and Hybrid (MPI+OpenMP) version of the MARSIS simulator. n° cores n° MPI process compute time (h) CPU time (h) pure MPI Hybrid (MPI+OpenMP) pure MPI Hybrid (MPI+OpenMP) pure MPI Hybrid (MPI+OpenMP) 48 48 4 11.6 11.5 555.2 552.9 96 96 8 5.8 5.4 559.0 106.7 168 168 14 3.3 3.3 558.8 184.0 336 336 28 1.7 1.7 563.7 561.9

4210 7.6 Installation of the MARSIS simulator on the CMCC Athena cluster

The MARSIS simulator, in its Hybrid version (MPI+OpenMP), was successfully installed also on the CMCC Athena cluster (see Section 2.7). A series of attempts were performed in order to identify the most appropriate configuration, as well as to test the calculation time necessary to simulate a 4215 whole orbit. By setting the computational environmental so to load the INTEL/intel_xe_2015.3.187 and the IMPI/intel_mpi_5.0.3.048 modules, the code was successfully compiled and than executed. In Table 7.4 the list of the various tests completed together with the compute time, is reported. As evident by consulting it, the time required to simulate a whole orbit with CMCC cluster is in accordance with the performance obtained with CINECA PLX cluster. 4220 Table 7.4: Calculation time registered on the CMCC Athena cluster for the MARSIS simulator. n° cores n° points compute time (h)

192 100 0.1 4225 192 500 0.35 192 1000 0.75 384 whole orbit 1.4

The testing orbit used for the tests was ID n° E_08915_SS3, which spanned a region of Mars 4230 starting from point having coordinates (7.176 °S, 263.1743° E) and ending at point (67.6767 °S, 67.8658 °E). Time calculation depends obviously on the number of points that each orbits presents, so it can change depending on this number: typically, computational time ranges from 30 m to 1.5 h.

During the research stay I spent at INAF (Bologna), 651 new orbits were simulated on the Athena 4235 cluster.

In order to test the reliability of the output produced, I used a script, written in Matlab by Roberto Orosei, named “readmarsisedrsim.m” and reported in Appendix E, that stores all the geometric, physical and instrumental parameters needed to reproduce the echoes expected for the testing orbit 4240 mentioned before. In Figure 7.11 the echoes so obtained are reported. By comparing them with the verified output for the same testing orbit performed with previous simulations carried out at

129 CINECA, I verified that the output generated with CMCC Athena cluster is genuine and can be then processed. All the 651 simulated orbits were carefully checked with the script presented in Appendix E and then plotted with ad hoc code. 4245 Each simulated orbit is characterized and defined by the parameters here listed: • ostline : current line of the Operation Sequence Table, the file containing commands for the sequence of observation • f0: the frequency at which the radar was collecting data (it is matrix, because MARSIS 4250 works by transmitting at 2 frequencies, not exactly simultaneously but close to each other); • theta_s : expected slope angle, a parameter used to compensate any large scale terrain slope; • frameid : a number identifying the current observation; • scetfw : spacecraft clock count, integer part; • scetff : spacecraft clock count, fractional part; 4255 • Vt: tangential component of the spacecraft velocity; • Vr : radial component of the spacecraft velocity; • NA : number of impulses used, which changes according to the frequency considered;

• x 0, y0, z0: reals position vectors of the spacecraft; • alt0 : altitude at which the spacecraft collected data with respect the Martian surface;

4260 • Vx 0, Vy0, Vz0: true velocity vectors of the spacecraft; • lon_0, lat_0 : longitude and latitude at which data were collected; • esm1f1, es00f1, esp1f1, esm1f2, es00f2, esp1f2 : a nxm matrices (where n is the number of the echo samples, usually 512, and m the number of points of the orbit), containing the physical information. In detail, their names are so established:

4265 es[filter][frequency][real/imaginary]

where “es” stands for echo, simulated; "filter" can assume three values, -1 (m1, radar looking back), 0 (00, nadir) and +1 (p1, radar looking forward) and corresponds to the three different directions of observation of the radar; "frequency" is the index of one of 4270 the two frequencies (f1 or f2) at which the radar was operating in that moment (no direct indication of the frequency in Hz is given by them: this information is stored in the f0 matrix); “real/imaginary” contains the sum of the real and the imaginary part (i.e., esm1f1 = esm1f1r + i ∙ esm1f1i). An example is shown in Figure 7.11.

4275 The new simulated orbits so processed were added to the pre-existing database of echoes so to perform global reflectivity maps discussed in the following Sections. The simulations used for this analysis, both the new and the pre-existing ones, are not yet published in the literature.

130 4280 Figure 7.11: Output generated with CMCC Athena cluster with the MARSIS simulator for the testing orbit E_08915_SS3. The meaning of the numbers here reported is explained in the text.

7.7 Reflectivity maps 4285 Before illustrating the procedures applied to make, from the simulated MARSIS radargrams, global reflectivity maps of the Red Planet, some physical parameters useful for the analysis presented in the following Sections are briefly described.

4290 7.7.1 Physical parameters

Reflectivity maps allow to provide unique information on the nature of the surface geological material, and more generally on a planet geology and climatology. Instead of looking at individual radargrams retrieved by MARSIS radar, it will be more interesting to build global map by extracting 4295 the surface echo power from each frame (pulse) of each radargram. This is the so-called “reflectivity map”, which gives important information on the composition and physical properties

131 of the upper part of the Martian crust at a global scale. Radar reflectivity maps of the Moon at different frequencies were already measured in the past from ground-based instruments and used to infer important properties of the lunar terrains (Evans, 1962; Evans and Pettengill, 1963). For 4300 example, Campbell and Hawke (2005) show that the reflectivity values measured at the wavelength λ=70 cm can be influenced by the composition of terrains buried more than 50 m deep in some cases, thus demonstrating the ability of this method to probe at large depth. In the case of Mars, some measurements were also retrieved by using ground based radio telescopes at λ= 3.5–70 cm (Simpson et al., 1992; Harmon et al., 1999) or spacecraft as Mars-3 and Mars-4 spacecraft and 4305 Viking orbiter 2 at λ=13.1 cm (Simpson et al., 1979) but were rather limited in terms of spatial resolution and/or geographic extent. The reflectivity values obtained from these measurements were then applied to estimate the dielectric constant of surface materials (Pettengill et al., 1973; Downs et al., 1973, 1975; Simpson et al., 1982). Spatial variability of the value of the dielectric constant were interpreted in terms of variations of bulk density and/or compositional variations (Campbell and 4310 Ulrichs, 1969) of subsurface materials.

Mouginot et al. (2010) were the first to create the global map of surface echo power at 3-5 MHz of Mars. Here the principals steps performed by them to reach this result are resumed: a similar approach was applied for creating the reflectivity maps reported in Appendix G: 4315 • firstly, the surface echo power values were extracted from the data. MARSIS radargrams are composed of about a thousand frames, with each frame corresponding to a vertical sounding of the Martian surface. Radar echoes appear when the transmitted waves meet discontinuities (i.e. brusque changes) in the dielectric constant (or relative permittivity, 4320 defined as the ratio between the complex frequency-dependent permittivity ε(ω) of a

material and the vacuum permittivity ε0). The first echo in the radargram is generally associated to the surface echo, because lateral (clutter) and subsurface echoes arrive later due to a longer distance between reflectors and spacecraft. Furthermore, the intensity of the surface echo is generally much higher than that of clutter or subsurface echoes. A selection 4325 criteria is fixed to localize the surface echo (for details, see Mouginot et al., 2010); • the surface echo power largely depends on the attenuation of the electromagnetic waves between the spacecraft and the surface, mainly caused by the range attenuation (see Eq. 7.8) and ionospheric absorption: these effects must be corrected with appropriate methods, varying according to the physical models used to describe the phenomena; 4330 • after extracting the surface echo power from the echo histories and correcting them for range dependence and ionospheric absorption, the global map of the surface echo power can be than constructed (see Figure 7.13a).

Finally, it must be underlined how several parameters might affect the surface echo power: surface 4335 roughness, slope distribution and the dielectric constant of the surface materials. Most backscattering models separate the effect of the dielectric constant (material chemistry) from those of topography (roughness, slopes) (Ulaby et al., 1986; Picardi et al., 2004b). All these effects must be adequately considered when reflectivity maps must be produced.

4340

132 7.7.2 Mars global reflectivity maps

In Appendix F the code named “bins_creation.m” written in Matlab to make global reflectivity maps from the simulated echos produced with the MARSIS simulator is reported. In this Section, an 4345 essential description is reported on the way by which these maps where obtained.

After extracting all the parameters stored in the files containing the echoes, by using the “readmarsisedrsim.m” script described in Appendix E, the surface echo power in each direction given by Eq. 7.9 can be calculated : 4350 I=max(20⋅log(|es 00f 1|)) (7.9)

where “00” indicates the nadir-direction and f1 the first of the two-working frequencies (see previous Section). 4355 MARSIS works with two frequencies simultaneously, for example f1 = 1.8 MHz and f2 = 3 MHz). If the radar is acquiring during hours beginning from nighttime and going towards daytime, the lower frequency available is used (f1= 1.8 MHz) in order to (hopefully) better penetrate the atmosphere and to be less influenced by the ionosphere; for safety, f2 = 3 MHz is set so to be sure 4360 that the radar will be able to acquire the signal if f1 fails. Going towards the central hours of the day, with f1 it is impossible to detect the signal because of the plasma frequency due to the Martian ionosphere being too high, so the other available frequencies are applied (3, 4 or 5 MHz). This is the reason why the two frequencies are separated and stored in two different lines (f1 and f2) that compose the f0 parameter of each orbit. To have an idea of the number of points available, I 4365 managed 429135 echoes for 1.8 MHz band, 3691243 for 3 MHz band, 6624572 for 4 MHz band and 3356798 for 5 MHz band.

In order to clarify the terminology used, I used the term “frequency” for referring to the two ways of acquisition, i.e. one of the two channels f1 and f2 (two-frequency mode) employed, while the 4370 term “band” refers to indicate the operating frequencies (band 1, band 2, band 3, band 4, i.e. 1.8 MHz, 3 MHz, 4 MHz, 5 MHz), or in other terms, to the frequency having a bandwidth of 1 MHz centered on this values.

After coupling the radar echoes associated to each band, the phase shift existing between an impulse 4375 and the following one must be corrected. A limit must be defined, below which the difference X, given by: 1 (Vr −Vr )⋅(N −1)⋅ reference computed A 127.27 X = ⋅2π (7.10) λ

can be tolerate. In Eq. 7.10, Vrreference is the radial velocity of reference, Vrcomputed is the deduced radial

velocity from X0, Y0, Z0, VX0, VY0 and VZ0, NA is number of impulses registered for that 4380 observation, 127.27 is the repetition frequency (i.e. the time passed between an echo and another) and λ is the wavelength considered. Only those points showing a X included in the intervals in

133 ]-π/4; π/4[ were considered, i.e. all those points having Vrreference – Vrcomputed (the effective shift) grater than ± π/4 were excluded from the calculations.

4385 Once extracted data for the desired frequency and eliminated points having extreme radial velocity, they can be put into grid cells so to make the maps. The idea is to create bins with resolution 0.5° (lat) x 0.5° (lon), placing the data for the studied band and direction in the bins and then compute the medians of the points belonging to the same bin. In Appendix G, Figure G1-G12 are reported all the global reflectivity maps produced for all the available direction (00, M1 and P1). 4390 7.8 Discussion of the results obtained

In Section 7.7 was showed how the surface echo power can be derived from MARSIS measurements. The retrieved values were calibrated to compensate for changes in the distance of 4395 the spacecraft to the surface and for the attenuation of the signal by the ionosphere. The results are used to build the global maps of surface echo power at 1.8, 3, 4 and 5 MHz in the three working directions of the radar (see Appendix G).

The surface echo power variations are primarily caused by kilometer-scale surface roughness. Then, 4400 the values of dielectric constant of the shallow subsurface materials are derived by normalizing the surface echo power map using a simulation of MARSIS signal from the MOLA topography (the MARSIS simulator). As a result, a map that characterizes the dielectric properties of the materials down to a few dam below the surface can be obtained. Dielectric properties vary with latitude, with high values in mid-latitudes belts (20° - 40°) and lower values at both equatorial and high altitudes. 4405 Two main parameters are likely to control the dielectric constant of the layer involved in the reflection process: the composition (chemistry, mineralogy, water content and physical state) and the density of the constituent materials. Because water ice presents a low dielectric constant (typically 3.1) compared to igneous rocks (typically, 8) at MARSIS wavelengths, the presence of a significant amount of ice in the layer involved in the reflection process will lead to a decrease in 4410 surface reflectivity, compared to a dry, dense rock layer. The MARSIS dielectric transition is not associated to a systematic change in surface albedo or thermal inertia, which implies that the surface geological material does not change much upon this cross transition.

In Figure 7.12 the reflectivity map obtained at 4 MHz in the nadir direction (00) is reported, labeled 4415 with numbers (1-13) in order to easily individuate the regions of Mars cited in the following discussion.

From the comparison of MARSIS reflectivity map to GRS (Mars Odyssey) observations, it can be stated that the reflectivity decrease observed poleward of 50°-60°S corresponds to the onset of 4420 water-ice occurrence within the regolith. The roughest terrains on Mars, such as the Olympus Mons aureole (Figure 7.12, n. 1), Valles Marineris (Figure 7.12, n. 2) and the Argyre crater rim (Figure 7.12, n. 3) displays very low surface echo power. Highlands Plateau (Figure 7.12, n. 4), which is a heavily cratered region in the SH, presents globally a lower reflectivity compared to the smoother northern plains (Vastitas Borealis, Figure 7.12, n. 5). The smoothest terrains as the volcanic plateau

134 4425 in Tharsis region (Figure 7.12, n. 6) or Amazonis Planitia (Figure 7.12, n. 14) are characterized by a very high reflectivity.

Examination of the global reflectivity map reveals significant spatial variations over the planet. The most obvious feature is the latitude-dependent pattern in reflectivity: the equatorial region displays 4430 low values, the mid-latitudes high values and the high latitudes low values again.

The low-reflectivity pattern in the equatorial regions is interrupted by very high reflectivity on the Tharsis volcanic plateau (Figure 7.12, n. 6), including Sinai (Figure 7.12, n. 7a), Solis (Figure 7.12, n. 7b) and Daedalia plana (Figure 7.12, n. 8), and the area between the Tharsis Montes and 4435 Olympus Mons (Figure 7.12, n. 9). In the mid-latitude bands, the largest continuous patch of high reflectivity is on the northern side of the Elysium Mons shield (Figure 7.12, n. 10). The northern high latitudes are generally higher in reflectivity than the southern high latitudes, with the exception of the area north of Alba Patera (Figure 7.12, n. 11). The south residual polar cap has a very low

reflectivity due to interferences within the thin layer of CO2 ice, causing mush weaker surface 4440 reflections compared to reflections from a pure water ice surface. Bands of apparent low reflectivity in the Terra Cimmeria region (Figure 7.12, n. 13) are probably artifacts related to the ionosphere.

The results now presented and derived by the reflectivity maps created with the MARSIS simulator are in accordance with Mouginot et al. (2010): by extracting the surface echo power from 2 years of 4445 MARSIS measurements, the authors were the first to build up a global map of surface echo power at 3-5 MHz showing similar features to those here developed (see Figure 7.13a). They also presented a method for simulating MARSIS echo histories due to local topography to help the interpretation of the observational data (Figure 7.13 b: for details about the method, see Mouginot et al., 2010). Similar evidences (with a greater detail) can be deduced by comparing it with the 4450 reflectivity maps produced by manipulating MARSIS simulator outputs.

By using the full MOLA dataset, Krevalsky and Head (2000) produced kilometer-scale roughness maps of Mars reported in Figure 7.13c. To produce these maps, they calculated the curvature (the second derivative) of MOLA profiles at each of ~6.4∙108 MOLA footprints using three baseline 4455 lengths: the smallest possible (three nearest MOLA footprints, 0.6 km baseline), four times longer (2.4 km baseline) and four more times longer (9.6 km). Krevalsky and Head (2000) used a 3 color- coded scheme, by computing 3 different scales, in order to investigate how the roughness varies depending on the scale considered. The red color is that related with the higher scale (about 10 km), i.e. to longer wavelength, the green is associated to 3 km-scale and the blue one to 1-km scale. The 4460 black regions are flat at all scales (and the topography here is quite stationary), while the regions with shades of red and blue show a predominant roughness that is visible at that scale.

In the roughness map, the Elysium region is not flat everywhere, while, according to the reflectivity maps deduced by the radar echoes, this region is very reflective and flat: so, a region that seems to 4465 present, from a topographic point of view, some surface roughness, for the radar is quite flat. This is very interesting because three regions (Elysium, Amazonis and Tharsis) having substantially the same reflectivity, regardless of topography (and where there is only the effect of the dielectric constant) are very useful to calibrate data. By checking the reflectivity map obtained for 5 MHz

135 band (see Figure G.4 of Appendix G), it can be confirmed that, because these regions are almost 4470 equally reflective also at this band, the ionosphere correction applied is correct. The reflectivity maps created could also be used as a threshold mask in order to define for what roughness values in the footprint we can be confident about the extrapolation of the dielectric constant derived by the simulations: under this limit, the estimation can be considered as reliable, over this limit not.

4475 The importance of having created reflectivity maps at different frequencies is fundamental for local or regional studies (e.g. Mouginot et al., 2008) because, by comparing the maps in several frequency bands, it could allow to study materials and/or structures that could change the surface reflectivity as a function of frequency.

136 Figure 7.12: Reflectivity map obtained from echoes registered at 4 MHz in nadir direction (00). The numbers are used to easily identify some regions of Mars cited 4480 in the text, in details: 1. Olympus Mons aureole; 2. Valles Marineris; 3. Argyre Crater rim; 4. Highlands Plateau; 5. Vastitas Borealis; 6. Tharsis region; 7a. Sinai Planum; 7b. Solis Planum; 8. Daedalia Planum; 9. area between Tharsis Montes and Olympus Mons; 10. northern side of Elysium Mons shield; 11. Alba Patera; 12. Hellas Planitia; 13. Terra Cimmeria region; 14. Amazonis Planitia.

137 4485

Figure 7.13: (A) Reflectivity map at 3–5 MHz of the martian surface as seen by MARSIS. Red corresponds to high reflectivity and blue to low reflectivity. Gray regions correspond to a lack of data. The map is in cylindrical projection. The spatial resolution is 0.5 bin per degree. Source: Mouginot et al. (2010). (B) 4490 Reflectivity map based on simulated radargrams. Gray regions correspond to a lack of data. The map is a cylindrical projection. The resolution is 0.5 bin per degree. Source: Mouginot et al. (2010). (C) Map of kilometer-scale roughness of Mars (simple cylindrical projection). The map is a composite RGB image, with red, green, and blue channels displaying roughness at baselines of 9.6, 2.4, and 0.6 km, respectively. Brighter shades denote rougher surfaces. Source: Kreslavsky and Head (2000).

138 4495 CONCLUSIONS

The main results achieved during the course of my PhD program are presented in this final Section. An outlook on future studies is also provided.

4500 The main topics covered during my PhD can be resumed in the following list:

• installation and configuration of the MarsCAM-NCAR GCM on the CMCC Athena cluster and optimization of the big-data managing CMCC Ophidia tool used to manipulate output data for astrophysical purposes; 4505 • study of the present Mars climate conditions with the MarsCAM-NCAR software by comparing climatic variables with landers/rovers observations; • installation of the Martian Climate Database (MCD) derived from GCM-LMD (Laboratoire de Météorologie Dynamique), validation with spacecraft measurements and comparisons with MarsCAM-NCAR output; 4510 • porting of the MARSIS simulator to the Athena cluster (CMCC). Simulation of the echoes expected for some orbits and comparison with the radargrams obtained from MARSIS radar, in search for the presence of subsurface liquid water; • production of simulated surface reflectivity maps and testing with similar maps based on observational data in order to identify the variations of the dielectric constant on the Martian 4515 surface.

All the demanding computational tasks I performed were achieved thanks to the scientific affiliation I signed with the Advanced Scientific Computing (ASC) Division of the CMCC Foundation, unit of Lecce, covering all the 3 years of my PhD: Prot. n. 1659/CMCC/2016 for 2016/2017; Prot n. 4520 268/CMCC/2018 for 2018; Prot. n. 020/CMCC/2018 for 2019.

The temporal trends evolution of the principle atmospheric variables (temperatures, pressure) was reconstructed by means of two of the most applied GCMs able to simulate the weather conditions of the Red Planet: GCM – LMD (Laboratoire de Météorologie Dynamique) and MarsCAM-NCAR. 4525 The aim was to systematically verify the reliability of these software programs in representing surface (TG) and near-surface (TSA) temperature temporal trends collected by the eight landers/rovers that successfully explored the Red Planet (till 2019): Viking 1, Viking 2, Mars Pathfinder, Spirit, Opportunity, Phoenix, Curiosity and InSight. This task is a necessary preliminary step in view of simulating ancient Mars climate conditions (Chapter 2), because only after 4530 thoroughly validating the outcomes of the simulation programs on data directly measured on Mars, the GCMs can be considered reliable tools to replicate the completely different climatic conditions that characterized the planet Gys ago. In fact, very probably, on ancient Mars, liquid water was hosted on its surface for an extended period of time, as evidenced by the numerous geological structures observed (Di Achille and Hynek, 2010; Matsubara et al., 2013) and by the recent 4535 discovery of a salty lake on the southern polar cap of Mars (Orosei et al., 2018). In particular, checking the ability of the GCMs to represent daily, seasonal and yearly temperature trends is at the

139 basis of any paleoclimatic simulation study, in which temperature is the most important parameter to be evaluated (Haberle, 1998) in search for favorable conditions for liquid water.

4540 The programs compared in this thesis present different computational features (the most significant ones are described in Chapter 3) that influence the output generated. A decisive role is also covered by the three physical parameters that mostly affect simulations: albedo, thermal inertia and dust OD. As evidenced in this thesis, from this point of view, the main discrepancy between the two GCMs is related to the last parameter: in fact, while MCD Scenarios take into account seasonal and 4545 geographical variations of dust OD (according to the values registered during MY 24-31, see Forget et al., 2017), MarsCAM-NCAR Runs are performed with a fixed dust OD, whatever the moment of the year and the locations studied. Sensitivity tests were performed to evidence how simulated TG and TSA variables react to a change of these parameters: altering thermal inertia seems to mostly impact on them, more than what happens for dust OD and albedo. 4550 The comparison carried out involved 15 Scenarios stored in the MCD database obtained by GCM- LMD, and 7 representative Runs for MarsCAM-NCAR program (Section 3.1), installed on the CMCC Athena cluster. The output produced by the latter software was first processed with CMCC Ophidia tool (Section 3.7) and then imported into Matlab for the main computations. Dedicated 4555 Matlab scripts were created to adequately manage the observational data collected by the eight landers/rovers on the Mars surface and downloaded principally from the PDS node (Section 3.5). As reference values for the comparisons, all the available TG and TSA measurements acquired till June 30, 2019 were considered, checking accurately the datasets so to make them as homogeneous as possible (Section 3.6). In fact, data are not assembled in the same way for all the probes, depending 4560 on the instrumentation onboard: for example, not all the spacecrafts had a meteorological station (SPI and OPP, see Chapter 1), and the time step used to collect data varied from probe to probe. Moreover, data in the various sols were not complete and, furthermore, data were not available for all the year, due in some cases to the short life of the mission (MPF, PHO), in others to problems occurred during the campaign of acquisition (see Tables 3.3 and 3.4). For these reasons, as 4565 described in Section 3.6, it was necessary to carefully check the datasets, eliminating corrupted or incomplete data, and then appropriately denoising and resampling them. In addition, data were also preliminary manipulated in order to consider the longitude of landing sites.

In order to investigate the grade of accordance between simulated and observational data, two 4570 distinct approaches were adopted (Chapter 4): Group 1 analyses, for evaluating temperature evolution (daily minima, averages and maxima trends) during seasonal and yearly time intervals (Section 4.2), and Group 2 analyses, for studying the diurnal temperature cycle (Section 4.7). For each Group, after separating TG from TSA datasets, two kinds of studies were performed:

4575 • type a , by assembling together all data of the various spacecrafts in the same aggregation case (seasons and the whole year for both Groups, and also maxima, minima and averages regardless of the year period for Group 1); • type b , by studying individually data referred to single probes.

140 4580 To quantify the discrepancies between modeled and experimental measures, the RMSE distance between the experimental curves and the model curves was calculated for each of the nine different data aggregation cases (Section 4.3). An assessment method based on a voting system, the Modified Borda-Count (MBC, Section 4.4) was then applied. MBC is able to rank the performances (on the basis of RMSE distances between experimental and model curves) of the two GCMs compared, by 4585 processing the output derived by the several Scenarios/Runs processed. This method also takes into account the weight of each voting dataset in terms of its numerousness of data available for each spacecraft by weights. Additional statistics were computed, in order to interpret each case-study from distinct points of view: Chebyshev distance (CHEB), Mean Signed Deviation (MSD), and maximum and minimum residual with sign (ERR, Section 4.2). 4590 The detailed discussion of the results of the comparisons performed is reported in Chapter 5. Over- and underestimations in terms of MSD statistics, are presented and arbitrarily considered as negligible when their absolute value was lower than 5K, in which case they are not reported. From TG comparisons, by matching the results obtained for Group 1a and Group 2a (seasonal and yearly 4595 trends, Section 5.2.1 and Section 5.3.1), it could be concluded that, according to MSD statistics:

• both models well reproduce the yearly trends, with average negligible fluctuations with respect to the experimental curves. MCD slightly overestimates, at most 5K, spring temperatures (Tables 5.1a and 5.3a), at the same time it tends to overestimate maxima trends 4600 and to underestimate minima and averages (about 10 K at most, Table 5.1a); • MarsCAM-NCAR slightly overestimates spring trends and (negligibly) summer trends, while it underestimates winter temperatures (about 5K) and (negligibly) autumn trends: similarly to MCD, it slightly underestimates minima and averages (about 7K), while maxima are (negligibly) overestimated; 4605 • finally, according to MBC method, the two simulations closer to the observational data in all the aggregation cases evaluated are, respectively, Scenario 7 for MCD and Run 4 for MarsCAM-NCAR.

For TSA instead: 4610 • MCD and MarsCAM-NCAR present a good accordance with observational data, both tending to globally underestimate the reference measurements, of about 7K for the first program and quite negligibly for the second; • in all the seasons and for minima, averages and maxima, MCD tends to slightly 4615 underestimate the observations, at most of 9K (Tables 5.1b and 5.3b); • MarsCAM-NCAR underestimates negligibly the spacecraft data in almost all the seasons (with winter registering a 5K deviation) but for a negligible overestimation in summer; averages and maxima trends are underestimated (respectively, in a negligible way and of about 5K) and minima are negligibly overestimated. 4620 • Scenario 7 for MCD and Run 4 for MarsCAM-NCAR, according to MBC method, result the most voted simulations.

141 Focusing on each individual lander/rover data, the comparisons showed that, according to the 4625 results collected from Groups 1b and 2b in MSD statistics (Section 5.2.2 and Section 5.3.2):

• for TG (Tables 5.2a and 5.4a), MCD seems to negligibly underestimate CUR (in all MYs), INS (for both datasets) observations and to overestimate SPI (at most 20K) and OPP (at most 5K) measurements; MarsCAM-NCAR underestimates negligibly CUR and INS data, 4630 slightly OPP temperatures (at most 13K), while it overestimates SPI ones (at most 12K); • for TSA (Tables 5.2b and 5.4b), MCD tends to negligibly underestimate VL2, MPF and PHO observations and underestimates more significantly OPP (at most 9K), SPI (at most 6K) and CUR (at most 14K) observations; on the other hand, it overestimates VL1 and INS trends of about 8K; MarsCAM-NCAR instead underestimates SPI (at most 5K), OPP (at 4635 most 8K) and CUR (at most 10K) trends, while it negligibly overestimates VL2 observations and, more notably, VL1 (at most 10K), MPF (at most 5K), PHO (at most 9K) and INS (at most 8K) measurements.

Further evidences that emerged from the other statistics considered (RMSE, CHEB and ERR) are 4640 reported in Section 5.4.

In conclusion, at the end of the comparisons, it can stated that the GCMs compared in this thesis, GCM-LMD (more precisely, MCD) and MarsCAM-NCAR, are in very good accordance with probe observational data for what concerns the reproduction of surface and near-surface temperature 4645 temporal trends. It could be very interesting to extend the comparison to further GCMs developed by other research centers (for examples those listed in Section 2.1), not only for simulating present Mars climate conditions, but also for paleoclimatic studies. It would be appealing also to extend the testing process by including data collected by the orbiters that explored the Red Planet, so covering a larger part of the planet. Additional comparisons could involve other significant atmospheric 4650 variables, such as surface pressure, atmospheric temperature (these two were briefly compared, with the results reported in Chapter 6), wind speed and magnitude and relative humidity, measured by the meteorological stations onboard the eight landers/rovers. Finally, dealing with this huge amount of simulated data could help to implement the features of the CMCC Ophidia tool used in this work for managing simulated astrophysical variables; in this way, it would be possible also to introduce, 4655 in the Ophidia framework, new primitives and workflows able to rapidly manage datasets collected by spatial missions and related to astrophysical parameters, at present in phase of development.

GCMs able to well reproduce present TG and TSA observational trends were applied by other authors to simulate ancient Mars weather (Urata and Toon, 2013b for MarsCAM; Wordsworth et al., 4660 2013; Forget et al., 2013 for GCM-LMD) 3.7 Gys ago, when very probably, wet and warm conditions allowed the presence of liquid water on the surface on the planet. The possibility that the Martian climate could be very different from the current one was deepened in the research stay I spent in Bologna at the "Istituto Nazionale di Astrofisica (INAF), Istituto di Radioastronomia” under the supervision of Prof. Roberto Orosei, P.I. of MARSIS (Mars Advanced Radar for 4665 Subsurface and Ionosphere Sounding) and member of the SHARAD (SHAllow RADar) experiments on board, respectively, of the ESA Mars Express and NASA Mars Reconnaissance Orbiter. During this period, I produced, by means of a series of simulations, the echoes expected for

142 some orbits of MARSIS that, together with the pre-existent simulations, were verified with the original data measured by the radar. By comparing the two signals, it is possible to find the 4670 composition of the subsoil and then search for water. I became familiar with the MARSIS simulator (the code written to simulate radar wave surface scattering, developed by Cantini et al., 2014) that I installed and tested on ATHENA cluster. To simulate the echo of an orbit, with 192 cores in parallel configuration, about 2h 40min are necessary to complete the job, in the hybrid version (MPI + OpenMP) of the code (Section 7.6). During my research period in Bologna, I enriched the previous 4675 datasets of simulated MARSIS echoes by adding about 650 new orbits to the database. From MARSIS measurements, the surface echo power can be derived and global maps of this quantity were created at 1.8, 3, 4 and 5 MHz. The surface echo power variations are primarily caused by kilometer-scale surface roughness. Then, the values of the dielectric constant of the shallow subsurface materials were derived by normalizing the surface echo power map using a simulation of 4680 MARSIS signal from the MOLA topography (the MARSIS simulator, Section 7.5). As a result, a map that characterizes the dielectric properties of the materials down to a few dm below the surface was obtained (Section 7.7 and Appendix G). Examination of the global reflectivity map revealed significant spatial variations over the planet. The most obvious feature was the latitude-dependent pattern in reflectivity: the equatorial region display low values, the mid-latitudes high values and 4685 the high latitudes low values again (Section 7.8). The importance of creating reflectivity maps at different frequencies is fundamental for local or regional studies (e.g. Mouginot et al., 2008) because, by comparing the maps in several frequency bands, materials and/or structures that could change the surface reflectivity can be studied as a function of radar frequency. Reproducing the echoes expected from the surface and the subsurface of Mars in an efficient manner, as it was 4690 demonstrated with the studies carried out by means of the MARSIS simulator, could introduce a very effective and easier procedure to investigate some specific regions of Mars where it is possible to detect subglacial liquid water. In fact, by analyzing reflectivity maps, it could be possible to focus the research only on potentially favorable zones where the maps suggest evidences for subsurface water. Moreover, by applying machine-learning techniques to radargrams selected with the above- 4695 mentioned procedure, it could be possible to detect new features still hidden in the MARSIS radargrams and not yet discovered. The research of liquid water in the subsurface of Mars could continue with the goal of identifying the presence of water in other regions, different from the southern Polar cap where the salty lake was detected (Orosei et al., 2018). The application of machine learning approaches to interpret 4700 MARSIS radargrams could also reduce significantly calculation time needed to manipulate them. The hypothesis of an underground system of lakes, already proposed in the literature (Salese et al., 2019) will be put to the test by Orosei’s Group. also thanks to the new simulations than can be performed with the MARSIS simulator by analyzing the latest orbits of this radar. Matching MARSIS data (no high spatial resolution but deep penetration in the subsurface down to a depth of 4705 5 km) with that of SHARAD, having complementary characteristics with respect to MARSIS (high spatial resolution, about 15 m, but lower penetration power, less than 1 km), it will be possible to reveal new unexpected features of the Martian subsurface.

4710

143 During my PhD, I also performed many collateral activities, the principal of them are briefly described here.

I am project leader of a research project named “Measurement system for the assessment of 4715 meteorological parameters and of the presence of pollutants in the atmosphere by means of a tethered balloon”, winner of the announcement “5 per mille per la ricerca – anno 2015” and funded by University of Salento. The collaboration involves the research group of the Laboratory “Aerosol e Clima” of the University of Salento. The aim is to develop a monitoring system that uses a tethered aerostatic balloon to measure the main meteorological parameters (temperature, relative 4720 humidity, wind speed and direction, atmospheric pressure) and the concentration and size distribution of atmospheric particulate.

Finally, on September 21, 2018, the first paper of my PhD, “Comparison of astronomical software programs for archaeoastronomical applications” was accepted and published on “Astronomy and 4725 Computing Journal”, Elsevier Editor. In Appendix H a pre-print version of this article is reported. I propose here the abstract as a summary of the topics addressed.

“Reproducing the movements of stars and planets across the sky has recently had notable insights thanks to the widespread use of astronomical software products with high mapping and graphical 4730 capabilities. Nonetheless, when it is necessary to determine the position of a star in the very remote past (or future), one must take into account two factors which have a profound impact on stellar positioning: the precession of the equinoxes and the proper motions of the stars, two mechanisms that are not always been properly considered, especially in the archaeoastronomical literature. The present work compares the principal commercial astronomical programs currently available 4735 with the goal to determine how correctly they evaluate the two aforementioned mechanisms. The comparison is carried out on a sample of 24 stars (among the brightest in the sky) using a subroutine which carefully evaluates the two phenomena. A discussion on the principal methods used to approximate precession is also given. The differences observed between the values of declination calculated with various approximations, as well as those between different astronomical software 4740 programs, may even exceed one degree, a value that is far beyond the resolving power of the human eye, making the evaluations and the consequent conclusions unreliable. Furthermore, via a reconstruction of the temporal trends of declination in the interval [25000 BC; AD 25000] for two stars with the highest (Toliman, α Cen) and the lowest (Mintaka, δ Ori) proper motions, the consequences of this effect on the stellar position are evaluated. Finally, as a consequence of the 4745 presented evidence, we test some alignments towards the brightest stars of the sky proposed for some enclosures of Gӧbekli Tepe, the most ancient megalithic site in the world.”

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5335 Web references - Landers/Rovers landed on Mars • Curiosity webpage in NASA website (last visited: December, 2019) https://mars.nasa.gov/msl/home/ • InSight webpage in NASA website (last visited: December, 2019) 5340 https://mars.nasa.gov/insight/ • MPF webpage in NASA website (last visited: December, 2019) https://www.nasa.gov/mission_pages/mars-pathfinder • MER webpage in NASA website (last visited: December, 2019) https://mars.nasa.gov/mer/ 5345 • Phoenix webpage in NASA website (last visited: December, 2019) https://www.nasa.gov/mission_pages/phoenix/main/index.html • Viking 1 and Viking 2 webpage in NASA website (last visited: December, 2019) https://mars.nasa.gov/mars-exploration/missions/viking-1-2/ - General Circulation Models 5350 • LMD – GCM website (last visited: December, 2019) http://www-mars.lmd.jussieu.fr/ • MarsCAM – NCAR website (last visited: December, 2019) https://osf.io/7ybze/ - CMCC facilities 5355 • Athena cluster website (last visited: December, 2019) https://sccmon.cmcc.it/ • Ophidia website (last visited: December, 2019) http://ophidia.cmcc.it/

157 APPENDIX A 5360 In the tables included in this appendix I reported the values of albedo, thermal inertia (TI) and dust OD set, at the begin of the simulations, in the grid cell containing the landing site of the eight landers/rovers for the two GCMs compared. In the second line the reference values derived from the observations (see Table 1.2) in this region is shown. 5365

Table A.1: Viking 1 Table A.2: Viking 2

RUN/SCENARIO ALBEDO TI DUST OD RUN/SCENARIO ALBEDO TI DUST OD VIKING 1 0.26 215 0.17 VIKING 2 0.23 240 0.10 5370 MARSCAM MARSCAM 2 0.22 290 0.30 2 0.24 232 0.30 4 0.22 215 0.30 4 0.24 240 0.30 5 0.26 215 0.30 5 0.22 240 0.30 8 0.26 215 0.10 8 0.22 240 0.10 10 0.22 215 0.10 10 0.24 240 0.10 11 0.26 215 0.25 11 0.22 240 0.25 5375 12 0.26 215 0.20 12 0.22 240 0.20

MCD MCD 1 0.20 299 0.17 1 0.23 231 0.10 2 0.20 299 0.17 2 0.23 231 0.10 3 0.20 299 0.17 3 0.23 231 0.10 7 0.20 299 0.37 7 0.23 231 0.30 5380 8 0.20 299 0.06 8 0.23 231 0.03 MY24 0.20 299 0.17 MY24 0.23 231 0.12 MY25 0.20 299 0.25 MY25 0.23 231 0.15 MY26 0.20 299 0.16 MY26 0.23 231 0.13 MY27 0.20 299 0.16 MY27 0.23 231 0.09 MY28 0.20 299 0.19 MY28 0.23 231 0.08 5385 MY29 0.20 299 0.19 MY29 0.23 231 0.09 MY30 0.20 299 0.16 MY30 0.23 231 0.08 MY31 0.20 299 0.17 MY31 0.23 231 0.08 MY32 0.20 299 0.18 MY32 0.23 231 0.08 MY33 0.20 299 0.17 MY33 0.23 231 0.07

5390

5395

5400

158 Table A.3: MPF Table A.4: Spirit RUN/SCENARIO ALBEDO TI DUST OD RUN/SCENARIO ALBEDO TI DUST OD 5405 MPF 0.19-0.23 376-396 0.18 SPIRIT 0.20-0.25 290 0.18 MARSCAM MARSCAM 2 0.20 343 0.30 2 0.26 157 0.30 4 0.20 343 0.30 4 0.26 157 0.30 5 0.20 343 0.30 5 0.26 157 0.30 8 0.20 343 0.10 8 0.26 157 0.10 10 0.20 343 0.10 10 0.26 157 0.10 5410 11 0.20 343 0.25 11 0.26 157 0.25 12 0.20 343 0.20 12 0.26 157 0.20

MCD MCD 1 0.19 346 0.18 1 0.25 163 0.18 2 0.19 346 0.18 2 0.25 163 0.18 3 0.19 346 0.18 3 0.25 163 0.18 5415 7 0.19 346 0.38 7 0.25 163 0.39 8 0.19 346 0.06 8 0.25 163 0.07 MY24 0.19 346 0.16 MY24 0.25 163 0.15 MY25 0.19 346 0.26 MY25 0.25 163 0.27 MY26 0.19 346 0.17 MY26 0.25 163 0.17 MY27 0.19 346 0.17 MY27 0.25 163 0.20 MY28 0.19 346 0.20 MY28 0.25 163 0.24 5420 MY29 0.19 346 0.20 MY29 0.25 163 0.19 MY30 0.19 346 0.17 MY30 0.25 163 0.16 MY31 0.19 346 0.18 MY31 0.25 163 0.17 MY32 0.19 346 0.19 MY32 0.25 163 0.17 MY33 0.19 346 0.18 MY33 0.25 163 0.17

5425 Table A.5: Opportunity Table A.6: Phoenix RUN/SCENARIO ALBEDO TI DUST OD RUN/SCENARIO ALBEDO TI DUST OD OPPORTUNITY 0.13 220 0.18 PHOENIX 0.21 250-283 0.09 MARSCAM MARSCAM 2 0.13 481 0.30 2 0.22 221 0.30 4 0.13 220 0.30 4 0.22 221 0.30 5430 5 0.13 220 0.30 5 0.22 221 0.30 8 0.13 220 0.10 8 0.22 221 0.10 10 0.13 220 0.10 10 0.22 221 0.10 11 0.13 220 0.25 11 0.22 221 0.25 12 0.13 220 0.20 12 0.22 221 0.20

MCD MCD 5435 1 0.14 221 0.18 1 0.21 204 0.09 2 0.14 221 0.18 2 0.21 204 0.09 3 0.14 221 0.18 3 0.21 204 0.09 7 0.14 221 0.39 7 0.21 204 0.22 8 0.14 221 0.07 8 0.21 204 0.03 MY24 0.14 221 0.17 MY24 0.21 204 0.08 MY25 0.14 221 0.31 MY25 0.21 204 0.09 5440 MY26 0.14 221 0.17 MY26 0.21 204 0.09 MY27 0.14 221 0.18 MY27 0.21 204 0.08 MY28 0.14 221 0.23 MY28 0.21 204 0.06 MY29 0.14 221 0.19 MY29 0.21 204 0.07 MY30 0.14 221 0.17 MY30 0.21 204 0.08 MY31 0.14 221 0.17 MY31 0.21 204 0.07 MY32 0.14 221 0.18 MY32 0.21 204 0.07 MY33 0.14 221 0.16 MY33 0.21 204 0.07

159 5445 Table A.7: Curiosity Table A.8: InSight RUN/SCENARIO ALBEDO TI DUST OD RUN/SCENARIO ALBEDO TI DUST OD CURIOSITY 0.20-0.25 295-452 0.18 INSIGHT 0.24-0.25 219-237 0.18 MARSCAM MARSCAM 2 0.22 237 0.30 2 0.24 229 0.30 4 0.22 237 0.30 4 0.24 229 0.30 5 0.24 229 0.30 5450 5 0.22 237 0.30 8 0.22 237 0.10 8 0.24 229 0.10 10 0.22 237 0.10 10 0.24 229 0.10 11 0.22 237 0.25 11 0.24 229 0.25 12 0.22 237 0.20 12 0.24 229 0.20

MCD MCD 5455 1 0.23 263 0.18 1 0.24 237 0.18 2 0.23 263 0.18 2 0.24 237 0.18 3 0.23 263 0.18 3 0.24 237 0.18 7 0.23 263 0.40 7 0.24 237 0.40 8 0.23 263 0.07 8 0.24 237 0.07 MY24 0.23 263 0.16 MY24 0.24 237 0.17 MY25 0.23 263 0.31 MY25 0.24 237 0.31 5460 MY26 0.23 263 0.17 MY26 0.24 237 0.18 MY27 0.23 263 0.21 MY27 0.24 237 0.21 MY28 0.23 263 0.25 MY28 0.24 237 0.24 MY29 0.23 263 0.20 MY29 0.24 237 0.20 MY30 0.23 263 0.16 MY30 0.24 237 0.17 MY31 0.23 263 0.17 MY31 0.24 237 0.17 MY32 0.23 263 0.16 MY32 0.24 237 0.17 5465 MY33 0.23 263 0.14 MY33 0.24 237 0.15

5470

5475

5480

5485

160 APPENDIX B

5490 The code of the Ophidia WF built in order to match, for MarsCAM-NCAR output, LS values to each climatic variables is here reported and described. Some comments (in red) are added so to better explain the meaning of some passages. Execution time: only 4 s for 100 GB!

5495 %%%%%%%% Header of the workflow %%%%%%%% { "name": "LS Extraction anni singoli export", 5500 "author": "Alessandro De Lorenzis", "abstract": "Mars climate analysis. Extraction, for a three years simulation, of a climatic variables in a declared interval of time in terms of LS (solar longitude)", "exec_mode": "sync", "ncores": "${1}", 5505 "on_exit": "oph_delete", "tasks":

/*

5510 List of the parameters (indicated in the code as “$1”, “$2” etc.) to be given on the Ophidia command line, when the wf must be submitted. Example of submission string:

./Scrivania/CMCC/Estrazione_LS_anni_singoli_long.json 20 https://ophidialab.cmcc.it/ophidia/331/69003 28|66 https://ophidialab.cmcc.it/ophidia/330/67953 0 360 TG-MPF-anno-run2 LS-MPF-anno-run2 TG 5515 1 number of cores to be used → 20 2 cube contatining LS values → https://ophidialab.cmcc.it/ophidia/331/69003 3 subset of lat/lon to identify the cell of the chosen landing site → 28|66 (MPF) 5520 4 cube containing climatic variable values → https://ophidialab.cmcc.it/ophidia/330/67953 5 lower limit of the LS extraction range → 0 6 upper limit of the LS extraction range → 360 7 description of the cube (climatic → TG-MPF-anno-run2 variable) to be extracted 5525 8 description of the cube (LS values) → LS-MPF-anno-run2 to be extracted 9 name of the observable → TG

*/ 5530 [ % subset of LS cube in order to extract only data referred to the cell to be investigated (MPF in this example) { 5535 "name": "Subset-LS", "operator": "oph_subset", "arguments": [ "subset_dims=lat|lon", "subset_filter=${3}", 5540 "cube=${2}" ] }, % the same subset for the cube containing simulated values for TG { 5545 "name": "Subset-variable", "operator": "oph_subset",

161 "arguments": [ "subset_dims=lat|lon", "subset_filter=${3}", 5550 "cube=${4}" ] },

% indication of the extremes of the LS range to be extracted 5555 { "name": "LS-extraction-time-interval", "operator": "oph_apply", "arguments": [ "query=oph_predicate3(measure,'x>${5} AND x<${6}','x','0')", 5560 "measure_type=auto" ], "dependencies": [ { "task": "Subset-LS", "type":"single" } ] 5565 }, % extraction of the time dimension to be used in the following passages in order to define the size parameter { "name": "LS-extract-dimension-for-size", 5570 "operator": "oph_apply", "arguments": [ "query=oph_cast('oph_double','oph_double',dimension)", "check_type=no" ], 5575 "dependencies": [ { "task": "LS-extraction-time-interval", "type":"single" } ] },

5580 % the “replace” parameter is applied in order to “throttle” the LS vector. This option allow to put at zero all % the data that are out of the LS range before defined { "name": "LS-time", "operator": "oph_apply", 5585 "arguments": [ "query=oph_replace ('oph_double', 'oph_double', oph_mul_array('oph_double| oph_double','oph_double',dimension,oph_predicate('oph_float','oph_double',measure,'x','>0','1','0')))", "check_type=no" ], 5590 "dependencies": [ { "task": "LS-extraction-time-interval", "type":"single" } ] },

5595 % the operator “oph_explorecube” serves for applying the next operator, “oph_set”: it does nothing but % showing the variables in the cube organized by rows in the sequence lat, lon, variable (TG) { "name": "Explorecube", "operator": "oph_explorecube", 5600 "arguments": [ "limit_filter=1" ], "dependencies": [ { "task": "LS-time", "type":"single" } 5605 ] },

162 % the operator “oph_set” allows to read the row containing the selected values of the LS “time” dimension % that must be after put as extraction parameters for the observable (TG). The time values are displayed % in the third column: this is why the “value” parameter is set to (1,3). 5610 { "name": "Extract-time-LS", "operator": "oph_set", "arguments": [ "key=datatype", 5615 "value=LS(1,3)" ], "dependencies": [ { "task": "Explorecube"} ] 5620 }, % extraction of the observable values (TG) by means of the time values of LS deduced with the previous % operator “oph_set”: this is the cube where the TG values related to the LS range indicated at the % beginning are stored for the three available MarsCAM-NCAR simulated-years of a standard simulation % (see text). 5625 { "name": "Extract-only-LS-from-variable", "operator": "oph_subset", "arguments": [ "subset_dims=time", 5630 "subset_type=coord", "subset_filter=@datatype", "description=$7" ], "dependencies": [ 5635 { "task": "Subset-variable", "type":"single" }, { "task": "Extract-time-LS"} ] }, % exit-cube containing the LS values 5640 { "name": "LS values", "operator": "oph_subset", "arguments": [ "subset_dims=time", 5645 "subset_type=coord", "subset_filter=@datatype", "description=$8" ], "dependencies": [ 5650 { "task": "LS-extraction-time-interval", "type":"single" }, { "task": "Extract-time-LS"} ] },

5655 % beginning of the WF part to be used for extracting LS data for single years. The cube in which all the LS % values are stored (in the wanted range for all the years of the Run) is considered and gaps are created, % i.e. data blocks, by assigning a “zero” flag to all LS data to be processed. { "name": "LS-gap", 5660 "operator": "oph_apply", "arguments": [ "query=oph_replace ('oph_double', 'oph_double', oph_mul_array('oph_double| oph_double','oph_double',dimension,oph_predicate('oph_float','oph_double',measure,'x','>0','0','1')))", "check_type=no" 5665 ], "dependencies": [

163 { "task": "LS-extraction-time-interval", "type":"single" } ] }, 5670 % calculation of the offset to be set so to have the first datum of the first year with dimension equal to % zero. { "name": "Extract-offset", "operator": "oph_explorecube", 5675 "arguments": [ "limit_filter=1", "subset_filter=1", "subset_dims=time" ], 5680 "dependencies": [ { "task": "LS-gap", "type":"single" } ] }, % extraction of the LS gaps, i.e. the empty spaces are taken into account 5685 { "name": "Extract-gap-LS", "operator": "oph_set", "arguments": [ "key=offset", 5690 "value=LS(1,3)" ], "dependencies": [ { "task": "Extract-offset"} ] 5695 }, % the idea at the basis of this WF is to isolate the data of the various years by dividing the whole time % series in as many blocks as the years ot the Run are. To do so, the size of the entire dataset must be % determined. It can be estimated by using the “oph_explorecube” operator, able to display the entire % content of the cube. 5700 { "name": "Extract-size", "operator": "oph_explorecube", "arguments": [ "limit_filter=1", 5705 "subset_filter=end", "subset_dims=time" ], "dependencies": [ { "task": "LS-extract-dimension-for-size", "type":"single" } 5710 ] }, % Part of the code related to the partition of the time series in blocks. By using the “oph_set” operator, the % third column (where the values of the time dimension for the variable LS are stored) having the size % before computed is divided for the total number of the years of the Run, i.e. 5. The division must be 5715 % executed per 5 becaues the complete Run of a standard simulation is made of 5 years, of which the first % two must be eliminated. We need to divide by the total number of years to not have conflicts with the % offset. Gaps are in this way created. { "name": "Extract-size-LS", 5720 "operator": "oph_set", "arguments": [ "key=size", "value=LS(1,3)" ], 5725 "dependencies": [ { "task": "Extract-size"}

164 ] }, % beginning of the for cycle in order to extract the 3 subsets, each for the three years. The parameter 5730 “key” is % set to “index” so to associate a flag to the group of data before divided. { "name": "FOR", "operator": "oph_for", 5735 "arguments": [ "key=index", "counter=1,2,3", // COUNTER: 3,4,5 are the evaluables years "values=0|1|2", // VALUES = COUNTER -1 "parallel=yes" 5740 ], "dependencies": [ { "task": "Extract-gap-LS"} ] }, 5745 % lower limit of the interval to be extracted { "name": "Set-lower-bound", "operator": "oph_set", "arguments": [ 5750 "key=lower&index", "value=EVAL(@offset + @size * @index /5)" ], "dependencies": [ { "task": "FOR"} 5755 ] }, % upper limit of the interval to be extracted { "name": "Set-upper-bound", 5760 "operator": "oph_set", // “&” is used to take the values of index "arguments": [ // “@ “ instead to take the counter of index "key=upper&index", "value=EVAL(@offset + @size * &index /5)" ], 5765 "dependencies": [ { "task": "FOR"} ] }, % extraction of the obsevarble (TG) for each years in the chosen LS range 5770 { "name": "Extract-year-variable", "operator": "oph_subset", "arguments": [ "subset_dims=time", 5775 "subset_filter=@{lower&index}:@{upper&index}", "time_filter=no", "subset_type=coord", "description=$9 year &index" ], 5780 "dependencies": [ { "task": "Extract-only-LS-from-variable", "type":"single" }, { "task": "Set-lower-bound" }, { "task": "Set-upper-bound" } ], 5785 "on_exit": "nop" },

165 % export of the cube containing the TG values in the LS range indicated { "name": "Export Observable", 5790 "operator": "oph_exportnc2", "arguments": [ "cdd=/home/adelorenzis/", "output_path=/public/data/adelorenzis", "output_name=$7-year&index" 5795 ], "dependencies": [ { "task": "Extract-year-variable", "type":"single" } ] }, 5800 % extraction of the LS values for each year in the chosen range { "name": "Extract-year-LS", "operator": "oph_subset", "arguments": [ 5805 "subset_dims=time", "subset_filter=@{lower&index}:@{upper&index}", "time_filter=no", "subset_type=coord", "description=LS year &index" 5810 ], "dependencies": [ { "task": "LS values", "type":"single" }, { "task": "Set-lower-bound" }, { "task": "Set-upper-bound" } 5815 ], "on_exit": "nop" }, % export of the cube containing the LS values in the LS range indicated. At the end, 6 cubes (i.e. 6 .nc files) % will be created and downloadable, 2 for each of the 3 simulated years: one containing the values of the 5820 % simulated observable (TG) and one with the related LS values. { "name": "Export LS", "operator": "oph_exportnc2", "arguments": [ 5825 "cdd=/home/adelorenzis/", "output_path=/public/data/adelorenzis", "output_name=$8-year&index" ], "dependencies": [ 5830 { "task": "Extract-year-LS", "type":"single" } ] }, % end for cycle { 5835 "name": "END-FOR", "operator": "oph_endfor", "arguments": [], "dependencies": [ { "task": "Extract-year-variable"}, 5840 { "task": "Extract-year-LS"}, { "task": "Export Observable"}, { "task": "Export LS"} ] } 5845 ] }

166 APPENDIX C

As mentioned in Section 5.2.2, the results obtained with MBC method and the other statistics 5850 considered for Group 1b comparisons (analysis per single probe) are here reported. The meaning of the columns, the same as that of Table 5.1 and common to all the tables, is the following:

• column 2 : the most voted Scenario/Run of one of the two GCMs for each of the nine aggregation cases evaluated; 5855 • columns 4-9 : the statistics evidences for the best MCD Scenario (column 3); • columns 15-20 : the statistics evidences for the best MarsCAM-NCAR Run (column 14); • columns 10-13: a global overview performed by considering together all the results registered by the related Scenarios for MCD; • columns 21-24 : the same for MarsCAM-NCAR Runs. 5860 As regards the meaning of the statistical quantities:

• columns 4 and 15 : the places in the classification for that case for the Scenario/Run considered, according to MBC; 5865 • columns 5 and 16: the MBC rank registered for the winner Scenario/Run in the related aggregation case.

For RMSE, CHEB and MSD, see Eq. 4.1, Eq. 4.2 and Eq. 4.3 respectively, for ERR see Section 4.2. In the MSD columns, when “<~1” is reported, it means that the deviations “model output - 5870 observational data” are in the range [-1, +1] K. When a “-” is reported, no data are available for that season.

List of the tables collected in this Appendix (organized cronologically according to the MY of landing): 5875 • TG variable Table C1: SPI, near; Table C6: CUR, MY 32; Table C2: SPI, upview; Table C7: CUR, MY 33; Table C3: OPP, near; Table C8: CUR, MY 34; 5880 Table C4: OPP, upview; Table C9: INS, FOV 1; Table C5: CUR, MY 31; Table C10: INS, FOV 2.

• TSA variable 5885 Table C11: VL1; Table C17: CUR, MY 31; Table C12: VL2; Table C18: CUR, MY 32; Table C13: MPF; Table C19: CUR, MY 33; Table C14: SPI; Table C20: CUR, MY 34; Table C15: OPP; Table C21: INS, BOOM +Y; 5890 Table C16: PHO; Table C22: INS, BOOM -Y;

167 TABLE C1 SPI TG NEAR MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 8 0.766 18 39 +14 [-10, +39] 18-23 33-43 [+14, +20] [-10, +43] 2 1 1 17 39 +11 [-14, +39] 16-18 38-39 [+11, +12] [-14, +39] B ------C ------D MARSCAM 7 8 0.766 18 39 +14 [-10, +39] 18-23 33-43 [+14, +20] [-10, +43] 2 1 1 17 39 +11 [-14, +39] 17-18 38-39 [+11, +12] [-14, +39] E MARSCAM 7 8 0.623 18 39 +14 [-10, +39] 18-23 33-43 [+14, +20] [-10, +43] 5 1 1 17 39 +11 [-14, +39] 17-18 38-39 [+11, +12] [-14, +39] F MCD MY 25 1 1 28 33 +28 [+19, +33] 28-37 33-43 [+28, +37] [+19, +43] 5 3 0.767 30 39 +30 [+18, +39] 30-31 38-39 [+30, +31] [+18, +39] G MARSCAM MY 28 6 0.727 15 22 +13 [+2, +22] 15-21 22-33 [+13, +20] [+2, +33] 4 1 1 14 26 +12 [-2, +26] 14-15 26-28 [+12, +14] [-2, +28] H MARSCAM 7 8 0.468 14 19 +14 [+6, +19] 14-18 19-22 [+14, +18] [+6, +22] 2 1 1 9 14 +8 [+1, +14] 9-10 13-15 [+8, +9] [+1, +14] I MARSCAM 7 3 0.884 7 19 +2 [-10, +19] 7-10 18-23 [+2, +7] [-10, +23] 8 1 1 7 17 <~ 1 [-12, +17] 7-8 16-18 [-2, -1] [-14, +17]

TABLE C2 SPI TG UPVIEW MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM MY 28 6 0.842 17 32 +14 [-9, +32] 15-20 26-34 [+11, +17] [-14, +34] 2 1 1 14 29 +8 [-18, +29] 14-15 28-29 [+8, +9] [-18, +29] B ------C ------D MARSCAM MY 28 6 0.842 17 32 +14 [-9, +32] 15-20 26-34 [+11, +17] [-14, +34] 2 1 1 14 29 +8 [-18, +29] 14-15 28-29 [+8, +9] [-18, +29] E MARSCAM 7 8 0.639 15 30 +11 [-14, +30] 15-20 26-34 [+11, +17] [-14, +34] 5 1 1 14 29 +8 [-18, +29] 14-15 28-29 [+8, +9] [-18, +29] F MCD MY 25 1 1 22 26 +22 [+15, +26] 22-31 26-34 [+21, +31] [+15, +33] 5 3 0.773 24 29 +24 [+15, +29] 24-25 28-29 [+24, +25] [+15, +29] G MARSCAM MY 28 5 0.801 14 19 +12 [0, +19] 14-20 19-30 [+12, +20] [-2, +30] 4 1 1 13 22 +11 [-4, +22] 13-15 22-24 [+11, +13] [-4, +24] H MARSCAM 7 8 0.478 12 19 +11 [+2, +14] 12-15 19-22 [+11, +15] [+4, +22] 2 1 1 7 13 +5 [+1, +13] 7-8 13-14 [+5, +7] [+1, +14] I MCD MY 25 1 1 8 15 +3 [-9, +15] 8-9 15-20 [-2, +4] [-14, +20] 10 16 0.291 9 16 -4 [-16, +14] 9-10 16-18 [-6, -4] [-18, +15]

TABLE C3 OPP TG NEAR MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 11 <~ 1 [-11, +11] 6-9 11-20 [0, +5] [-11, +20] 8 7 0.579 8 17 <~ 1 [-15, +17] 8-14 16-26 [-12, -1] [-26, +17] B ------C ------D MCD 7 1 1 6 11 <~ 1 [-11, +11] 6-9 11-20 [0, +5] [-11, +20] 8 7 0.579 8 17 <~ 1 [-15, +17] 8-14 16-26 [-12, -1] [-26, +17] E MCD MY 28 1 1 6 13 +3 [-7, +13] 6-9 11-20 [0, +6] [-11, +20] 8 15 0.324 8 17 <~ 1 [-15, +17] 8-14 16-26 [-12, -1] [-26, +17] F MCD 7 1 1 2 6 +2 [0, +6] 2-13 6-15 [+2, +12] [-2, +15] 2 3 0.788 4 5 -4 [-5, -2] 4-7 5-10 [-4, +7] [-5, +10] G MARSCAM MY 28 2 0.744 7 12 +5 [-5, +12] 7-16 11-20 [+5, +16] [-5, +20] 2 1 1 4 7 <~ 1 [-7, +4] 4-11 7-17 [-1, +11] [-7, +17] H MCD 7 1 1 6 10 +2 [-10, +10] 7-8 10-13 [+2, +5] [-10, +13] 10 2 0.951 7 13 -2 [-13, +6] 7-14 13-24 [-12, -2] [-24, +7] I MCD MY 29 1 1 3 8 -2 [-8, +3] 3-6 7-11 [-5, 0] [-11, +6] 10 16 0.233 8 15 -7 [-15, +1] 8-19 15-26 [-18, -7] [-26, +1]

168 5900 TABLE C4 OPP TG UPVIEW MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 11 <~ 1 [-11, +9] 6-8 11-17 [-1, +4] [-11, +17] 4 14 0.486 9 17 -4 [-17, +10] 8-15 14-26 [-13, -3] [-26, +12] B ------C ------D MCD 7 1 1 6 11 <~ 1 [-11, +9] 6-8 11-17 [-1, +4] [-11, +17] 4 14 0.486 9 17 -4 [-17, +10] 8-15 14-26 [-13, -3] [-26, +12] E MCD MY 28 1 1 6 12 <~ 1 [-8, +12] 6-8 11-17 [-1, +4] [-11, +17] 10 15 0.313 8 14 -2 [-14, +12] 8-15 14-26 [-13, -2] [-26, +12] F MCD 7 1 1 1 4 <~ 1 [-2, +4] 1-11 4-13 [0, +11] [-3, +13] 4 3 0.746 4 6 +4 [+3, +6] 4-6 6-8 [-6, +6] [-7, +8] G MCD MY 28 1 1 4 4 +2 [-6, +7] 4-13 6-17 [+2, +12] [-6, +17] 2 3 0.824 6 10 -5 [-10, -1] 6-8 10-12 [-5, +7] [-10, +12] H MCD 7 1 1 6 11 <~ 1 [-11, +9] 6-7 11-12 [+1, +4] [-11, +12] 10 14 0.389 7 14 -3 [-14, +5] 7-15 14-25 [-13, -3] [-25, +5] I MCD 8 1 1 4 7 -2 [-7, +5] 4-7 7-11 [-7, -2] [-11, +5] 10 16 0.219 9 14 -8 [-14, 0] 9-20 14-26 [-19, -8] [-26, 0]

TABLE C5 CUR TG MY 31 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 4 0.920 7 12 <~ 1 [-10, +12] 7-12 12-20 [-2, 0] [-17, +20] 2 1 1 6 13 <~ 1 [-9, +13] 6-8 12-20 [-2, 0] [-13, +14] B MCD 7 1 1 5 8 <~ 1 [-8, +6] 5-12 8-17 [-11, -1] [-17, +15] 5 2 0.719 6 9 -3 [-9, +7] 6-9 9-13 [-7, -3] [-13, +7] C MARSCAM 7 8 0.561 7 10 -7 [-10, -4] 7-9 10-11 [-9, -7] [-11, -2] 2 1 1 4 7 -4 [-7, -1] 4-6 7-9 [-6, -4] [-9, -1] D MARSCAM 7 7 0.897 8 12 +8 [0, +12] 8-15 12-20 [+6, +14] [-6, +20] 2 1 1 8 13 7 [-2, +13] 8-9 13-14 [+7, +8] [-2, +14] E MARSCAM 7 4 0.935 7 12 <~ 1 [-10, +12] 7-12 12-20 [-2, 0] [-17, +20] 2 1 1 6 13 <~ 1 [-9, +13] 6-8 13-14 [-2, 0] [-13, +14] F MCD 7 1 1 6 10 <~ 1 [-9, +10] 6-12 10-20 [-1, +1] [-14, +20] 2 2 0.982 7 13 <~ 1 [-8, +13] 7-8 13-14 [-1, +1] [-12, +14] G MARSCAM MY 28 4 0.874 8 13 -2 [-9, +13] 8-13 12-18 [-3, -2] [-17, +18] 5 1 1 7 11 -2 [-9, +11] 7-9 11-13 [-3, -2] [-13, +12] H ------I MARSCAM 7 8 0.782 5 9 <~ 1 [-10, +7] 5-9 9-11 [-2, 0] [-11, +11] 12 1 1 3 8 <~ 1 [-8, +4] 3-4 6-9 [-2, +1] [-9, +5]

TABLE C6 CUR5905 TG MY 32 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 4 0.946 6 13 <~ 1 [-10, +13] 6-11 13-23 [-2, -1] [-18, +23] 2 1 1 6 16 -2 [-10, +16] 6-8 16-17 [-4, -2] [-13, +17] B MCD 7 1 1 3 10 -2 [-10, +4] 3-10 10-18 [-9, -2] [-18, +9] 4 2 0.878 4 8 -3 [-8, +4] 4-8 8-13 [-7, -3] [-13, +4] C MARSCAM 7 5 0.716 8 10 -8 [-10, -4] 8-9 10-12 [-9, -8] [-12, -3] 2 1 1 7 10 -6 [-10, +1] 7-9 10-12 [-8, -6] [-12, +1] D MARSCAM 7 8 0.948 7 13 +6 [-2, +13] 7-12 13-23 [+6, +11] [-5, +23] 5 1 1 7 16 +3 [-9, +16] 7-8 16-17 [+3, +4] [-9, +17] E MCD 7 1 1 6 13 <~ 1 [-10, +13] 6-11 13-23 [-2, -1] [-18, +23] 5 2 0.988 6 16 -2 [-10, +16] 6-8 16-17 [-4, -2] [-13, +17] F MARSCAM 7 2 0.978 7 13 <~ 1 [-7, +13] 6-14 13-23 [-1, +1] [-15, +23] 2 1 1 8 16 <~ 1 [-8, -16] 8-10 16-17 [-1, +1] [-13, +17] G MARSCAM MY 28 4 0.960 7 12 -3 [-11, +12] 7-12 11-21 [-4, -2] [-14, +21] 4 1 1 6 13 -2 [-10, +13] 6-8 13-15 [-4, -2] [-12, +15] H MARSCAM 7 4 0.862 6 10 -2 [-10, +10] 6-9 10-12 [-4, -2] [-12, +12] 4 1 1 6 10 -4 [-10, +3] 6-8 10-12 [-7, -4] [-12, +3] I MARSCAM 7 5 0.925 5 10 <~ 1 [-10, +7] 5-8 10-12 [-2, -1] [-11, +12] 5 1 1 5 8 -2 [-10, +6] 5-6 10-12 [-4, -2] [-12, +6]

169 TABLE C7 CUR TG MY 33 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 4 0.891 7 13 -3 [-13, +11] 7-10 13-18 [-4, -3] [-18, +16] 4 1 1 6 16 -3 [-16, +9] 6-8 15-16 [-5, -3] [-16, +9] B MARSCAM 7 2 0.972 5 13 -4 [-13, +5] 5-11 13-18 [-11, -4] [-18, +8] 4 1 1 5 11 -4 [-11, +3] 5-9 11-16 [-8, -4] [-16, +3] C MARSCAM 7 6 0.669 9 13 -8 [-13, -2] 9-10 13-14 [-10, -8] [-14, -2] 2 1 1 8 13 -7 [-13, 0] 8-10 13-15 [-9, -7] [-15, 0] D MARSCAM 7 2 0.947 6 11 +4 [-9, +11] 5-10 11-16 [+4, +9] [-13, +16] 5 1 1 5 16 <~ 1 [-16, +9] 5-6 15-16 [0, +1] [-16, +9] E MARSCAM 7 4 0.883 7 13 -3 [-13, +11] 7-10 13-18 [-4, -3] [-18, +16] 5 1 1 6 16 -3 [-16, +9] 6-8 15-16 [-5, -3] [-16, +9] F MCD MY 25 1 1 5 10 <~ 1 [-10, +7] 5-12 10-15 [-3, -1] [-15, +15] 2 3 0.954 5 9 <~ 1 [-7, +9] 5-8 9-12 [-3, -1] [-12, +9] G MARSCAM 7 5 0.846 4 11 -2 [-11, +4] 4-8 11-14 [-3, -2] [-14, +11] 5 1 1 3 7 -2 [-7, +3] 3-5 7-12 [-3, -2] [-12, +5] H MARSCAM 7 5 0.771 8 13 -4 [-13, +11] 8-11 13-18 [-6, -4] [-18, +13] 4 1 1 7 13 -6 [-13, +4] 7-10 13-15 [-9, -6] [-16, +4] I MARSCAM 7 5 0.917 7 11 -3 [-11, +10] 7-10 11-16 [-4, -3] [-14, +16] 4 1 1 7 16 -4 [-16, +8] 7-9 15-16 [-6, -4] [-16, +8]

TABLE C8 CUR TG MY 34 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 8 40 <~ 1 [-17, +40] 7-12 30-46 [-2, -1] [-39, +46] 4 2 0.772 9 39 -2 [-19, +39] 9-11 39-40 [-4, -2] [-24, +40] B MCD 7 1 1 6 17 -4 [-17, +6] 6-12 14-28 [-11, -4] [-29, +8] 4 2 0.915 7 19 -4 [-19, +7] 7-11 19-24 [-9, -4] [-24, +7] C MCD 7 1 1 5 8 -4 [-8, +4] 5-6 8-9 [-5, -4] [-9, +6] 4 2 0.978 5 9 -2 [-9, +6] 5-6 9-11 [-4, -2] [-11, +6] D MCD 7 1 1 12 40 +5 [-8, +40] 9-16 30-46 [+5, +9] [-9, +46] 12 11 0.418 14 39 <~ 1 [-16, +39] 13-14 39-40 [0, +1] [-16, +40] E MCD 7 1 1 8 40 <~ 1 [-17, +40] 7-12 30-46 [-2, -1] [-29, +46] 4 2 0.829 9 39 -2 [-19, +39] 9-11 39-40 [-4, -2] [-24, +40] F MCD MY 29 1 1 18 44 +4 [-22, +44] 10-21 30-46 [+3, +5] [-29, +46] 5 14 0.485 16 39 +5 [-20, +39] 16-17 39-40 [+3, +5] [-24, +40] G MCD MY 28 1 1 3 9 -2 [-9, +3] 3-12 9-18 [-2, 0] [-15, +18] 2 2 0.814 6 10 <~ 1 [-7, +10] 6-8 10-12 [0, +1] [-9, +12] H MCD 7 1 1 5 10 -3 [-10, +6] 5-7 10-18 [-5, -3] [-18, +8] 4 2 0.736 6 16 -5 [-16, +7] 6-8 15-16 [-7, -5] [-16, +7] I MCD 7 1 1 4 8 -3 [-8, +8] 4-7 8-13 [-4, -3] [-13, +12] 4 3 0.694 5 11 -4 [-11, +5] 5-6 10-13 [-6, -4] [-13, +5]

5910 TABLE C9 INS TG FOV 1 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 5 12 <~ 1 [-12, +7] 5-11 12-20 [-1, 0] [-17, +20] 8 12 0.519 9 20 -2 [-20, +11] 9-11 17-20 [-2, 0] [-20, +14] B MCD 8 1 1 3 6 +2 [0, +6] 3-13 6-20 [+2, +13] [0, +20] 8 2 0.829 5 11 +4 [+1, +11] 5-10 11-14 [+4, +10] [+1, +14] C MCD 8 1 1 3 6 +2 [-1, +7] 3-5 6-8 [+2, +5] [-1, +8] 8 12 0.475 4 8 +2 [-1, +8] 4-5 7-9 [+2, +5] [-3, +10] D MCD 8 1 1 7 12 -6 [-12, -2] 7-12 12-17 [-12, -6] [-17, -2] 10 16 0.196 14 17 -14 [-18, -9] 14-15 17-20 [-15, -14] [-20, -9] E ------F ------G ------H ------I MCD 8 1 1 5 12 <~ 1 [-12, +7] 5-11 12-20 [-1, +2] [-17, +20] 8 12 0.519 9 20 -2 [-20, +11] 9-11 12-20 [-2, 0] [-20, +14]

170 TABLE C10 INS TG FOV 2 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 33 1 1 3 8 -2 [-8, +3] 3-6 7-18 [-3, -1] [-18, +11] 11 6 0.913 6 15 -4 [-15, +3] 6-7 13-16 [-5, -3] [-16, +5] B MCD MY 33 1 1 1 3 <~ 1 [-2, +3] 1-5 3-11 [-5, +5] [-8, +11] 11 3 0.895 1 3 <~ 1 [-2, +3] 1-4 3-6 [-3, +2] [-6, +5] C MCD 7 1 1 1 1 <~ 1 [-1, +1] 1-2 1-4 [-2, 0] [-4, +1] 5 2 0.946 1 2 <~ 1 [-1, +2] 1-3 1-5 [-2, 0] [-5, +2] D MCD 8 1 1 3 5 -3 [-5, +2] 3-9 5-18 [-8, -3] [-18, +2] 10 16 0.196 10 14 -10 [-14, -6] 10-11 13-16 [-11, -10] [-16, -6] E ------F ------G ------H ------I MCD MY 33 1 1 3 8 -2 [-8, +3] 3-6 8-18 [-3, -1] [-18, +11] 11 6 0.913 6 15 -4 [-15, +3] 6-7 13-16 [-5, -3] [-16, +5]

TABLE C11 VL1 TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 1,2,3 1 1 6 17 +4 [-7, +17] 6-8 16-21 [+3, +7] [-9, +21] 8 8 0.789 7 27 +4 [-9, +27] 7-11 26-29 [+4, +10] [-9, +29] B MARSCAM 8 3 0.700 7 11 +5 [-8, +11] 7-11 11-16 [+5, +11] [-8, +16] 10 1 1 7 12 +5 [-8, +12] 7-13 12-20 [+4, +12] [-9, +20] C MCD 8 1 1 5 9 +5 [+1, +9] 5-7 7-13 [+5, +7] [+1, +13] 8 6 0.903 5 11 +5 [+1, +11] 5-10 11-14 [+5, +10] [+1, +14] D MCD MY 25 1 1 5 17 <~ 1 [-7, +17] 5-6 16-21 [+1, +3] [-9, +21] 12 16 0.312 9 26 +6 [-6, +26] 9-10 26-29 [+4, +8] [-9, +29] E MCD MY 24 1 1 6 16 +4 [-7, +16] 6-8 16-21 [+3, +7] [-9, +21] 8 6 0.762 7 27 +4 [-9, +27] 7-11 26-29 [+4, +9] [-9, +29] F ------G MCD MY 26 1 1 7 12 +5 [-6, +12] 6-8 11-14 [+4, +7] [-8, +14] 8 8 0.835 6 12 +4 [-8, +12] 6-11 12-20 [+4, +10] [-8, +20] H MCD 8 1 1 5 10 +3 [-5, +10] 5-8 10-16 [+3, +6] [-7, +16] 8 5 0.989 5 14 +3 [-8, +14] 5-9 14-16 [+3, +9] [-8, +16] I MCD 1,2,3 1 1 8 17 +4 [-5, +17] 7-11 16-21 [+3, +9] [-8, +21] 5 13 0.683 9 19 +9 [-5, +27] 13-14 26-29 [+8, +11] [-7, +29]

TABLE C12 VL2 TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 28 1 1 4 15 -2 [-15, +5] 4-6 14-18 [-4, -2] [-18, +9] 10 3 0.941 4 14 <~ 1 [-12, +14] 4-6 13-16 [+1, +4] [-12, +16] B MCD MY 32 1 1 3 12 <~ 1 [-12, +4] 2-4 6-14 [-3, 0] [-14, +9] 8 16 0.369 6 12 +2 [-12, +10] 6-8 12-15 [+2, +6] [-12, +15] C MCD MY 28 1 1 3 7 -2 [-7, +3] 3-5 7-16 [-4, -2] [-16, +8] 10 3 0.888 3 10 <~ 1 [-10, +7] 3-5 9-10 [+1, +4] [-10, +9] D MARSCAM MY 33 8 0.518 6 14 -5 [-14, +4] 6-8 14-18 [-7, -5] [-18, +8] 10 1 1 4 14 <~ 1 [-5, +14] 3-4 12-16 [0, +2] [-6, +16] E MCD MY 28 1 1 4 15 -2 [-15, +5] 4-6 14-18 [-4, -2] [-18, +9] 10 3 0.790 4 12 <~ 1 [-12, +11] 4-6 12-15 [+1, +4] [-12, +15] F MARSCAM 1,2,3 4-6 0.928 5 12 -3 [-12, +3] 4-6 11-14 [-5, -3] [-14, +5] 12 1 1 3 8 +2 [-4, +8] 2-4 6-10 [0, +3] [-4, +10] - MCD 1,2,3 1 1 2 7 <~ 1 [-7, +3] 2-3 5-7 [-2, 0] [-7, +4] 10 14 0.592 6 11 +4 [-4, +11] 6-9 11-15 [+4, +8] [-4, +15] H MCD MY 32 1 1 4 10 -2 [-10, +5] 3-5 10-12 [-3, -1] [-12, +8] 10 14 0.596 4 14 <~ 1 [-5, +14] 3-4 12-16 [+1, +3] [-6, +16] I MCD MY 28 1 1 4 13 -3 [-13, +3] 4-10 13-18 [-8, -3] [-18, +4] 2 2 0.959 4 11 <~ 1 [-11, +10] 4-5 10-12 [-1, +1] [-12, +11]

171 TABLE C13 MPF TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 1,2,3 1 1 5 10 -2 [-10, +4] 5-6 8-11 [-4, -1] [-11, +6] 11 16 0.517 7 11 +4 [-5, +11] 6-8 8-13 [+1, +5] [-8, +13] B MCD 8 1 1 1 4 <~ 1 [-4, +3] 1-4 3-6 [0, +4] [-4, +6] 8 16 0.217 7 8 +7 [+2, +8] 7-11 8-13 [+7, +11] [+2, +13] C MCD MY 25 1 1 0 1 <~ 1 [-1, 0] 0-1 1-2 [-1, +1] [-2, +2] 8 16 0.259 3 5 +3 [+1, +5] 3-6 5-8 [+3, +6] [+1, +8] D MARSCAM 7 8 0.505 8 8 -7 [-8, -5] 7-10 8-11 [-10, -7] [-11, -5] 2 1 1 3 5 -3 [-5, +3] 3-6 5-8 [-6, -3] [-8, +3] E ------F ------G MCD 1,2,3 1 1 5 10 -2 [-10, +4] 5-6 8-11 [-4, -1] [-11, +6] 11 16 0.517 7 11 +4 [-5, +11] 6-8 8-13 [+1, +5] [-8, +13] H ------I ------

5920 TABLE C14 SPI TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 4 14 <~ 1 [-7, +14] 4-7 9-14 [-6, 0] [-13, +14] 5 2 0.866 4 9 -2 [-9, +9] 4-6 9-15 [-5, -2] [-15, +9] B ------C ------D MCD 7 1 1 4 14 <~ 1 [-7, +14] 4-7 9-14 [-6, 0] [-13, +14] 5 2 0.866 4 9 -2 [-9, +9] 4-6 9-15 [-5, -2] [-15, +9] E MARSCAM 7 4 0.857 4 14 <~ 1 [-7, +14] 4-7 9-14 [-6, 0] [-13, +14] 5 1 1 4 9 -2 [-9, +9] 4-6 9-15 [-5, -2] [-15, +9] F MARSCAM MY 28 4 0.819 3 7 +2 [-4, +7] 3-7 7-14 [-3, +7] [-9, +14] 8 1 1 2 9 <~ 1 [-10, +3] 2-4 7-9 [0, +4] [-10, +9] G MCD 7 1 1 2 4 -2 [-4, 0] 2-10 4-13 [-9, -2] [-13, 0] 5 2 0.889 3 7 -2 [-7, +2] 3-6 7-11 [-5, -2] [-11, +2] H MCD 7 1 1 2 6 <~ 1 [-6, +1] 2-6 6-13 [-5, -1] [-13, +1] 2 2 0.935 2 6 -2 [-6, 0] 2-3 6-8 [-3, -2] [-8, 0] I MCD 7 1 1 4 7 -4 [-7, +1] 4-8 7-13 [-7, -4] [-13, +1] 5 15 0.322 6 9 -6 [-9, -2] 6-11 9-15 [-10, -6] [-15, -2]

TABLE C15 OPP TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 12 -5 [-12, +3] 6-9 12-15 [-9, -5] [-15, +3] 5 2 0.936 6 12 -4 [-12, +4] 6-9 12-16 [-8, -4] [-16, +4] B ------C ------D MCD 7 1 1 6 12 -5 [-12, +3] 6-9 12-16 [-9, -5] [-15, +3] 5 2 0.936 6 12 -4 [-12, +4] 6-9 12-16 [-8, -4] [-16, +4] E MCD 7 1 1 6 12 -5 [-12, +3] 6-9 12-15 [-9, -5] [-15, +3] 5 2 0.941 6 12 -4 [-12, +4] 6-9 12-16 [-8, -4] [-16, +4] F MCD MY 26 1 1 0 1 <~ 1 [-1, 0] 0-3 1-3 [-2, +1] [-3, +2] 2 14 0.382 1 2 <~ 1 [-2, -1] 1-3 2-4 [-1, +3] [-2, +4] G MARSCAM 7 3 0.902 4 7 -2 [-7, +1] 4-8 7-13 [-7, -2] [-13, +2] 5 1 1 3 8 <~ 1 [-8, +4] 3-6 8-12 [-5, -1] [-12, +4] H MARSCAM 7 5 0.78 4 8 -4 [-8, -1] 4-8 8-11 [-8, -4] [-11, -1] 4 1 1 4 7 -3 [-7, 0] 4-7 7-11 [-7, -3] [-11, 0] I MCD 7 1 1 8 12 -8 [-12, -2] 8-13 12-15 [-13, -8] [-15, -2] 5 2 0.913 9 12 -9 [-12, -6] 9-13 12-16 [-13, -9] [-15, -2]

172 TABLE C16 PHO TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 29 1 1 5 12 <~ 1 [-12, +11] 5-7 11-14 [-3, -1] [-14, +14] 4 16 0.561 13 22 +9 [-7, +22] 12-13 22-23 [+7, +9] [-11, +23] B MCD 7 1 1 3 8 +3 [0, +8] 3-6 8-14 [+3, +5] [-2, +14] 8 16 0.093 20 22 +20 [-2, +9] 19-20 22-23 [+19, +20] [+14, +23] C MCD MY 26 1 1 2 4 <~ 1 [-4, +3] 2-3 4-6 [-3, +1] [-6, +5] 8 16 0.202 8 11 +8 [+5, +11] 8-9 11-13 [+8, +9] [+4, +13] D MARSCAM MY 29 8 0.483 8 12 -8 [-12, -4] 8-11 12-14 [-11, -8] [-14, -4] 2 1 1 4 7 -4 [-7, 0] 4-7 7-11 [-6, -4] [-11, 0] E MCD MY 29 1 1 5 12 <~ 1 [-12, +11] 5-7 12-14 [-3, -1] [-14, +14] 4 15 0.471 13 22 +9 [-7, +22] 12-13 22-23 [+7, +9] [-11, +23] F MCD 1,2,3 1 1 5 9 -2 [-9, +4] 5-7 8-12 [-4, -1] [-12, +7] 4 15 0.551 13 21 +9 [-4, +21] 12-13 21-22 [+8, +9] [-6, +22] G MCD MY 29 1 1 6 12 <~ 1 [-12, +11] 5-7 11-14 [-3, -1] [-14, +14] 5 15 0.465 13 22 +8 [-8, +22] 12-13 22-23 [+7, +8] [-11, +23] H ------I ------

TABLE C17

CUR TSA MY 31 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 4 0.889 9 15 -8 [-15, +2] 9-14 15-19 [-14, -8] [-19, +6] 5 1 1 7 11 -7 [-11, +2] 7-10 11-17 [-10, -7] [-17, +2] B MARSCAM 7 4 0.946 5 8 -4 [-8, -1] 5-11 8-13 [-11, -4] [-13, +6] 5 1 1 5 7 -4 [-7, +2] 5-7 8-13 [-7, -4] [-10, +2] C MARSCAM 7 5 0.735 10 14 -10 [-14, -6] 10-15 14-18 [-15, -10] [-18, -3] 2 1 1 9 11 -8 [-11, -5] 8-11 11-14 [-11, -8] [-14, -5] D MARSCAM 7 4 0.917 10 15 -8 [-15, +2] 9-16 15-19 [-15, -8] [-19, +2] 5 1 1 7 10 -7 [-10, -3] 7-11 10-17 [-11, -7] [-17, -2] E MARSCAM 7 5 0.840 9 15 -8 [-15, +2] 9-14 15-19 [-14, -8] [-19, +6] 5 1 1 7 11 -7 [-11, +2] 7-10 11-17 [-10, -7] [-17, +2] F MARSCAM 7 4 0.888 7 13 -6 [-13, +1] 7-14 13-16 [-13, -5] [-16, +6] 2 1 1 6 9 -6 [-9, +1] 6-9 9-12 [-9, -6] [-12, +1] G MARSCAM 7 6 0.726 10 15 -10 [-15, -2] 10-16 15-19 [-15, -10] [-19, +1] 5 1 1 8 11 -8 [-11, +2] 8-11 11-17 [-11, -8] [-17, +2] H ------I MARSCAM 7 2 0.999 5 7 -3 [-7, +2] 5-12 7-14 [-11, -3] [-14, +2] 2 1 1 4 7 -4 [-7, +1] 4-9 7-12 [-9, -4] [-12, +1]

TABLE C18 CUR TSA MY 32 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 4 0.842 8 16 -7 [-16, 0] 8-13 16-21 [-12, -7] [-21, +6] 5 1 1 7 12 -6 [-12, +2] 7-10 12-18 [-9, -6] [-18, +2] B MARSCAM 7 4 0.857 4 7 -3 [-8, 0] 4-9 7-13 [-9, -3] [-13, +6] 5 1 1 3 7 -2 [-7, +2] 3-6 7-9 [-5, -2] [-10, +2] C MARSCAM 7 6 0.733 9 14 -9 [-14, -6] 9-13 14-18 [-13, -9] [-18, -4] 2 1 1 8 11 -8 [-11, -4] 8-11 11-15 [-11, -8] [-15, -4] D MARSCAM 7 4 0.912 8 16 -7 [-16, -2] 8-14 16-20 [-14, -7] [-21, -2] 5 1 1 7 12 -7 [-12, -2] 7-12 12-18 [-11, -7] [-18, -2] E MARSCAM 7 4 0.818 8 16 -7 [-16, 0] 8-13 16-20 [-12, -7] [-21, +6] 5 1 1 7 12 -6 [-12, +2] 7-10 12-18 [-9, -6] [-18, +2] F MARSCAM 7 4 0.942 7 10 -6 [-10, -1] 7-13 10-19 [-13, -5] [-19, +6] 2 1 1 6 11 -6 [-11, +1] 6-9 11-17 [-9, -6] [-17, +1] G MARSCAM 7 6 0.690 10 16 -10 [-16, -4] 10-15 16-20 [-15, -10] [-21, +2] 4 1 1 8 11 -8 [-11, -2] 8-11 11-15 [-10, -8] [-15, -2] H MARSCAM 7 6 0.716 6 12 -6 [-12, 0] 6-11 12-20 [-10, -6] [-20, 0] 5 1 1 5 12 -4 [-12, 0] 5-8 12-20 [-7, -4] [-15, +1] I MARSCAM 7 3 0.949 6 10 -5 [-10, 0] 6-11 10-19 [-10, -5] [-20, 0] 2 1 1 7 12 -6 [-12, +1] 7-11 12-18 [-10, -6] [-18, +2]

173 5930 TABLE C19 CUR TSA MY 33 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 5 0.814 7 14 -6 [-14, +3] 7-12 14-18 [-11, -6] [-18, +6] 5 1 1 6 10 -5 [-10, +2] 6-9 10-14 [-8, -5] [-14, +2] B MARSCAM 7 5 0.847 4 7 -3 [-7, +2] 4-9 7-12 [-9, -3] [-12, +6] 4 1 1 3 6 -2 [-6, +2] 3-6 6-9 [-5, -2] [-9, +2] C MARSCAM 7 6 0.711 8 13 -8 [-13, -4] 8-12 13-17 [-12, -8] [-17, -3] 2 1 1 7 10 -7 [-10, -4] 7-10 10-13 [-10, -7] [-13, -3] D MARSCAM 7 4 0.852 7 14 -5 [-14, +3] 7-12 14-18 [-12, -5] [-18, +3] 5 1 1 6 9 -5 [-9, -2] 6-10 9-14 [-9, -5] [-14, -2] E MARSCAM 7 5 0.751 7 14 -6 [-14, +3] 7-12 14-18 [-11, -6] [-18, +6] 5 1 1 6 10 -5 [-10, +2] 5-9 10-14 [-8, -5] [-14, +2] F MARSCAM 7 4 0.931 7 12 -6 [-12, +1] 7-13 12-17 [-13, -5] [-17, +6] 2 1 1 6 10 -6 [-10, +1] 6-9 10-13 [-9, -6] [-13, +1] G MARSCAM 7 6 0.626 8 14 -7 [-14, -2] 8-13 14-18 [-13, -7] [-18, +3] 5 1 1 5 9 -5 [-9, -1] 5-8 9-14 [-8, -5] [-14, -1] H MARSCAM 7 6 0.743 6 10 -6 [-10, 0] 6-11 10-14 [-10, -6] [-14, 0] 5 1 1 5 8 -4 [-8, +1] 5-8 8-11 [-7, -4] [-11, +1] I MARSCAM 7 3 0.962 5 10 -4 [-10, +3] 5-9 10-15 [-9, -4] [-15, +3] 4 1 1 6 9 -4 [-9, +2] 6-9 9-14 [-9, -4] [-14, +2]

TABLE C20 CUR TSA MY 34 MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 5 0.809 7 23 -4 [-12, +23] 7-11 18-24 [-10, -4] [-24, +23] 5 1 1 6 20 -4 [-16, +20] 6-9 19-22 [-7, -4] [-22, +20] B MARSCAM 7 5 0.792 7 12 -7 [-12, -3] 7-12 12-21 [-12, -7] [-21, +1] 5 1 1 6 12 -5 [-12, -1] 6-9 12-15 [-9, -5] [-15, -1] C MARSCAM 7 6 0.714 5 8 -4 [-8, +2] 5-9 8-12 [-8, -4] [-12, +5] 4 1 1 4 7 -3 [-7, +2] 4-7 6-10 [-6, -3] [-10, +2] D MARSCAM 7 2 0.931 8 23 -2 [-10, +23] 8-12 17-24 [-9, -2] [-24, +23] 5 1 1 9 20 -3 [-16, +20] 9-12 19-22 [-7, -3] [-22, +20] E MARSCAM 7 4 0.877 7 23 -4 [-12, +23] 7-11 18-24 [-10, -4] [-24, +23] 5 1 1 6 20 -4 [-16, +20] 6-9 19-22 [-7, -4] [-22, +20] F MCD MY 25 1 1 8 22 +2 [-14, +22] 8-12 18-24 [-8, +2] [-24, +23] 4 2 0.994 9 20 <~ 1 [-16, +20] 9-10 18-21 [-4, 0] [-21, +20] G MARSCAM MY 28 6 0.862 4 10 -3 [-10, +1] 4-10 10-13 [-10, -3] [-13, +1] 5 1 1 4 6 -2 [-6, +5] 4-5 6-8 [-4, -2] [-8, +5] H MARSCAM 7 6 0.743 6 10 -6 [-10, -1] 6-10 10-18 [-10, -6] [-18, -1] 5 1 1 4 9 -4 [-9, 0] 4-8 9-13 [-7, -4] [-13, 0] I MARSCAM 7 3 0.940 6 10 -6 [-10, +3] 6-11 10-24 [-11, -6] [-22, -1] 2 1 1 7 16 -6 [-16, -1] 7-11 16-22 [-10, -6] [-22, -1]

TABLE C21

INS5935 TSA BOOM +Y MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 7 12 <~ 1 [-12, +11] 7-11 12-21 [+1, +7] [-13, +21] 8 10 0.739 8 15 +3 [-11, +15] 8-10 15-18 [+3, +7] [-12, +18] B MCD 8 1 1 8 11 +7 [+4, +11] 8-16 11-21 [+7, +16] [+4, +21] 8 2 0.776 11 15 +10 [+7, +15] 11-15 15-18 [+10, +15] [+7, +18] C MCD 8 1 1 3 4 +3 [0, +4] 3-8 4-9 [+3, +8] [0, +9] 8 12 0.424 5 8 +5 [+3, +8] 3-8 4-9 [+3, +8] [+3, +10] D MARSCAM 7 2 0.924 5 9 -3 [-9, +3] 5-9 9-13 [-8, -3] [-13, +4] 4 1 1 4 7 -3 [-7, +5] 4-8 7-12 [-7, -3] [-12, +5] E ------F ------G ------H ------I MCD 8 1 1 7 12 <~ 1 [-12, +11] 7-11 12-21 [+1, +7] [-13, +21] 8 10 0.739 8 15 +3 [-11, +15] 8-10 15-18 [+3, +7] [-12, +18]

174 TABLE C22

INS TSA BOOM -Y MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 9 21 +2 [-21, +14] 9-13 18-24 [+2, +8] [-21, +24] 8 3 0.859 10 18 +5 [-18, +18] 10-13 18-22 [+4, +8] [-19, +22] B MCD 8 1 1 11 14 +11 [+7, +14] 11-20 14-24 [+11, +19] [+7, +24] 8 2 0.776 14 17 +14 [+10, +18] 14-18 17-22 [+14, +18] [+11, +22] C MCD 8 1 1 6 7 +5 [+3, +7] 6-11 7-12 [+5, +11] [+3, +12] 8 12 0.426 8 11 +8 [+5, +11] 8-11 11-12 [+8, +11] [+5, +12] D MARSCAM 7 4 0.827 7 17 -5 [-17, 0] 7-11 17-21 [-10, -5] [-21, 0] 4 1 1 6 16 -4 [-16, -1] 6-10 16-19 [-9, -4] [-19, -1] E ------F ------G ------H ------I MCD 8 1 1 9 21 +2 [-21, +14] 9-13 18-24 [+2, +8] [-21, +24] 8 3 0.859 10 18 +5 [-18, +18] 10-13 18-22 [+4, +8] [-19, +22]

5940

5945

5950

175 APPENDIX D

5955 The results obtained with MBC method and the other statistics considered for Group 2b comparisons (analysis per single probe, see Section 5.3.2) are here reported. The meaning of the columns is the same as that of Table 5.3 (see Appendix C for the detailed explanation).

List of the tables collected in this Appendix (organized chronologically according to the MY of 5960 landing):

• TG variable Table D1: SPI, near; Table D6: CUR, MY 32; Table D2: SPI, upview; Table D7: CUR, MY 33; 5965 Table D3: OPP, near; Table D8: CUR, MY 34; Table D4: OPP, upview; Table D9: INS, FOV 1; Table D5: CUR, MY 31; Table D10: INS, FOV 2.

5970 • TSA variable Table D11: VL1; Table D17: CUR, MY 31; Table D12: VL2; Table D18: CUR, MY 32; Table D13: MPF; Table D19: CUR, MY 33; Table D14: SPI; Table D20: CUR, MY 34; 5975 Table D15: OPP; Table D21: INS, BOOM +Y; Table D16: PHO; Table D22: INS, BOOM -Y;

5980

5985

176 TABLE D1

SPI TG MCD MARSCAM NEAR SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 8 21 +3 [-16, +21] 8-12 21-28 [+3, +9] [-16, +28] 2 13 0.417 12 28 +9 [-13, +28] 12-13 28-29 [+9, +10] [-16, +29] F MCD MY 25 1 1 9 23 +4 [-15, +23] 8-14 19-28 [+3, +10] [-16, +28] 5 15 0.290 14 25 +11 [-13, +25] 14-15 25-26 [+11, +12] [-16, +26] G MCD 7 1 1 9 19 +4 [-16, +19] 9-13 19-28 [+4, +10] [-16, +28] 2 16 0.241 13 28 +11 [-9, +28] 13-15 28-29 [+11, +13] [-10, +29] H MCD 7 1 1 7 21 +3 [-16, +21] 7-11 21-28 [+3, +7] [-16, +28] 2 8 0.535 10 23 +8 [-5, +23] 10-11 23-24 [+8, +9] [-5, +24] I MCD 7 1 1 7 21 +4 [-13, +21] 7-11 21-28 [+4, +9] [-13, +28] 2 9 0.590 10 23 +6 [-13, +23] 10-11 23-24 [+6, +7] [-16, +24]

TABLE D2

SPI TG MCD MARSCAM UPVIEW SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 8 21 +2 [-18, +21] 8-11 21-27 [+2, +7] [-21, +27] 2 13 0.430 11 27 +7 [-17, +27] 11-12 27-28 [+7, +9] [-17, +28] F MCD MY 27 1 1 8 20 +2 [-17, +20] 7-10 17-21 [-1, +5] [-19, +21] 2 15 0.366 10 25 +6 [-13, +25] 7-10 17-21 [+6, +9] [-13, +25] G MCD 7 1 1 10 21 +5 [-18, +21] 10-14 21-27 [+4, +9] [-21, +27] 2 15 0.336 14 27 +10 [-15, +27] 14-15 27-28 [+10, +12] [-15, +28] H MCD 7 1 1 8 21 +4 [-14, +21] 8-11 21-25 [+4, +8] [-18, +25] 2 8 0.521 11 27 +8 [-11, +27] 11-12 27-28 [+8, +9] [-12, +28] I MCD 7 1 1 6 16 +2 [-14, +16] 6-9 16-21 [+2, +5] [-21, +19] 2 11 0.390 9 18 +5 [-17, +18] 8-9 18-19 [+5, +6] [-17, +19]

5990 TABLE D3

OPP TG MCD MARSCAM NEAR SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 27 1 1 6 23 <~ 1 [-23, +14] 6-7 22-27 [-3, +2] [-27, +20] 10 16 0.613 8 25 +4 [-15, +25] 8-9 24-27 [-3, +4] [-27, +26] F MCD MY 25 1 1 4 11 <~ 1 [-6, +11] 4-9 9-17 [+1, +8] [-11, +17] 2 15 0.348 7 18 +4 [-9, +18] 7-13 18-25 [+4, +11] [-9, +25] G MCD MY 25 1 1 5 15 +2 [-8, +15] 4-7 11-20 [-1, +6] [-12, +20] 2 15 0.401 7 20 <~ 1 [-14, +20] 7-11 20-26 [+1, +9] [-14, +26] H MARSCAM MY 26 7 0.929 7 24 <~ 1 [-24, +11] 7-8 22-27 [-3, +1] [-27, +12] 4 1 1 7 18 <~ 1 [-18, +15] 6-10 15-27 [-6, +1] [-27, +20] I MCD MY 28 1 1 6 23 -2 [-23, +8] 6-8 22-27 [-5, -1] [-27, +10] 8 16 0.776 6 16 <~ 1 [-16, +12] 6-11 15-27 [-6, 0] [-27, +20]

TABLE D4

OPP TG MCD MARSCAM UPVIEW SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 26 1 1 6 23 <~ 1 [-23, +17] 6-7 22-27 [-3, +2] [-27, +22] 10 16 0.723 8 22 +3 [-17, +22] 8-9 22-29 [-4, +3] [-24, +29] F MCD MY 29 1 1 4 9 +2 [-9, +9] 4-7 9-15 [-2, +6] [-14, +15] 2 15 0.336 6 16 <~ 1 [-11, +16] 6-11 16-22 [+1, +9] [-11, +22] G MCD MY 25 1 1 5 18 +2 [-8, +18] 5-7 12-22 [-2, +5] [-14, +22] 2 10 0.718 6 15 <~ 1 [-14, +15] 6-10 15-29 [0, +8] [-14, +29] H MCD 7 1 1 8 27 -3 [-27, +11] 7-8 21-27 [-3, +1] [-27, +15] 4 2 0.995 7 20 <~ 1 [-20, +19] 7-10 20-24 [-7, +2] [-24, +20] I MARSCAM MY 28 2 0.962 6 22 -2 [-22, +17] 6-8 22-27 [-6, -2] [-27, +18] 10 1 1 6 20 <~ 1 [-17, +20] 6-12 20-23 [-7, -1] [-23, +20]

177 TABLE D5

CUR TG MCD MARSCAM a MY 31 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 16 <~ 1 [-16, +14] 6-12 16-21 [-3, -1] [-17, +21] 2 15 0.244 11 26 <~ 1 [-14, +26] 11-13 26-27 [-1, +1] [-18, +27] F MCD 7 1 1 5 11 <~ 1 [-11, +11] 5-12 11-21 [-2, 0] [-17, +21] 2 15 0.210 11 26 <~ 1 [-13, +26] 11-13 26-27 [-1, +1] [-18, +27] G MCD MY 28 1 1 7 15 -3 [-14, +15] 7-13 15-19 [-4, -3] [-17, +19] 4 15 0.238 12 21 <~ 1 [-14, +21] 12-14 21-22 [-2, -1] [-18, +22] H ------I MCD 7 1 1 3 8 <~ 1 [-8, +7] 3-8 8-12 [-3, 0] [-11, +12] 5 12 0.347 6 14 +3 [-3, +14] 6-7 13-14 [0, +3] [-9, +14]

TABLE D6

CUR TG MCD MARSCAM MY 32 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 5 14 <~ 1 [-14, +13] 5-10 14-24 [-3, -1] [-19, +24] 4 9 0.526 9 27 <~ 1 [-13, +27] 9-11 27-28 [-2, 0] [-18, +28] F MCD 7 1 1 5 13 <~ 1 [-10, +13] 5-13 13-24 [-2, 0] [-16, +24] 2 14 0.296 12 27 <~ 1 [-13, +27] 12-14 27-28 [-1, +1] [-18, +28] G MCD 7 1 1 6 13 -2 [-13, +12] 6-11 13-22 [-3, -2] [-19, +22] 4 12 0.466 10 22 <~ 1 [-11, +22] 10-12 22-24 [-2, -1] [-14, +24] H MCD 7 1 1 5 14 -2 [-14, +10] 5-7 14-19 [-3, -2] [-19, +12] 4 2 0.886 6 14 <~ 1 [-11, +14] 6-8 13-14 [-4, -1] [-14, +14] I MCD 7 1 1 4 14 <~ 1 [-14, +6] 4-7 14-16 [-2, -1] [-16, +10] 5 3 0.688 5 12 <~ 1 [-10, +12] 5-7 11-12 [-2, 0] [-12, +12]

TABLE D7

CUR TG MCD MARSCAM MY 33 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 18 -3 [-18, +10] 6-10 18-20 [-4, -3] [-20, +17] 2 6 0.628 8 17 -2 [-16, +17] 8-11 17-21 [-4, -2] [-19, +21] F MCD 7 1 1 5 11 -2 [-11, +9] 5-11 11-20 [-4, -2] [-20, +17] 2 14 0.301 10 16 <~ 1 [-14, +16] 10-12 16-21 [-2, -1] [-18, +21] G MCD 7 1 1 5 15 -3 [-15, +10] 5-9 15-16 [-4, -3] [-16, +13] 2 13 0.422 8 14 <~ 1 [-12, +14] 8-10 14-17 [-2, -1] [-17, +14] H MCD 7 1 1 7 15 -4 [-15, +10] 7-9 15-19 [-5, -4] [-19, +13] 4 2 0.913 8 16 -3 [-16, +14] 8-11 16-19 [-6, -3] [-19, +14] I MARSCAM 7 3 0.957 6 18 -3 [-18, +9] 6-9 18-20 [-5, -3] [-20, +15] 2 1 1 7 17 -3 [-11, +17] 7-10 16-17 [-5, -3] [-15, +17]

6000 TABLE D8 CUR TG MCD MARSCAM MY 34 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 9 36 -3 [-21, +36] 8-13 29-42 [-4, -3] [-33, +42] 2 5 0.617 12 45 -2 [-26, +45] 12-14 44-45 [-4, -2] [-30, +45] F MCD MY 25 1 1 8 26 <~ 1 [-13, +26] 8-17 26-42 [-2, +1] [-26, +42] 2 10 0.389 17 45 +2 [-23, +45] 17-19 44-45 [0, +2] [-26, +45] G MCD 7 1 1 8 21 -4 [-21, +9] 8-13 21-33 [-5, -4] [-33, +18] 4 10 0.527 11 26 -2 [-26, +18] 11-13 26-30 [-4, -2] [-30, +19] H MCD 7 1 1 7 21 -5 [-21, +9] 7-11 21-33 [-6, -5] [-33, +9] 2 2 0.746 8 26 -5 [-26, +8] 8-11 26-30 [-7, -5] [-30, +9] I MCD 7 1 1 7 18 -5 [-18, +5] 7-9 18-20 [-6, -5] [-20, +7] 2 4 0.697 8 13 -5 [-13, +8] 7-9 13-18 [-7, -5] [-18, +8]

178 TABLE D9

INS TG MCD MARSCAM FOV 1 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 6 17 +2 [-12, +17] 6-10 15-19 [+2, +4] [-16, +19] 8 9 0.568 8 25 +2 [-10, +25] 8-9 23-25 [+2, +5] [-10, +25] F MCD 8 1 1 5 12 <~ 1 [-12, +8] 5-9 12-16 [-1, +2] [-16, +14] 8 2 0.933 6 10 <~ 1 [-10, +9] 6-7 9-10 [-1, +2] [-10, +10] G ------H ------I MCD 8 1 1 6 17 +2 [-12, +17] 6-10 15-19 [+2, +4] [-16, +19] 8 9 0.568 8 25 +2 [-10, +25] 8-9 23-25 [+2, +5] [-10, +25]

6005 TABLE D10

INS TG MCD MARSCAM FOV 2 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 31 1 1 4 10 <~ 1 [-10, +6] 3-6 7-17 [-2, 0] [-17, +12] 5 15 0.311 5 13 <~ 1 [-13, +12] 5-6 11-13 [-2, 0] [-13, +13] F MCD MY 32 1 1 4 7 -2 [-7, +3] 4-5 6-10 [-4, -1] [-10, +6] 11 14 0.400 4 8 <~ 1 [-8, +8] 4-6 8-9 [-4, 0] [-9, +9] G ------H ------I MCD MY 31 1 1 4 10 <~ 1 [-10, +6] 3-6 7-17 [-2, 0] [-17, +12] 5 15 0.311 5 13 <~ 1 [-13, +12] 5-6 11-13 [-2, 0] [-13, +13]

TABLE D11

VL1 TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 7 18 +5 [-4, +18] 6-8 14-18 [+5, +7] [-5, +18] 8 1 1 8 31 +5 [-8, +31] 8-11 29-32 [+5, +10] [-8, +32] F ------G MARSCAM 8 2 0.827 7 14 +5 [-4, +14] 7-9 14-15 [+5, +7] [-4, +15] 8 1 1 5 16 +5 [-3, +16] 6-11 16-21 [+5, +10] [-3, +21] H MCD 1,2,3 1-3 1 5 13 +4 [-5, +13] 5-8 12-15 [+4, +7] [-5, +15] 8 14 0.410 8 19 +4 [-8, +19] 8-10 19-21 [+4, +9] [-8, +21] I MCD MY 26 1 1 7 15 +4 [-5, +15] 7-10 14-18 [+4, +9] [-5, +18] 12 14 0.356 12 30 +7 [-5, +30] 12-13 29-32 [+7, +10] [-5, +32]

TABLE D12 VL2 TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD MY 28 1 1 4 11 -2 [-11, +6] 4-6 11-16 [-4, -2] [-16, +7] 2 14 0.556 6 16 +3 [-10, +16] 5-6 15-16 [+1, +4] [-11, +16] F MCD MY 33 1 1 4 11 -2 [-11, +6] 4-5 11-13 [-3, -2] [-13, +6] 10 12 0.581 5 11 +2 [-6, +11] 5-6 11-13 [+2, +4] [-7, +13] G MCD MY 33 1 1 3 10 <~ 1 [-10, +5] 3-4 9-11 [-1, 0] [-11, +6] 8 16 0.289 6 12 +4 [-6, +12] 6-8 11-16 [+4, +7] [-7, +16] H MCD MY 29 1 1 4 10 -2 [-10, +7] 3-6 8-15 [-5, -2] [-15, +7] 2 14 0.636 6 14 +2 [-10, +14] 5-6 14-16 [0 , +2] [-11, +16] I MCD MY 28 1 1 4 10 -3 [-10, +5] 4-8 10-16 [-7, -3] [-16, +6] 4 3 0.694 5 12 <~ 1 [-9, +12] 5-6 11-14 [-1, +1] [-11, +14]

179 TABLE D13

MPF TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 1,2,3 1-3 1 4 9 <~ 1 [-9, +8] 4-5 9-11 [-1, +1] [-11, +10] 8 5 0.816 4 7 +4 [-1, +7] 4-7 7-13 [+4, +7] [-1, +13] F ------G MCD 1,2,3 1-3 1 4 9 <~ 1 [-9, +8] 4-5 9-11 [-1, +1] [-11, +10] 8 5 0.816 4 7 +4 [-1, +7] 4-7 7-13 [+4, +7] [-1, +13] H ------I ------

TABLE D14

SPI TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM MY 29 8 0.633 6 16 -4 [-16, +7] 6-8 15-17 [-6, -4] [-17, +10] 11 1 1 4 18 <~ 1 [-18, +8] 4-5 16-18 [-1, +1] [-17, +10] F MARSCAM 7 6 0.753 5 12 -3 [-12, +10] 5-7 12-16 [-6, -3] [-16, +10] 10 1 1 5 13 <~ 1 [-11, +13] 4-5 8-13 [-6, -3] [-16, +10] G MARSCAM 7 8 0.618 6 15 -4 [-15, +10] 6-9 15-17 [-8, -4] [-17, +10] 8 1 1 4 16 <~ 1 [-16, +7] 4-5 16-18 [-1, 0] [-18, +7] H MARSCAM MY 24 8 0.687 5 13 -4 [-13, +3] 5-6 11-16 [-5, -3] [-16, +10] 11 1 1 3 8 <~ 1 [-5, +8] 2-3 8-10 [+1, +2] [-6, +10] I MARSCAM MY 29 6 0.580 6 13 -5 [-13, +7] 6-8 13-16 [-7, -4] [-16, +7] 2 1 1 3 10 <~ 1 [-10, +7] 3-6 10-16 [-5, -1] [-16, +7]

6015 TABLE D15

OPP TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MARSCAM 7 8 0.429 8 18 -7 [-18, +6] 8-10 18-20 [-9, -7] [-20, +6] 4 1 1 5 13 -2 [-13, +13] 5-7 13-17 [-5, -2] [-17, +13] F MARSCAM 1,2,3 8-10 0.586 6 10 -4 [-10, +5] 6-7 10-12 [-5, -4] [-12, +6] 2 1 1 4 10 <~ 1 [-7, +10] 4-5 9-10 [+1, +4] [-7, +10] G MARSCAM 7 8 0.517 7 16 -6 [-16, +3] 7-10 15-18 [-8, -6] [-18, +4] 4 1 1 4 13 <~ 1 [-5, +13] 4-5 12-13 [-2, +1] [-11, +13] H MARSCAM MY 33 8 0.448 7 16 -7 [-16, +2] 7-9 15-17 [-8, -6] [-17, +3] 4 1 1 4 9 <~ 1 [-9, +8] 4-6 9-15 [-4, -1] [-15, +11] I MARSCAM 7 8 0.431 10 18 -9 [-18, +6] 10-12 18-20 [-8, -5] [-20, +6] 4 1 1 6 13 -5 [-13, +7] 6-12 13-17 [-8, -5] [-17, +8]

TABLE D16

CUR TSA MCD MARSCAM b MY 31 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 7 14 -5 [-14, +5] 7-11 14-21 [-10, -5] [-21, +5] 5 3 0.821 8 15 -4 [-15, +12] 8-9 15-18 [-7, -4] [-18, +12] F MCD MY 25 1 1 6 13 -4 [-13, +5] 6-11 13-20 [-10, -4] [-20, +5] 5 3 0.685 8 15 -5 [-15, +11] 8-10 15-18 [-7, -5] [-18, +11] G MARSCAM 7 4 0.819 9 14 -8 [-14, -1] 8-13 14-21 [-12, -8] [-21, -1] 5 1 1 8 13 -6 [-13, +6] 8-10 13-15 [-8, -6] [-15, +6] H ------I MCD 7 1 1 4 11 -2 [-11, +5] 4-9 10-14 [-8, -2] [-14, +5] 5 4 0.831 5 12 <~ 1 [-11, +12] 5-7 11-14 [-6, -1] [-14, +12]

180 TABLE D17

CUR TSA MCD MARSCAM MY 32 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 5 14 -4 [-14, +5] 5-9 14-21 [-8, -4] [-21, +5] 5 2 0.840 6 13 -3 [-13, +9] 6-8 13-16 [-6, -3] [-16, +9] F MCD 7 1 1 6 13 -5 [-13, +2] 6-11 13-21 [-10, -4] [-21, +4] 5 3 0.719 7 13 -5 [-13, +9] 7-9 13-16 [-7, -5] [-16, +9] G MARSCAM 7 3 0.953 8 14 -7 [-14, +3] 8-12 14-21 [-11, -7] [-21, +3] 5 1 1 7 13 -5 [-13, +8] 7-9 13-14 [-7, -5] [-14, +8] H MCD 7 1 1 4 13 -3 [-13, +5] 4-7 13-16 [-6, -3] [-16, +5] 4 2 0.901 5 10 <~ 1 [-10, +9] 5-6 10-12 [-4, -1] [-12, +9] I MCD 7 1 1 4 11 -3 [-11, +4] 4-7 11-19 [-6, -3] [-19, +4] 5 2 0.832 5 13 -2 [-13, +9] 5-7 10-13 [-6, -2] [-13, +9]

TABLE D18

CUR TSA MCD MARSCAM MY 33 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 6 15 -5 [-15, +5] 6-10 15-22 [-9, -5] [-22, +5] 5 2 0.946 6 12 -3 [-12, +8] 6-8 12-16 [-6, -3] [-16, +8] F MCD 7 1 1 6 15 -5 [-15, +1] 6-11 15-22 [-10, -5] [-22, +3] 5 3 0.808 7 12 -5 [-12, +8] 7-9 12-16 [-7, -5] [-16, +8] G MARSCAM 7 4 0.857 7 14 -6 [-14, -1] 7-11 13-20 [-10, -6] [-20, 0] 5 1 1 7 12 -4 [-12, +8] 7-8 12-15 [-6, -4] [-15, +8] H MARSCAM 7 4 0.912 5 14 -4 [-14, +5] 5-8 13-17 [-7, -4] [-17, +5] 4 1 1 5 10 -2 [-10, +8] 5-7 10-13 [-5, -2] [-13, +8] I MCD 7 1 1 4 12 -3 [-12, +5] 4-8 11-17 [-7, -3] [-17, +5] 5 2 0.858 5 11 -3 [-11, +8] 5-7 11-14 [-6, -2] [-14, +8]

TABLE D19

CUR TSA MCD MARSCAM MY 34 SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 7 1 1 7 22 -4 [-16, +22] 7-10 17-22 [-8, -4] [-21, +22] 4 2 0.801 9 27 -3 [-16, +27] 9-10 21-27 [-6, -3] [-19, +27] F MCD MY 25 1 1 7 21 <~ 1 [-13, +21] 7-11 17-22 [-8, -1] [-21, +22] 4 10 0.496 11 27 -2 [-16, +27] 11-12 21-27 [-4, -2] [-19, +27] G MCD 7 1 1 6 13 -5 [-13, -1] 6-10 12-17 [-9, -5] [-17, 0] 4 2 0.862 7 11 -3 [-11, +9] 7-8 11-13 [-5, -3] [-13, +9] H MARSCAM 7 2 0.997 7 16 -5 [-16, +5] 7-10 16-17 [-9, -5] [-17, +5] 4 1 1 7 13 -4 [-13, +8] 7-9 13-15 [-7, -4] [-15, +8] I MCD 7 1 1 7 13 -5 [-13, +4] 7-10 13-21 [-9, -5] [-21, +4] 4 2 0.989 7 14 -5 [-14, +7] 7-10 13-15 [-9, -5] [-15, +7]

6025 TABLE D20

PHO TSA MCD MARSCAM SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 1,2,3 1-3 1 3 9 <~ 1 [-6, +9] 3-4 7-11 [-2, +1] [-11, +11] 8 16 0.232 10 19 +9 [0, +19] 10-11 18-19 [+8, +10] [0, +19] F MCD 1,2,3 1-3 1 2 5 <~ 1 [-4, +5] 2-4 5-9 [-3, +2] [-9, +7] 8 16 0.176 11 16 +10 [+3, +16] 11-12 16-17 [+10, +11] [+3, +17] G MCD MY 29 1 1 3 8 <~ 1 [-5, +8] 3-4 7-11 [-2, +1] [-11, +11] 8 16 0.218 10 19 +9 [0, +19] 10-11 18-19 [+9, +10] [0, +19] H ------I ------

181 TABLE D21

INS TSA MCD MARSCAM BOOM +Y SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 6 13 +3 [-8, +13] 6-11 13-21 [+3, +8] [-9, +21] 8 2 0.828 7 23 +5 [-5, +23] 7-10 20-25 [+5, +8] [-5, +25] F MCD 8 1 1 7 12 3 [-7, +12] 7-11 12-18 [+3, +9] [-7, +18] 10 2 0.925 7 16 +5 [-2, +16] 7-11 16-24 [+5, +9] [-5, +24] G ------H ------I MCD 8 1 1 6 13 +3 [-8, +13] 6-11 13-21 [+3, +8] [-9, +21] 8 2 0.828 7 23 +5 [-5, +23] 7-10 20-25 [+5, +8] [-5, +25]

6030 TABLE D22

INS TSA MCD MARSCAM BOOM -Y SINGLE SCENARIO ALL SCENARIOS, RANGE SINGLE SCENARIO ALL SCENARIOS, RANGE CASE MOST VOTED BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) BEST PLACE RANK RMSE (K) CHEB (K) MSD (K) ERR (K) RMSE (K) CHEB (K) MSD (K) ERR (K) A MCD 8 1 1 9 16 +6 [-11, +16] 9-14 16-24 [+6, +11] [-11, +24] 8 2 0.912 9 18 +8 [-5, +18] 9-12 18-22 [+8, +11] [-9, +22] F MCD 8 1 1 9 16 +6 [-11, +16] 9-14 16-21 [+6, +11] [-11, +21] 8 2 0.940 9 16 +8 [-5, +16] 9-13 16-21 [+8, +12] [-9, +21] G ------H ------I MCD 8 1 1 9 16 +6 [-11, +16] 9-14 16-24 [+6, +11] [-11, +24] 8 2 0.912 9 18 +8 [-5, +17] 9-12 18-22 [+8, +11] [-9, +22]

6035

182 APPENDIX E

6040 The “readmarsisedrsim.m” script, written by R. Orosei in Matlab and used to interpret simulated MARSIS echoes produced with the MARSIS simulator, is reported, with the Author's permission to clarify how the calculation is carried out. Some comments (in red) were added so to better explain the meaning of some passages.

6045 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% The function “readmarsisedrsim” receives in input the name of the simulated orbit generated with the MARSIS simulator (EdrSimFile) and return a list of geometric, instrumental and physical variables related 6050 to the processed orbit (see Section 7.6 for the detailed description). function [ ostline, f0, theta_s, frameid, scetfw, scetff, Vt, Vr, NA, x0, y0, z0, alt0, Vx0, Vy0, Vz0, lon_0, lat_0, esm1f1, es00f1, esp1f1, esm1f2, es00f2, esp1f2 ] = readmarsisedrsim( EdrSimFile )

% read simulation data of a MARSIS orbit 6055 RecordBytes = 49312;

% The simulation data file is opened.

6060 fid = fopen( EdrSimFile, 'r', 'ieee-le' );

if fid < 0 error( 'ReadMarsisEdrSim:MissingInputFile', ... 'The required simulation data file %s could not be opened.', ... 6065 EdrSimFile ) end

% The length in bytes of the simulation data file is retrieved, and divided by the length of a file record in % bytes to obtain the number of records in the file. 6070 fseek( fid, 0, 'eof' ); FileBytes = ftell( fid ); FileRecords = FileBytes / RecordBytes;

6075 if round( FileRecords ) ~= FileRecords fclose( fid ); error( 'ReadMarsisSimData:FractionalNumberOfRecords', ... 'The simulation data file %s contains %f records, a non integer number of records.', ... EdrSimFile, FileRecords ) 6080 end

% Instrument and geometric parameters and simulated echo spectra are read

fseek( fid, 0, 'bof' ); ostline = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); 6085 fseek( fid, 8, 'bof' ); f0 = fread( fid, [ 2, FileRecords ], '2*double', RecordBytes - 16 ); fseek( fid, 24, 'bof' ); theta_s = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 32, 'bof' ); frameid = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 40, 'bof' ); scetfw = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 48, 'bof' ); scetff = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); 6090 fseek( fid, 56, 'bof' ); Vt = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 64, 'bof' ); Vr = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 72, 'bof' ); NA = fread( fid, [ 2, FileRecords ], '2*double', RecordBytes - 16 ); fseek( fid, 88, 'bof' ); x0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 96, 'bof' ); y0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); 6095 fseek( fid, 104, 'bof' ); z0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 );

183 fseek( fid, 112, 'bof' ); alt0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 120, 'bof' ); Vx0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 128, 'bof' ); Vy0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 136, 'bof' ); Vz0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); 6100 fseek( fid, 144, 'bof' ); lon_0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 152, 'bof' ); lat_0 = fread( fid, [ 1, FileRecords ], 'double', RecordBytes - 8 ); fseek( fid, 160, 'bof' ); esm1f1r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 4256, 'bof' ); esm1f1i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 8352, 'bof' ); es00f1r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); 6105 fseek( fid, 12448, 'bof' ); es00f1i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 16544, 'bof' ); esp1f1r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 20640, 'bof' ); esp1f1i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 24736, 'bof' ); esm1f2r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 28832, 'bof' ); esm1f2i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); 6110 fseek( fid, 32928, 'bof' ); es00f2r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 37024, 'bof' ); es00f2i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 41120, 'bof' ); esp1f2r = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 ); fseek( fid, 45216, 'bof' ); esp1f2i = fread( fid, [ 512, FileRecords ], '512*double', RecordBytes - 4096 );

6115 fclose( fid );

esm1f1 = esm1f1r + 1i * esm1f1i; es00f1 = es00f1r + 1i * es00f1i; esp1f1 = esp1f1r + 1i * esp1f1i; 6120 esm1f2 = esm1f2r + 1i * esm1f2i; es00f2 = es00f2r + 1i * es00f2i; esp1f2 = esp1f2r + 1i * esp1f2i;

6125

6130

6135

6140

6145

184 APPENDIX F 6150 The “bins_creation.m” script, written during my research stay at INAF (Bologna) under the supervision of Prof. R. Orosei in Matlab and performed to create the global reflectivity maps with the simulated echoes obtained with the MARSIS simulator, is shown. The example is referred to the surface echo power registered for 1.8 MHz band in direction 00. Some comments (in red) were 6155 added so to better explain the meaning of some passages.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

6160 % Specify the path where is the workspace containing processable data, previously extracted % with a loop applied to the “readmarsisedrsim” function and saved in a matrix named % ‘orbita_data_complete’. load ('orbita_data_complete.mat')

6165 % Specify the path where to store the new workspace for future manipulations filename = 'test.mat';

% Variables used to indicate the frequency and the direction to be investigated FREQ = '1.8 MHz'; 6170 DIR = '00';

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % A resume of the meaning of variables stored in the 'orbita_data_complete' matrix. The % extended explanantion of each variables can be found in Sections 7.6 and 7.7. 6175 % % COLUMN 1 ----> F1 % COLUMN 2 ----> F2 % COLUMN 3 ----> ALTITUDE % COLUMN 4 ----> LONGITUDE 6180 % COLUMN 5 ----> LATITUDE % COLUMN 6 ----> MAX SIGNAL ES00F1 % COLUMN 7 ----> MAX SIGNAL ES00F2 % COLUMN 8 ----> MAX SIGNAL ESM1F1 % COLUMN 9 ----> MAX SIGNAL ESM1F2 6185 % COLUMN 10 ----> MAX SIGNAL ESP1F1 % COLUMN 11 ----> MAX SIGNAL ESP1F2 % COLUMN 12 ----> REFERENCE RADIAL VELOCITY Vr % COLUMN 13 ----> NUMBER OF RECORDS NA LINE 1 % COLUMN 14 ----> NUMBER OF RECORDS NA LINE 2 6190 % COLUMN 15 ----> X0 % COLUMN 16 ----> Y0 % COLUMN 17 ----> Z0 % COLUMN 18 ----> VX0 % COLUMN 19 ----> VY0 6195 % COLUMN 20 ----> VZ0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

6200

185 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Memo of the script-parameters to be changed for exploring different directions and/or %frequencies

6205 % A. filename, FREQ and DIR; % B. indices for the band (1.8, 3, 4 o 5); % C. freq_18_a(i,xxx) e freq_18_b(i,xxx), depending on the desidered direction to be studied (see % the list before) % D. freq in order to calculate the corresponding wavelength 6210 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Beginning of the analysis. It can be divided into into three steps.

%%%%%%%%%%%%%%%%%%%%%%%%%% 6215 %1. FILTERING IN FREQUENCY % Extraction, from the 'orbita_data_complete' matrix, of the data related to the wanted band, % in this example 1.8 MHz one %%%%%%%%%%%%%%%%%%%%%%%%%%

6220 % indices for the BAND 1.8 MHz idx1_freq_18 = orbita_data_complete(:, 1) == 1.8e6; % first line of frequency vector idx2_freq_18 = orbita_data_complete(:, 2) == 1.8e6; % second line of frequency vector

% extract data associated to BAND 1.8 MHz 6225 freq_18_a = orbita_data_complete (idx1_freq_18, :); freq_18_b = orbita_data_complete (idx2_freq_18, :);

% creating vectors containing the power echo for the chosen direction (here, 00). P_es00_a = freq_18_a(i,6); % power echo for frequency f1 6230 P_es00_b = freq_18_a(i,7); % power echo for frequency f2

% intermediate saving workspace save (filename);

6235 % a print on the screen to check the status of the manipulation fprintf ('\nPART 1 - COMPLETED!!!\n') fprintf ('\nFilter in frequency finished. Start with filtering for radial velocity (PART A)\n')

% %%%%%%%%%%%%%%%%%%%%%%%%%% 6240 % 2. FILTERING FOR RADIAL VELOCITY % %%%%%%%%%%%%%%%%%%%%%%%%%% % % The following formula is computed: % 6245 % X = [(Vrreference - Vrcomputed) ∙ (NA-1) ∙ (1/(127.27))/λ] ∙ 2π % % where Vrcomputed is the deduced radial velocity from X0, Y0, Z0, VX0, VY0 and VZ0; Vrreference is that % extracted from readmarsisedrsim (col. 12 of orbita_data_complete matrix); NA number of % impulses; 127.27 is the repetition frequency; λ is the wavelength considered. 6250 % Only points having X in ]-π/4; π/4[ were processed (see Section 7.7).

% connecting the two datasets, one for f1 and one for f2, in a single matrix: the meaning of the % columns of this matrix is the same of those of ‘orbita_data_complete’ 6255 freq_18 = [freq_18_a; freq_18_b];

186 % initializing the vector for extracting the deduced radial velocity Vrcomputed Vr_deduced_a = []; % f1 Vr_deduced_b = []; % f2

6260 % Vrcomputed for PART A (f1) for i = 1:length(freq_18_a)

scalar_product = freq_18_a(i,15)*freq_18_a(i,18) + freq_18_a(i,16)*freq_18_a(i,19) + freq_18_a(i,17)*freq_18_a(i,20); 6265 module = sqrt(freq_18_a(i,15).^2 + freq_18_a(i,16).^2 + freq_18_a(i,17).^2); Vr_deduced_a = [Vr_deduced_a; scalar_product/module];

clear scalar_product module end 6270 clear i; save (filename);

fprintf ('\nPART 2 - COMPLETED\n') 6275 fprintf ('\nRadial velocity calculations PART A finished. Start with radial velocity caluclations PART B\n')

% Vrcomputed for PART B (f2) for i = 1:length(freq_18_b) 6280 scalar_product = freq_18_b(i,15)*freq_18_b(i,18) + freq_18_b(i,16)*freq_18_b(i,19) + freq_18_b(i,17)*freq_18_b(i,20); module = sqrt(freq_18_b(i,15).^2 + freq_18_b(i,16).^2 + freq_18_b(i,17).^2); Vr_deduced_b = [Vr_deduced_b; scalar_product/module]; 6285 clear scalar_product module end

clear i; 6290 save (filename);

fprintf ('\nPART 3 - COMPLETED!\n') fprintf ('\nRadial velocity calculations PART B finished. Start with NA calculations PART A\n')

6295 % Extraction of the reference radial velocity Vrreference Vr = freq_18 (:,12);

% merging of Vrcomputed for PART A and PART B Vr_deduced = [Vr_deduced_a; Vr_deduced_b]; 6300 % Plot histograms of Vrreference and Vrcomputed % save as: histogram banda direction calculated Vr.jpg % save as: histogram banda direction reference Vr.jpg

6305 figure, histogram (Vr); title (['Reference Vr - FREQ. ' FREQ ' DIR ' DIR]); xlim([-1200 1450]) %, ylim([0 1450]) figure, histogram (Vr_deduced); xlim([-1200 1450]) % , ylim([-1200 1450]) 6310 title (['Calculated Vr - FREQ. ' FREQ ' DIR ' DIR])

187 save (filename);

% constants for following calculations c = 3.0e8; 6315 freq = 1.8e6; %%%%%%%% <------lambda = c/freq;

% Calculation of the X pamareter. The number of impulses, NA, is organised as f0, so we have 2 % different lines: number 13 for f1 and number 14 for f2. When we calculate the difference, 6320 % we must pay attention to these lines. In details, if the frequency we are looking for is in the % first line of f0 (col. 1), the related value of NA for that point must be taken from the first line % of NA (col. 13). The same happens for the second line of f0 (col. 2) and NA (col. 14).

% initializing vectors for calculating X for PART A and PART B 6325 Xa = []; Xb = [];

% first line of f0 and NA for j = 1:length(freq_18_a) 6330 NA = freq_18_a(j,13); Xa = [Xa; (( (Vr(j,1)-Vr_deduced_a(j,1)) * (NA-1) * (1/127.27) ) / lambda) * 2*pi];

clear NA 6335 end

save (filename);

6340 fprintf ('\nPART 4 - COMPLETED!\n') fprintf ('\nNA calculations PART A finished. Start with NA calculations PART B\n')

% second line of f0 and NA for k = 1:length(freq_18_b) 6345 NA = freq_18_b (k, 14); Xb = [Xb; (( (Vr((length(freq_18_a)+k),1)-Vr_deduced_b(k,1)) * (NA-1) * (1/127.27) ) / lambda) * 2*pi];

6350 clear NA

end

save (filename); 6355 clear j k;

% Merging the two vectors Xa and Xb: the size of X must be the sum of (freq_a+freq_b), % i.e. the size of freq_18 X = [Xa;Xb]; 6360 save (filename);

fprintf ('\nPART 5 - COMPLETED!\n') fprintf ('\nNA calculations PART B finished. Start with Vr-NA filter PART A\n')

6365

188 % Creating the matrices where new data will be stored. Meaning of the columns % matrix = [X_values echo_power longitude latitude] Ma = [Xa P_es00_a freq_18_a(:,4) freq_18_a(:,5)]; % PART A Mb = [Xb P_es00_b freq_18_b(:,4) freq_18_b(:,5)]; % PART B 6370 % initializing other matrices containing only the processable data Ma_filter = []; Mb_filter = [];

6375 % Filter for PART A for i= 1:length(Xa)

if (Ma(i,1) > -(pi/4) && Ma(i,1) < (pi/4))

6380 Ma_filter = [Ma_filter; Ma(i,2) Ma(i,3) Ma(i,4)];

end

end 6385 save (filename); clear i; fprintf ('\nPART 6 - COMPLETED\n') fprintf ('\nVr-NA filter PART A finished. Start with Vr-NA filter PART B\n') 6390 % Filter for PART B for i= 1:length(Xb)

if (Mb(i,1) > -(pi/4) && Mb(i,1) < (pi/4)) 6395 Mb_filter = [Mb_filter; Mb(i,2) Mb(i,3) Mb(i,4)];

end

6400 end

save (filename); clear i; fprintf ('\nPART 7 - COMPLETED!\n') 6405 fprintf ('\nVr-NA filter PART B finished. Start with bins creation\n')

% PLOT MAP FILTERED FOR VR % save as: direzione - FREQ. xxx - filtered VR.jpg

6410 axis equal figure, scatter (Ma_filter(:, 2), Ma_filter(:, 3), 10, Ma_filter(:, 1)) hold on scatter (Mb_filter(:, 2), Mb_filter(:, 3), 10, Mb_filter(:, 1)) title (['DIR ' DIR ' - FILTERED Vr - FREQ.' FREQ]); 6415 colormap jet colorbar caxis([120 200]) hold off save (filename); 6420

189 %%%%%%%%%%%%%%%%%%%%%%%%%%% % 3. BINS CREATION % Once extracted data for the wanted frequency (step 1) and eliminated points having extreme % radial velocity (step 2), we can now put it into grid cells so to make the maps. The idea is to 6425 % create bins with resolution 0.5° (lat) x 0.5° (lon), placing the data for the studied band and % direction in the bins and then compute the medians of the points belonging to the same bin. %%%%%%%%%%%%%%%%%%%%%%%%%%%

% First of all, merge data for PART A and PART B together 6430 % data_matrix = [echo_power lon lat] data_matrix = [Ma_filter;Mb_filter];

% Define the dimension of the bins of the grid cell: 0.5°x0.5° lat/lon st = 0.5; 6435 % Define the limits of the cells lonc = 0.25:st:359.75; latc = -87.75:st:87.75;

6440 % Define how many lat/lon values exist nlat = length(latc); nlon = length(lonc);

% find the indeces for lon and lat 6445 i_lon = interp1 (lonc, 1:nlon, data_matrix(:,2), 'nearest'); i_lat = interp1 (latc, 1:nlat, data_matrix(:,3), 'nearest');

% create the matrix divided into bins medians = zeros(nlat, nlon); 6450 % fill the matrix and calculate medians for each bins for r = 1 : nlat for l = 1 : nlon idx = (i_lon == l) & (i_lat == r); 6455 medians(r, l) = median(data_matrix(idx, 1));

end end

6460 clear r l;

% plot bins final maps % save as: direzione banda medians.jpg

6465 [XX, YY] = meshgrid (lonc, latc); figure, scatter (XX(:), YY(:), 10, medians(:)) colormap jet colorbar title (['BINS DIVISION, MEDIANS - DIR. ' DIR, ' FREQ.' FREQ]) 6470 save (filename); fprintf ('\nPART 8 - COMPLETED!\n') fprintf ('\nBins creation finished. END OF THE SCRIPT\n')

6475 exit;

190 APPENDIX G

In this Appendix all the global reflectivity maps built during the research stay at INAF (Bologna) are reported. In details: 6480 • Figure G.1 : direction 00, Frequency 1.8 MHz; • Figure G.2 : direction 00, Frequency 3 MHz; • Figure G.3 : direction 00, Frequency 4 MHz; • Figure G.4 : direction 00, Frequency 5 MHz; 6485 • Figure G.5 : direction M1, Frequency 1.8 MHz; • Figure G.6 : direction M1, Frequency 3 MHz; • Figure G.7 : direction M1, Frequency 4 MHz; • Figure G.8 : direction M1, Frequency 5 MHz; • Figure G.9 : direction P1, Frequency 1.8 MHz; 6490 • Figure G.10 : direction P1, Frequency 3 MHz; • Figure G.11 : direction P1, Frequency 4 MHz; • Figure G.12 : direction P1, Frequency 5 MHz;

6495

191 FIGURE G.1

192 6500 FIGURE G.2

193 FIGURE G.3

194 FIGURE G.4

195 FIGURE G.5

196 FIGURE G.6

197 6505 FIGURE G.7

198 FIGURE G.8

199 FIGURE G.9

200 FIGURE G.10

201 FIGURE G.11

202 6510 FIGURE G.12

203 APPENDIX H

I insert here a pre-print version of the paper I wrote during the first year of my PhD.

6515 TITLE: COMPARISON OF ASTRONOMICAL SOFTWARE PROGRAMS FOR ARCHAEOASTRONOMICAL APPLICATIONS YEAR: September 21, 2018 JOURNAL: Astronomy and Computing EDITOR: Elsevier 6520 AUTHORS: A. DE LORENZIS, V. Orofino DOI: https://doi.org/10.1016/j.ascom.2018.09.006 WEB-LINK: https://www.sciencedirect.com/science/article/pii/S2213133718300064

ABSTRACT 6525 Reproducing the movements of stars and planets across the sky has recently had notable insights thanks to the widespread use of astronomical software products with high mapping and graphical capabilities. Nonetheless, when it is necessary to determine the position of a star in the very remote past (or future), one must take into account two factors which have a profound impact on stellar positioning: the precession of the equinoxes and the proper motions of the stars, two mechanisms 6530 that are not always been properly considered, especially in the archaeoastronomical literature. The present work compares the principal commercial astronomical programs currently available with the goal to determine how correctly they evaluate the two aforementioned mechanisms. The comparison is carried out on a sample of 24 stars (among the brightest in the sky) using a subroutine which carefully evaluates the two phenomena. A discussion on the principal methods used to 6535 approximate precession is also given. The differences observed between the values of declination calculated with various approximations, as well as those between different astronomical software programs, may even exceed one degree, a value that is far beyond the resolving power of the human eye, making the evaluations and the consequent conclusions unreliable. Furthermore, via a reconstruction of the temporal trends of declination in the interval [25000 BC; AD 25000] for two 6540 stars with the highest (Toliman, α Cen) and the lowest (Mintaka, δ Ori) proper motions, the consequences of this effect on the stellar position are evaluated. Finally, as a consequence of the presented evidence, we test some alignments towards the brightest stars of the sky proposed for some enclosures of Gӧbekli Tepe, the most ancient megalithic site in the world. Keywords: Applied computing: astronomy – Archaeoastronomy – Astrometry – Ephemerides 6545 1. Introduction

The knowledge of the ancient stellar positions is of basic importance in Archeoastronomy. This interdisciplinary science, by combining different disciplines (mainly Astronomy and Archeology), allows 6550 one to interpret archeological evidence which lets one follow the activities of ancient populations in their observation and study of celestial bodies. As observed by Magli (2006), the knowledge possessed by these very old civilizations in the astronomical field is often by no means negligible and cannot be seen as the fruit of a handful of enlightened religious figures. There are a number of examples that confirm the deep and abiding interest that past civilizations showed in what happened above their heads. In fact, they

204 6555 built immense megalithic sites (Magli, 2009), showing alignments towards particular points of the paths on the sky of the brightest stars as well as of the Sun and the Moon. Among the most interesting cases, there are: Gӧbekli Tepe, the most ancient megalithic site in the world (Collins, 2013; Magli, 2013; De Lorenzis & Orofino, 2015; Hancock, 2015); the structures built on the plain of Natba Playa (Brophy & Rosen, 2005; Bauval & Brophy, 2011); the Egyptian pyramids (Bauval & Gilbert, 1994; Bauval, 2006; 6560 Belmonte et al, 2008); other buildings dispersed across Europe and its surrounds, as in Sardinia, Italy (Calledda & Proverbio, 2004; Zedda & Belmonte, 2004), Great Britain (Thom, 1967; in particular Stonehenge - North, 1996), Western Europe (Thom, 1974) and in the rest of the world (Magli, 2009). Usually, in archaeoastronomical studies, the information regarding the positions of the stars are obtained via commercial software products that reproduce the appearance of the sky back to the presumed epoch of 6565 construction of a given archeological site. These software programs give a global perspective of a large portion of the sky, but they do not always yield a precise determination of stellar coordinates objects by objects. This is a necessary approach to save time during calculation. These products can be seen as relatively trustworthy so long as the deviation does not surpass the resolving power of the human eye, defined as the minimum angular distance between two point sources necessary to see them as distinct 6570 objects. Depending upon the observed sources and the sky condition, this parameter could range between 5 and 10 arcmin, that is 0.08° and 0.17° (Silvestro, 1989) and, in favorable conditions, it may reach 3 arcmin (0.05° - Herrmann, 1975; Gribbin & Gribbin, 1996). It must be noticed that already Tycho Brahe in 1600 was able to measure angles (and hence positions of stars) with a greater precision, approaching 1 arcmin (about 0.02° - Verbunt & van Gent, 2010), equivalent to 1/30 the diameter of the full Moon. In this 6575 work, however, we use 0.05° as reference limit and not that obtained by Brahe (see Section 8), since the former is a more appropriate value for very ancient civilizations that made their observations with naked eye and without sophisticated pointing tools. In order to make research in the archaeoastronomical field as reliable as possible, it is necessary, in the evaluation of the possible stellar alignments for the various megalithic structures dispersed around the 6580 world, to employ software programs that are as precise as possible in the reproduction of stellar positions, especially in very remote epochs. In this paper, we present a deep inquiry about the way in which it is necessary to implement, in stellar position programs, the most appropriate developments to take correctly into account both the effects of the proper motions of a star and that of precessional phenomenon upon stellar mappings. This work is necessary to highlight the characteristics that an astronomical program 6585 must present to adequately reproduce stellar positions in the remote past, as well as in the distant future. 2. The evaluation of the proper motion of a star The sky that the first humans could admire several thousands of years ago had merely slight resemblance to that which one can see today, due to the inherent movements of the stars. Actually, although the stars seem to be immobile on the celestial sphere, with constellations that assume a well-defined shape, 6590 seemingly immutable through time, they move with respect to one another. Only the great distances that separate Earth from the stars impede the perception of these movements, which can be easily measured by astronomers thanks to the modern techniques of observation. This motion is called proper motion, because it is a movement intrinsic to the star, juxtaposed with the apparent motion caused by the movement of the Earth. Proper motion, denoted by μ, is expressed as an angular velocity, usually in 6595 arcsec per year. The proper motion of a star can occur in any direction and usually is decomposed into two components: μα, corresponding to the variation in right ascension (α), and μδ, corresponding to a variation in declination (δ). These two quantities can be defined as: dα dδ μ = ; μ = (1) α dt δ dt 6600 If the distance of a star is known, the proper motion can be converted into a linear velocity, that is the tangential velocity vT(in km/s). The component of proper motion of an approaching star or one moving

205 away from Earth is, instead, the radial velocity vR (also in km/s). The total velocity of a star in the space is given by the sum vector of its radial and tangential components. To evaluate the proper motion of a star, one can follow two different approaches which take into account 6605 short- term and long-term effects - see De Lorenzis (2011) for details. Short-term effects affect the stellar position in the near past or near future. One assumes that proper motions, both in α and δ, are constant through time. This assumption is all the more valid the smaller the evaluated time interval (usually assumed to be less than 10000 years). In this way, it is possible to calculate stellar coordinates (α and δ) in the considered epoch using the following simple equations:

6610 α=α0 +μα t (2)

δ=δ0+μδ t (3)

in which α0 and δ0 are, respectively, the right ascension and the declination of the object in the reference epoch, while t is the time elapsed from the reference epoch. The results obtained from such approximations nevertheless diverge quite a bit from actual values when 6615 considering epochs more remote than 10000 years or for stars with elevated proper motions: in fact, the distances of the stars from Earth changes notably, as do their proper motions, and these changes invalidate the approach just described. Long-term effects affect the position of a star in a very remote past or future which covers an arc of time even up to millions of years. To accurately determine stellar movements, it is necessary to know in detail 6620 the proper motion of a star in three dimensions, while proper motion gives us only a two-dimensional projection. Let consider a fixed cartesian reference system (with the origin setted at the center of the Sun) having axes xyz for velocity defined as follows: • Direction + x: from the origin towards the point with δ = 0° and α = 0h (the so called γ Point or 6625 Vernal Point of Aries, that is the position of the Sun at the Spring Equinox); • Direction + y: from the origin towards the point with δ = 0° and α = 6.0h; • Direction + z: from the origin towards the point with δ = + 90.0° (North Celestial Pole, NCP). To calculate the position of a celestial object at time t, it is necessary to know how it moves. For intervals of time of thousands or millions of years, stellar motion is essentially linear, that is the stars are too far to 6630 curve their trajectories in a substantial way. Hence, after a lapse of time t, the coordinates x, y, z of a star at any time are:

x=x0+vx t

y= y0+v y t (4)

{ z=z0+v zt

where x0, y0 and z0 are the cartesian coordinates of the initial position of the star, vx, vy and vz are the Cartesian components of velocity. These components can be derived from the star’s radial velocity v R and 6635 the two components in α and δ of the transverse velocity vTA and vTD, as follows:

v x=(v R cosδ cosα )−( vTA sin α )−(vTD sin δ cosα )

v y= (v R cosδ sin α )+( vTA cos α )−( vTD sin δ sin α ) (5)

{ vz=vR sin δ+vTD cosδ

vTA and vTD depend on the star’s proper motions and can be written as linear velocity by multiplying μα 6640 and μδ by the star’s distance d (in pc). The last one is calculated by considering the parallax π, which can be found in an astronomical catalog.

206 Being interested in determining the coordinates of the star in the equatorial coordinate system, the cartesian coordinates must be converted into the equatorial system via the following transformation:

2 2 d xy=( x + y ) z δ=arctan 6645 ( dxy ) (6) y α=arctan { ( x )

where dxy is the projection of d on the xy plane. It is worthwhile to note that the function arctan(u) gives a result in the range [- 90°, + 90°] for -1 < u < 1, so the value of α calculated with Eq. (6) must be corrected and reported in the right quadrant “manually”, 6650 depending on the sign of x and y. Then, the value so obtained must be converted in hours, minutes and seconds. The equations (6) give the temporal evolution of the stellar position across large spans of time.

3. The evaluation of the precession of the equinoxes

6655 Everything said in the previous Section does not take into account a wide plurality of external factors that inevitably influence stellar position as time passes. These external factors are due, above all, to the fact that the Earth is a physical system that, beyond having its own rotation motion around its axis (diurnal motion), is a member of the Solar System and it is affected by the gravitational interactions with the Sun, the Moon, and also the other planets (in particular Jupiter). Moreover, the atmosphere affects the position 6660 of the celestial bodies as observed from Earth, refracting and diffusing light rays that reach it, thus distorting observations. The principal effects due to gravitational interactions are nutation (period of 18.6 years) and precession of the Earth’s rotation axis (precession of the equinoxes), having a period of about 26000 years. One important consequence of such millenary motion is the variation of the NCP: for example, about 5000 6665 years ago, when the first pyramids in Egypt were built, this coincided almost exactly with the star Thuban (α Draconis), which was considered by people of the time to be the North Star of reference. Even for precession one can follow two approaches, considering (such as in the case of proper motion) short-term and long-term effects. The formulas that keep track of the lunisolar precession effects upon α and δ in the short-term are (H.M. 6670 Nautical Almanac Office, 1961):

cosδ sin ( α−zA )=cosδ 0sin (α 0+ζ A)

cosδ cos (α−z A )=cosθA cosδ 0cos ( α0+ζ A )−sin ϑ A sin δ 0 (7)

{ sin δ=cosϑ A sin δ0 +sin θA cos δ0 cos(α 0+ζ A)

where θA, ζA and zA are the so-called Newcomb angles (for details, see H.M. Nautical Almanac Office, 6675 1961). The latter were redefined by Capitaine et al. (2003a), extending the dependence upon time till the fifth order, with a nominal uncertainty of stellar coordinates less than 10-6 arcsec in a period of four centuries. One can observe how the perturbations due to nutation and to the presence of other Solar System bodies, in particular of the largest planets like Jupiter, and the closest, like Venus (planetary precession), are negligible in first approximations with respect to lunisolar precession. 6680 Parameterization (7) is polynomial: this approach is that followed both in the old model of precession IAU 1976 (see Lieske et al., 1977), adopted by the IAU (International Astronomical Union) and in the IAU 2000 model (see Capitaine et al., 2003b), which includes, as opposed to the first, a series of terms for nutation. Such polynomial developments were added to obtain greater precision for not so remote past

207 epochs (within a few centuries) from the current reference epoch, that is 12:00 T.U. of 1 January 2000, 6685 according to the Gregorian calendar (corresponding to the Julian epoch J2000.0). The IAU 2000/2006 (Wallace & Capitaine, 2006) model relative to precession-nutation was developed to obtain the X,Y coordinates of the CIP (Celestial Intermediate Pole) with respect to the GCRS (Geocentric Celestial Reference System). GCRS is a reference system for spatial-temporal coordinates having as origin the center of the Earth, and which takes into account the space-time distortions caused by 6690 the mass of the Earth. These coordinates do not rotate with respect to those of the ICRS (International Celestial Reference System), a different reference system with space-time coordinates which also does not rotate, having however as origin the center of mass of the Solar System. In particular, in these IAU models, the X,Y coordinates of the CIP (which, in the GCRS system, cover the same role developed by the NCP in the traditional equatorial reference system) are obtained via a process which adopts both time 6695 polynomials t (which principally describe precession) and a series of Fourier and Poisson terms (which represent the contribution of nutation). These developments assure a precision on the order of 10 -6 arcsec valid for intervals of several centuries. Beyond these intervals errors grow rapidly with time. Actually, precession represents a complicated procedure with a high periodicity that polynomial developments cannot describe, as demonstrated by numeric integrations of the equations reproducing the movement of 6700 the Earth in the Solar System and of its rotation. It has thus been necessary to elaborate a more realistic model to describe the long-term behavior of the planetary configurations, in order to obtain results with a precision which approaches that of the IAU 2006 model (Wallace & Capitaine, 2006) for epochs close to J2000 and a reasonable agreement with the numeric integrations referred to much longer time intervals. The accuracy to be obtained in the new 6705 parameterization must be of the same order of that of the IAU 2006 model in the proximity of J2000, and still sufficiently good outside the interval of amplitude Δt = ± 1000 years centered around J2000 (in particular, a few arcmin for Δt = 200000 years). The long-term expression for the coordinate X,Y of the CIP was given by (Vondrák et al. 2011):

14 2 −7 3 2πT 2 πT X =5453.270624+0.4252850 T−0.00037173 T −1.52∙10 T +∑ C xi cos +Sxi sin 6710 i=1 ( Pi Pi ) (8)

14 2 −7 3 2πT 2 πT Y =−73750.937353−0.7675456 T−0.00018725 T +2.31 ∙10 T + C cos +S sin ∑ yi P yi P i=1 ( i i )

The values of the periodic terms Ci, Si and Pi of Eq. (8), where T (as Pi) is expressed in centuries starting from Julian epoch J2000, are reported in Vondrák et al. (2011, 2012) works, as their physical explanation: 6715 for example, C1 and S1 are those related to the lunisolar precession. Eq. (8) demonstrates the possibility of building a model that is equivalent to the IAU 2006 model of precession in the case of a short-term development (up to a few centuries around J2000) and, at the same time, that is consistent with the modern numeric integrations in the long-term regarding the movements of the bodies of the Solar System. 6720 4. Identification of the astronomical software products to be compared Among the numerous routines that allow acquisition of stellar coordinates in past and future epochs, even very remote, in the present work we have compared the following programs2: a) Cartes du Ciel – Sky Charts (in figures and tables, denoted as CDC); 6725 b) CyberSky (CS); c) Star Calc (SC); d) Stellarium (ST);

2 The versions of these programs, tested to collect stellar position data, are those available and updated as of December 31, 2017.

208 e) SkyMap Pro (SM); f) Starry Night Pro (SNP); 6730 g) TheSky (TS). Among these, Cartes du Ciel, Star Calc and Stellarium are freely available, while the others here examined are paid software programs. Some of the latter offer the opportunity of a trial version of the package for a limited period of time. Obviously, those herein chosen are the most diffused and used but are only some of the available 6735 astronomical programs. Others are not included in the comparison because they are not able to evaluate stellar positions beyond a certain past epoch, such as Winstars2 (back to 3000 BC), Asynx Planetarium (back to AD 1753), Hallo Northern Sky (back to 999 BC), Solex (back to 1000 BC), C2A (only from AD 1987) and Swiss Ephemeris (back to 3000 BC). Obviously, this does not imply that such programs are not able to reproduce correctly stellar positions in their time ranges. 6740 The data obtained with the chosen programs were then compared with the output of Orion (a reference program that will be presented in Section 6), which can be considered as the most reliable instrument in the evaluation of stellar coordinates. The comparisons were carried out on a well-defined sample of stars (see next Section), having similar characteristics, highlighting the cases that diverge from general behavior. For each stars of this sample, the declination δ was determined for five dates: 2500 BC, 4500 6745 BC, 6000 BC, 8000 BC and 10000 BC. 5. Choice of star sample The comparison among the outputs of various programs introduced in the previous Section was carried out upon a group of stars having high apparent luminosity (low magnitude). In detail, we selected:  all stars with an apparent magnitude V ≤ 1.0, i.e. of I magnitude (16 stars); 6750  some of the main stars of constellations such as Orion (Alnitak, Alnilam and Mintaka) and the Big Dipper (Alioth, Dubhe and Alkaid), two of the constellations most studied by many ancient civilizations;  Thuban, the North Star in the time of the pyramids;  Deneb, which forms, along with Altair and Vega (already included in the sample), the so-called 6755 Summer Triangle, an asterism that was probably a celestial target for ancient populations since the Paleolithic (Rappenglück, 2004). In Tab. 1 are reported the selected 24 stars, in growing order of magnitude, according to SIMBAD (Set of Identifications, Measurements, and Bibliography for Astronomical Data), an astronomical database created by the Centre de Données Astronomiques de Strasbourg, France. 6760 Table 1: List of the selected stars. The proper name of each object is reported along with its magnitude and the common nomenclature, due to J. Bayer (Source: SIMBAD catalogue). SIRIUS -1.46 CANOPUS -0.74 TOLIMAN -0.1 ARCTURUS -0.05 (α Canis Majoris) (α Carinae) (α Centauri) (α Bootis) VEGA 0.03 CAPELLA 0.08 RIGEL 0.13 PROCYON 0.37 (α Lyrae) (α Aurigae) (β Orionis) (α Canis Minoris) ACHERNAR 0.46 BETELGEUSE 0.42 HADAR 0.60 ACRUX 0.81 (α Eridani) (α Orionis) (β Centauri) (α Crucis) ALTAIR 0.76 ALDEBARAN 0.86 SPICA 0.97 ANTARES 0.91 (α Aquilae) (α Tauri) (α Virginis) (α Scorpii) DENEB 1.25 ALNILAM 1.69 ALIOTH 1.77 ALNITAK 1.79 (α Cygni) (ε Orionis) (ε Ursae Majoris) (ζ Orionis) DUBHE 1.79 ALKAID 1.86 MINTAKA 2.41 THUBAN 3.68 (α Ursae Majoris) (η Ursae Majoris) (δ Orionis) (α Draconis)

209 6. The Orion program The reliability of various stellar programs in the reproduction of the sky was analyzed using a comparison 6765 with the program Orion, written expressly for archaeoastronomical applications by Patrick Wallace of STFC Rutherford Appleton Laboratory, UK. This program has been used as the reference and considered as the most reliable instrument for the determination of past stellar coordinates. The Orion program, written in Fortran, computes the stellar coordinates α and δ in the past and future. It keeps exact track of proper motions of the stars (see Section 2) and accurately evaluates the effects of the 6770 precession using a periodic long term parameterization, based on the progression of the CIP coordinates proposed by Vondrák et al. (2011) (see Section 3). Orion uses the SOFA library (Standards of Fundamental Astronomy), a series of subroutines (both in Fortran and C) that implement the official IAU algorithms for calculations of fundamental astronomy (International Astronomical Union - Division 1, 2010). 6775 Input parameters of the program are: the latitude of the point of observation, the coordinates (α and δ), the components of the proper motion (μα and μδ), the parallax π and the radial velocity vR of the star which one want to examine, relative to the epoch J2000, and finally, the epoch NE (New Epoch) in which one wants to determine the position of the object. These stellar input (α, δ, μα, μδ, π and vR, at J2000) were obtained from SIMBAD. 6780 Once fixed these parameters, the program performs the following steps:

 the Julian epoch NE is converted to the corresponding Julian date;  starting from α, δ, μα, μδ, π, and vR relative to the initial epoch, these same quantities are calculated for the stars in the NE, evaluating accurately firstly proper motion, but without taking into account 6785 precession;  CIP coordinates are evaluated according to the IAU 2006 model;  CIP coordinates are then determined using long-term precession parameterization (Vondrák et al., 2011);  the precession matrix is obtained by transforming the CIP coordinates in the ICRS system into the 6790 GCRS system. In this way, the celestial reference point is determined, that is the collocation of the CIP in the NE. Using a special conversion matrix and a series of products rows per columns, the positions of the star is then determined (i.e. α and δ) in the NE, linking it to the CIP position. In summary, using the IAU 2006 model, the coordinates of the star and those of the CIP are determined, finding the relative position of the former with respect to the latter (which turns to be independent of the 6795 precession phenomenon). Subsequently, using the Vondrák et al. (2011) model, the correct CIP position is calculated and, consequently, that of the star (given that its position with respect to CIP is known). It must be pointed out that, since Orion does not take into account the effects due to the nutation of the terrestrial axis and the aberration of stellar radiation, the position of each star given in output by this subroutine is the so-called “mean place of the date”. This fact, however, does not compromise the 6800 meaningfulness of the results since such effects modify stellar coordinates only in negligible quantities (on the order of few tens of arcseconds  Urban & Seidelmann, 2013). 7. Comparison between the analyzed programs and Orion

Unlike Orion, the commercial programs have already stored in them all the stellar data relative to the J2000 epoch, necessary to determine the star position in different epochs. Some of the initial data differ 6805 slightly from those of SIMBAD, since the source from which they are obtained is different. For each star, some programs give, in addition to the above defined mean place of date, also the apparent coordinates, which take into account variations of the stellar position due to nutation, aberration and effects of parallax. In these cases the comparison was performed between the data taken from Orion and the mean places of date taken from each commercial program. Instead, for those software products like SkyMap Pro, Star 6810 Calc and TheSky that provide only the apparent coordinates, the investigation was necessarily made by comparing these kind of outputs with the mean place of date given by Orion. We note, however, that the mismatch between the package under test and the reference data from Orion, due to this non-strict

210 comparison, could lead to spurious disagreements of up to 30 arcseconds or so (Urban & Seidelmann, 2013), to which nutation contributed about 10 arcseconds and the rest is from aberration (Urban & 6815 Seidelmann, 2013). This is well below naked-eye resolution and so unimportant for our application. Moreover, while Orion requires the insertion of the Julian epoch (for example, J-2499.000 corresponding to 12 am of 1 January of the year 2500 BC of the Julian calendar), some commercial products ask for the insertion of the exact day and hour in which one wishes to determine the position of the star, thus using the date as given in the Gregorian calendar. It is, at any rate, easy to obtain the corresponding Julian date 6820 using one of many conversion routines available on the web. It must be evident that SkyMap Pro and TheSky only allow users to obtain the stellar coordinates back until 4700 BC: consequently, the comparisons for these programs were carried out only back to this date. The comparison with the commercial astronomical programs was carried out by comparing the δ values of the stars of the sample, as obtained by the programs, and the one derived by Orion. The deviations in δ 6825 among the output of the commercial programs and that of Orion for all the 24 stars were then calculated. The results so obtained are reported in Tab. 2, 3 and 4.

8. Discussion of results: analysis of deviations in the chosen epochs

6830 To have a more general idea of the deviation between the output of Orion and those of the seven analyzed commercial programs, we carried out cross-referenced comparisons among the data obtained, in order to understand the reason of the differences reported in Tab. 2, 3 and 4. As a comparison parameter, we chose the resolving power of the human eye that we conservatively fixed at 0.05° (equal to three arcmin), as discussed in Section 1. It is possible to consider the programs reliable 6835 as long as they provide discrepancies of stellar position acceptable in comparison to a routine that is able to describe correctly the proper motion of the stars and precession (Orion), i.e. until they give discrepancies less than the resolving power of the human eye. For this purpose, three classes were chosen according to the value of x =|Δδ|, as follows:

6840  x ≤ 0.05° : if the differences in δ observed between the Orion output and that obtained from the commercial programs are below this value (about three arcmin), being smaller than the resolving power of the human eye in favorable conditions, these can be considered negligible;  0.05° < x ≤ 0.08° : if the differences are included within this range, they begin to be important and can give erroneous information on the position of the star; 6845  x > 0.08° : beyond this value (about five arcmin), the deviations are noteworthy and, consequently, the information on the position of the star given by the program is not precise or reliable. In Fig. 1 are reported the deviations in δ observed in the five epochs processed for the seven analyzed commercial programs, sorted according to the above three defined classes. 6850 For the first epoch considered (2500 BC – see Fig. 1a and Tab. 2), only one of the seven programs analyzed, Stellarium, present a considerable group of stars (5, equal to approximately 21% of the sample) in which deviations in δ fall within the third class. In other words, the output diverges from that of Orion by a value that far exceeds the resolving power of the human eye. As evident in Tab. 2, for Arcturus, 6855 Dubhe, Sirius, Toliman and Vega, there are differences above 0.1° with respect to Orion output, with also Acrux and Thuban included in the intermediate class. All these stars have a common feature: they are “fast” stars, that is, they are animated by a high proper motion. This characteristic is decisive to understand the reason for why these deviations were obtained, as we will clarify in Section 9.2. For the other six programs, on the other hand, at maximum only one case beyond the reference limit is registered 6860 (Toliman).

211 Table 2: Deviations Δδ between the declinations of Orion and those of the commercial programs, obtained for all the stars of the sample, for the gregorian epochs 2500 BC and 4500 BC. Note that the reported values are rounded to two decimal places.

2500 BC 4500 BC Stars ORION CDC CS SC ST SM SNP TS ORION CDC CS SC ST SM SNP TS δ Δδ Δδ Δδ Δδ Δδ Δδ Δδ δ Δδ Δδ Δδ Δδ Δδ Δδ Δδ (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) Achernar (α Eri) -81.12 0.00 0.02 0.01 -0.02 0.00 0.00 0.00 -79.91 0.00 0.03 -0.01 0.02 -0.04 0.00 0.00 Acrux (α Cru) -39.89 0.00 0.00 -0.01 0.06 -0.01 -0.01 0.01 -32.75 -0.01 0.02 0.00 0.08 0.00 0.00 0.01 Aldebaran (α Tau) -2.25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -13.40 0.00 0.02 0.00 -0.01 0.01 0.00 0.00 Alioth (ε Uma) 77.60 0.00 -0.03 0.00 0.04 0.00 0.00 0.00 73.75 0.00 -0.05 0.00 0.02 0.03 0.00 0.01 Alkaid (η Uma) 73.53 0.00 0.01 0.01 -0.03 0.00 0.00 0.00 78.33 0.00 0.09 0.00 -0.03 0.03 0.00 0.00 Alnilam (ε Ori) -14.76 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -25.53 0.00 0.02 0.00 0.00 0.02 0.00 0.00 Alnitak (ζ Ori) -15.06 0.02 0.00 -0.01 0.00 0.00 0.00 0.00 -25.75 0.00 0.03 -0.01 0.00 0.03 0.00 0.00 Altair (α Aql) 8.50 0.00 0.01 0.01 0.00 0.00 0.01 0.00 15.55 0.00 -0.03 0.00 0.00 -0.03 0.00 0.00 Antares (α Sco) -6.71 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 4.48 0.00 -0.01 0.01 -0.01 -0.01 0.00 0.00 Arcturus (α Boo) 45.71 0.00 -0.01 0.00 -0.32 0.00 -0.01 0.00 55.92 0.00 0.00 0.00 -0.46 0.01 -0.01 0.01 Betelgeuse (α Ori) -5.06 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 -15.78 0.00 0.02 -0.01 0.00 0.02 0.00 0.00 Canopus (α Car) -55.42 0.00 -0.01 0.00 0.00 0.00 0.00 0.01 -59.68 0.00 0.02 0.00 0.00 0.03 0.00 0.00 Capella (α Aur) 28.69 0.00 -0.01 0.00 0.02 0.00 0.00 0.00 17.66 0.00 0.01 0.01 0.02 0.01 0.01 0.01 Deneb (α Cyg) 36.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 37.43 0.00 -0.03 0.00 0.00 -0.03 0.01 0.00 Dubhe (α UMa) 71.07 0.00 0.07 -0.01 0.15 0.00 -0.03 0.00 61.67 0.00 0.14 0.00 0.15 0.02 0.00 0.00 Hadar (β Cen) -36.12 0.00 -0.01 0.00 0.04 -0.01 0.00 0.01 -27.19 0.00 0.00 0.00 0.07 0.00 0.00 0.01 Mintaka (δ Ori) -14.27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -25.12 0.00 0.02 0.00 0.00 0.03 0.00 0.00 Procyon (α CMi) 4.55 0.00 0.01 0.01 -0.01 0.00 -0.01 0.01 -3.01 0.00 0.03 0.01 -0.02 0.03 -0.01 0.01 Rigel (β Ori) -23.19 0.00 0.00 0.00 0.00 0.00 0.00 0.01 -34.10 0.00 0.02 -0.01 0.00 0.02 0.00 0.00 Sirius (α CMa) -20.83 0.00 0.01 0.00 -0.13 0.01 -0.02 0.02 -28.61 0.00 0.03 -0.01 -0.23 0.04 -0.04 0.03 Spica (α Vir) 12.89 0.00 0.00 0.00 -0.01 0.00 0.00 0.00 20.13 0.00 0.02 0.01 -0.01 0.01 0.00 0.00 Thuban (α Dra) 88.32 0.00 -0.02 0.01 -0.07 -0.05 0.00 0.00 80.42 0.00 0.05 -0.01 0.08 0.10 0.00 0.00 Toliman (α Cen) -37.70 0.01 0.01 0.33 3.48 0.00 0.06 0.18 -27.79 0.02 0.46 0.43 5.32 0.00 0.04 0.04 Vega (α Lyr) 42.67 0.00 0.03 0.00 0.13 0.00 0.01 0.00 49.26 0.00 0.02 0.00 0.21 -0.03 0.01 0.00

212 Table 3: Same as Tab. 2 but for the gregorian epochs 6000 BC and 8000 BC. Note that SkyMap Pro and TheSky do not give results for these epochs.

6000 BC 8000 BC Stars ORION CDC CS SC ST SNP ORION CDC CS SC ST SNP δ Δδ Δδ Δδ Δδ Δδ δ Δδ Δδ Δδ Δδ Δδ (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) (°) Achernar (α Eri) -71.90 0.00 -0.03 -0.02 0.04 0.00 -60.56 0.00 -0.28 -0.02 0.05 0.03 Acrux (α Cru) -29.41 -0.01 0.05 -0.01 0.10 0.03 -28.06 -0.01 0.24 -0.02 0.11 0.05 Aldebaran (α Tau) -20.99 0.00 0.05 0.01 -0.01 -0.02 -28.16 0.00 0.04 0.02 -0.01 -0.04 Alioth (ε UMa) 65.88 0.00 0.00 -0.01 0.01 0.00 54.49 0.00 0.26 -0.01 0.01 -0.03 Alkaid (η UMa) 73.47 0.00 0.21 -0.01 -0.02 0.01 62.62 0.00 0.57 -0.02 -0.01 -0.02 Alnilam (ε Ori) -34.02 0.00 0.09 0.00 0.00 -0.01 -44.03 0.00 0.20 -0.01 0.00 -0.05 Alnitak (ζ Ori) -34.25 0.00 0.09 -0.01 0.00 -0.01 -44.42 0.00 0.22 -0.01 0.00 -0.05 Altair (α Aql) 22.87 0.00 -0.12 0.00 0.00 -0.01 34.05 0.00 -0.45 0.00 -0.01 0.01 Antares (α Sco) 11.92 0.00 -0.04 0.00 -0.01 0.03 18.85 0.00 0.00 0.01 -0.01 0.06 Arcturus (α Boo) 60.04 0.00 0.08 -0.02 -0.52 0.02 58.31 0.00 0.54 -0.04 -0.48 0.01 Betelgeuse (α Ori) -24.29 0.00 0.08 -0.01 0.00 -0.01 -34.47 0.00 0.22 -0.01 0.00 -0.05 Canopus (α Car) -63.76 0.00 0.09 -0.01 -0.01 0.03 -69.83 0.00 0.38 -0.01 -0.02 0.04 Capella (α Aur) 10.14 0.00 0.05 0.02 0.01 -0.01 2.53 0.00 0.10 0.03 -0.01 -0.03 Deneb (α Cyg) 40.37 0.00 -0.11 0.01 0.01 -0.03 46.76 0.00 -0.45 0.01 0.01 -0.03 Dubhe (α UMa) 53.24 0.00 0.24 0.01 0.18 -0.01 42.42 0.00 0.50 0.00 0.25 -0.05 Hadar (β Cen) -22.39 0.00 0.02 0.00 0.08 0.03 -19.20 0.00 0.16 0.00 0.08 0.05 Mintaka (δ Ori) -33.60 0.00 0.08 0.00 0.00 -0.01 -43.45 0.00 0.19 0.00 0.00 -0.05 Procyon (α CMi) -10.42 0.00 0.12 0.00 -0.03 -0.02 -21.07 0.00 0.40 -0.01 -0.04 -0.06 Rigel (β Ori) -42.56 0.00 0.08 0.00 0.00 -0.02 -52.18 0.00 0.16 0.00 0.00 -0.05 Sirius (α CMa) -35.98 0.00 0.11 -0.03 -0.30 -0.04 -46.61 0.00 0.39 -0.06 -0.42 -0.10 Spica (α Vir) 22.37 0.00 0.06 0.00 -0.02 0.03 20.35 0.00 0.37 -0.01 -0.03 0.04 Thuban (α Dra) 72.22 0.00 0.12 -0.01 0.09 -0.02 62.06 0.00 0.36 -0.01 0.08 -0.04 Toliman (α Cen) -21.61 0.02 1.02 0.42 6.68 -0.03 -15.82 0.02 2.10 0.22 8.19 -0.30 Vega (α Lyr) 55.74 0.00 -0.05 0.01 0.27 -0.01 65.93 0.00 -0.39 0.01 0.34 -0.01

213 6870 Table 4: Same as Tab. 3 but for the gregorian epoch 10000 BC.

10000 BC Stars ORION CDC CS SC ST SNP δ Δδ Δδ Δδ Δδ Δδ (°) (°) (°) (°) (°) (°) Achernar (α Eri) -50.25 0.00 -0.86 0.00 0.05 -0.24 Acrux (α Cru) -30.37 -0.01 0.84 -0.05 0.10 0.09 Aldebaran (α Tau) -30.01 0.00 -0.44 0.05 0.00 0.01 Alioth (ε UMa) 44.07 0.00 0.83 -0.02 0.04 0.24 Alkaid (η UMa) 51.56 0.00 1.31 -0.04 -0.01 0.26 Alnilam (ε Ori) -49.68 0.00 -0.05 0.02 0.00 0.07 Alnitak (ζ Ori) -50.38 0.00 0.00 0.01 0.01 0.08 Altair (α Aql) 44.96 0.00 -1.03 0.02 0.00 -0.25 Antares (α Sco) 20.75 0.00 0.46 -0.02 -0.01 0.01 Arcturus (α Boo) 50.26 0.00 1.66 -0.08 -0.45 0.23 Betelgeuse (α Ori) -40.80 0.00 0.10 0.01 0.00 0.09 Canopus (α Car) -75.51 0.00 0.81 -0.04 -0.02 0.10 Capella (α Aur) -1.00 0.00 -0.10 0.07 -0.04 0.08 Deneb (α Cyg) 55.46 0.00 -1.34 0.05 0.01 -0.23 Dubhe (α UMa) 33.38 0.00 0.92 -0.02 0.38 0.15 Hadar (β Cen) -20.05 0.00 0.69 -0.02 0.07 0.05 Mintaka (δ Ori) -48.80 0.00 -0.08 0.02 0.01 0.06 Procyon (α CMi) -30.58 -0.01 0.84 -0.01 -0.04 0.18 Rigel (β Ori) -56.55 0.00 -0.28 0.02 0.01 0.02 Sirius (α CMa) -56.05 0.00 0.74 -0.08 -0.52 0.10 Spica (α Vir) 13.29 0.00 1.30 -0.04 -0.03 0.21 Thuban (α Dra) 53.31 0.00 0.84 -0.01 0.06 0.20 Toliman (α Cen) -13.51 0.01 3.64 -0.27 8.97 -0.90 Vega (α Lyr) 77.17 0.00 -1.25 0.03 0.40 -0.29

214

d 6875

6880

6885

6890 Figure 1: Distribution of deviations in declination for the 24 stars of the sample, with respect to Orion output, observed for the seven commercial programs compared at the five epochs selected: a) 2500 BC; b) 4500 BC; c) 6000 BC; d) 8000 BC; e) 10000 BC.

At 4500 BC (Fig. 1b and Tab. 2), the situation remains more or less the same, except for one case. In fact, 6895 for CyberSky there is an increase in the number of cases of deviation above 0.08°, since also Alkaid and Dubhe enter the third group together with Toliman. For SkyMap Pro, Thuban enters in the third class. At 6000 BC (Fig. 1c and Tab. 3), the situation is further clarified. While the results of Cartes du Ciel, Star Calc and Starry Night Pro continue to be in the first class for all the chosen stars (with the exception of Toliman for Star Calc), CyberSky presents a remarkable percentage of stars outside this class. In fact, the 6900 number of sampled stars for which the deviations are higher than the reference limit, increases from 3 in 4500 BC to 14 for this date, with another 5 stars which are found in the second class. For the fourth epoch analyzed, 8000 BC (Fig. 1d and Tab. 3), even with Starry Night Pro there are deviations in δ beyond 0.08°. For Toliman and Sirius there are significant differences with the reference value obtained by means of Orion. The reason could be due to the way in which the former program

215 6905 evaluates the proper motion of the star. Stellarium, instead, presents 3 stars (Achernar, Hadar and Thuban) that are in the intermediate class, while for other 6, deviations above the reference limit of 0.08° are registered. Even with CyberSky, one can observe a remarkable increase in stars that fall in the third class. Only for Aldebaran and Antares there are no appreciable deviations, while for the other 22 stars the disagreement is beyond 0.08°. By contrast, Cartes du Ciel and Star Calc continue to have an optimal 6910 agreement with data taken from Orion. For the last analyzed date, 10000 BC (Fig. 1e), the situation is as follows. Cartes du Ciel gives for all the stars of the sample deviations with respect to Orion below the limit of 0.05°. Star Calc presents for 19 stars of the sample, negligible deviations when compared to Orion. For 3 stars we observe differences greater than the resolving power of human eye that fall in the intermediate class and only 2 stars (Sirius 6915 and Toliman) in the third category. Stellarium gives for 6 stars deviations that exceed the reference limit, reaching 0.5° in the case of Sirius and the biggest deviation registered (9°) in the case of Toliman, and only 2 cases (Hadar and Thuban) in the intermediate class. CyberSky gives for 22 of the 24 sampled stars divergences beyond 0.08° in δ, with only Alnilam and Alnitak showing negligible deviations. For 7 stars (Alkaid, Altair, Arcturus, Deneb, Spica, Toliman and Vega) the divergences in δ are beyond one degree. 6920 Starry Night Pro is the program that presents the most notable differences with respect to the previous epoch. In fact, it goes from 8 cases beyond the limit of 0.05° at 8000 BC to 21 cases in 10000 BC. It must be noticed, at any rate, that the deviations are never beyond one degree, all showing to be below 0.3° for the whole sample processed, with the exception of Toliman, which rises to 1°. In summary, the agreement between the data obtained with Orion and with the other analyzed commercial 6925 products is satisfactory for not too remote epochs in the past, decreasing in a significant way after 6000 BC. Cartes du Ciel is the program which best suits itself to correctly evaluate the effects, on stellar position, of proper motion, as well as precession of the equinoxes. Its percentage of agreement (POA, that is the fractional number of cases for which x ≤ 0.05°) is always equal to 100% in the analyzed sample. CyberSky, on the other hand, shows a poor agreement with Orion starting from 6000 BC. The POA 6930 reaches about 21% for this epoch (that is, only for 5 stars of the sample there are negligible deviations in δ with respect to the reference values) showing a larger disagreement (only about 8%, that is 2 stars) in the two most remote analyzed epochs. This is most likely due to the way in which the program evaluates the precession and, also, proper motions. The cases of the other programs are between the previous two. In particular, the case of Starry Night Pro 6935 is interesting. The POA with Orion is optimal for the first three epochs chosen (ranging between 96% and 100%), relatively good for 8000 BC (about 67%), and low for the last date chosen for examination, in which only 3 stars show negligible deviations. The reason of these observed discrepancies may be found in the development used by the program to describe the precessional phenomenon, which seems to be in the short-term, as that of the proper motion. Stellarium presents a constant POA for all the epochs 6940 investigated (on average about 68%): cause of the discrepancies is the way by which the software evaluates proper motions, especially for fast stars (see Section 9.2). In Tab. 5 we summarize the situation.

Table 5: Percentage of agreement (POA, see text) for δ values between Orion and the analyzed commercial programs for the five epochs tested. The chosen reference threshold is equal to 0.05°. EPOCH (BC) 2500 4500 6000 8000 10000 CDC 100.0 100.0 100.0 100.0 100.0 CS 95.8 83.3 20.8 8.3 8.3 SC 95.8 95.8 95.8 91.7 79.2 ST 70.8 66.7 66.7 62.5 66.7 SM 100.0 95.8 - - - SNP 95.8 100.0 100.0 66.7 12.5 TS 95.8 100.0 - - -

216 6945 9. Causes of the discrepancies with Orion

What was outlined in the previous Section requires further analyses to better understand the reason for which the registered differences are in some cases very significant. This will be done in this Section. In particular, the effects of the treatment of precession and proper motions, as well as the influence of the position of the star will be discussed. In addition, we will treat in detail the special case of Toliman and 6950 the importance of the use of updated releases of the various software packages.

9.1 Impact upon stellar positioning due to reproduction of precession The largest factor that influences the determination of the position in the sky of a star in remote epochs is, without doubt, the parameterization method used to approximate precession. In Section 3 the importance of this aspect has been already underlined, addressing the problem relative to the expression (polynomial 6955 or periodical) with which the phenomenon must be evaluated. The evident deviations in δ between the output of Orion (which uses Eq. 8) and those of the commercial programs (some of which use other approaches), as seen in Section 8, are illustrative of the fact that the use of an inadequate parameterization could lead to contrasting evaluations of the position of a star. Over the course of the time, with the advancement of computational progress, many different 6960 approximation methods for reproducing the precession have been proposed. With a modified version of the program Orion, it has been possible to make a comparison between the trends proposed and discussed in Section 3: i.e. IAU 1976, IAU 2000, IAU 2006 and Vondrák et al., (2011). For each of these parametrizations, the declination δ is analyzed from 25000 BC to AD 25000, for two stars of the sample: Toliman (Fig. 2) and Mintaka (Fig. 3). The chosen pair represent two opposite cases. The first is 6965 characterized by the highest proper motion (see Section 9.4 for details) among the analyzed stars, while the second has the lowest values (μα = 0.64 mas/yr and μδ = -0.69 mas/yr).

Fig. 2 and Fig. 3 show how the four above reported methods give δ values, for the two stars, that are nearly in agreement for not too remote past epochs, but then present noteworthy differences going further 6970 back in time. In detail, up to 6000 BC, the deviations from the Vondrák et at., (2011) approximation given by the IAU 1976 and IAU 2006 developments are below the resolving power of human eye and, consequently, negligible. Going further back into the past, the deviations with respect to the Vondrák et al. (2011) model implemented in Orion start to become significant also for the other two models. In fact, the differences increase, for IAU 1976 model, from 0.2° at 8000 BC up to 1.5°-1.8° at 12000 BC, while the 6975 discrepancies for IAU 2006 model range from 0.1° at 8000 BC to 0.6° at 12000 BC. In the case of the IAU 2000 model, we notice deviations over the limit of 0.05° from Vondrák et al. (2011) beyond about 4000 BC. In fact, this model presents discrepancies, for both stars, on the order of 0.2° at this date, growing up to 1.1°- 1.3° at 8000 BC and reaching about 2° and over at 12000 BC. The Vondrák et al. (2011) model comes to be the most reliable one for accurately taking into account the 6980 precession when trying to determine the position of the stars in very remote past. In fact, this is the only model that is able to correctly reproduce the periodicity of the precessional phenomenon. As a consequence, from the analysis previously carried out, we can affirm that the other three approximations tested, IAU 1976, IAU 2000 and IAU 2006 are not sufficiently accurate to reproduce the precession, thus affecting negatively the evaluations of stellar positioning in the remote past. 6985 One can thus deduce how most of the deviations reported in Section 8 between Orion and the other commercial programs are largely due to the different way by which these products evaluate the precession of the equinoxes, according to the development they implement. In fact, the differences are on the order of those just shown between Vondrák et al. (2011) and the IAU models. Such a conclusion can surely be applied to CyberSky, whose discrepancies with respect to Orion output are caused, primarily, by the way 6990 in which it approximates precession, taking into account very likely the short-term effects and not the long term ones, as in that of Vondrák et al. (2011). Cartes du Ciel, by contrast, does not present notable deviations even in very remote epochs in the, i.e. the program uses an adequate evaluation model of

217 6995 Figure 2: Trend of the declination of Toliman in function of time as generated by the four developments processed to reproduce the precession of equinoxes. The initial parameters used here are the average ones, both in position and proper motions, of this stellar system (see Section 9.4) as reported by SIMBAD. The epochs denoted with a negative sign must be interpreted as BC.

218 Figure 3: Same as Fig. 2 but for the declination of Mintaka.

219 7000 precession in the long term, such as that of Vondrák et al. (2011). Also for Star Calc one can deduce similar conclusions. Probably, the observed differences are due not to the way by which precession is evaluated but may be caused by other factors like proper motions evaluation and approximations adopted (see Section 9.2) or even by the particular position occupied by the star at the epoch analyzed (see Section 9.3). For SkyMap Pro, instead, because it cannot go far into the past (only until 4700 BC), for the sample 7005 evaluated one can say that the registered deviations are due not so much to the evaluation of precession but to the proper motion approximation (see Section 9.2). On the contrary, for TheSky, although with the same temporal limitations as SkyMap, no appreciable deviations are registered (apart for the case of Toliman at 2500 BC): the programs correctly approximates precession. In the case of Starry Night Pro, the differences with respect to Orion output are due to the way by which precession is considered and, at 7010 the same time, because they are not so high, to the approximation used to reproduce proper motions effects. Finally, in the case of Stellarium, the observed deviations are mainly due to the way by which the program treats proper motions rather than precession. In fact, as we will justify in Section 9.2, its behaviour clearly emerges by comparing the outputs obtained for stars with different proper motions (low and high). 7015 9.2 The influence of proper motion upon position of stars The other important factor that we examined to complete the comparison among astronomical software programs is the influence that the approximation of the proper motion has on the determination of the position of the stars across the time. Let us consider a subset of seven stars chosen according to the value of their respective proper motion μ α 7020 in right ascension and μδ in declination. High proper motion stars are Toliman (see next subSection), Sirius (μα = -546.01 mas/yr, μδ = -1223.07 mas/yr) and Arcturus (μα = -1093.39 mas/yr, μδ = -2000.06 mas/ yr). Intermediate proper motion stars are Vega (μα = -200.94 mas/yr, μδ = 286.23 mas/yr) and Dubhe (μα = - 134.11 mas/yr, μδ = -34.70 mas/yr). Low proper motion stars are Deneb (μα = 2.01mas/yr, μδ = 1.85 mas/yr) and Mintaka. 7025 As evident in Tab. 2-4, the observed deviations for the two stars with high proper motion are quite relevant in the most remote epochs analyzed: they are in fact well above the resolving power of human eye. The software that presents significant differences, even at 2500 BC, is Stellarium. In the case of Sirius and Arcturus high differences are observed, on the order of 0.1° - 0.3° in 2500 BC growing up to 0.4° - 0.5° in the subsequent epochs. A similar situation has been registered for Star Calc. The registered 7030 discrepancies are not attributable to the parametrization used to reproduce the precessional phenomenon. Thus, the increase is, for both stars, due to the high proper motion of the stars, which in this case strongly influence stellar positioning. This growth is caused by the development used to approximate proper motion, in the short term and not in the long term, which amplifies the effect (especially in the remote past) for “fast” stars like the two now considered. In fact, as will be seen in the following cases, such 7035 differences are not observed for stars like Mintaka and Deneb, animated by low proper motion. Consider now the case of stars with intermediate proper motions, Dubhe and Vega. From Tab. 2-4, in the case of stars characterized by not so high proper motion, the situation is similar to the previous instance. In fact, for Dubhe, the growth of the divergences in the cases of Stellarium and CyberSky, on the order of about 0.2° - 0.4° from one epoch to the previous one (especially from 6000 BC onwards) are more due to 7040 the way proper motion is evaluated by the program rather than to precession. For Vega, by contrast, if the divergences in the case of CyberSky depend on the way it treats precession (being on the order of 0.4° - 1.2° in very remote epochs), in the case of Stellarium they seem to be determined always by the way it treats proper motion (divergences on the order of 0.1° - 0.4°). For Starry Night Pro, it can be observed discrepancies for both stars on the order of 0.1°- 0.3° for the more distant epochs, a sign that in this case 7045 there is a mixed effect between proper motion evaluation and that of precession. Finally, for Star Calc, since the divergences for very remote epochs are on the order of 0.02°– 0.03°, it can be said that these are due to the way by which the stars’ proper motion is evaluated by the program. Moving on to the final part of the analysis, by considering stars which present low proper motions, such as Mintaka and Deneb. Surely, for both stars, the reason for the high deviations registered for CyberSky is 7050 the way with which the programs evaluate precession. Indeed, since the proper motion for both stars are

220 very low, their contributions do not significantly influence the determination of stellar positioning in very remote epochs in the past. The low deviations obtained in these cases for Starry Night Pro and Stellarium, two programs that not adequately evaluates proper motions, are emblematic and representative of the conclusions now obtained. 7055 It must be pointed out that, in the previous discussion, the differences observed between commercial packages and Orion have been attributed to proper motions. This could be due, in particular, to the fact of neglecting the effects of the radial velocity. In fact, as reported in Section 2, the equations that correctly describe proper motions (that is which take into account long term effects), show the contribution due to this parameter and to the parallax (see Eq. 5). On the contrary, considering only short term effects and 7060 neglecting the contribution of both vR and π (see Eq. 2 and 3) can lead to significant deviations from the actual values of the stellar coordinates. This is the case of Stellarium (see Section 9.4). 9.3 Additional observations about stellar positioning It should be noted that the deviations caused by the different parameterizations used to reproduce precession, regardless of the effects of the proper motions, are due to the position that the star occupied 7065 on the celestial sphere at the given epoch, which could maximize the effects of precession. The latter in fact are not constant, as one might imagine, for the same epoch, regardless of the position occupied on the Celestial Sphere (Wallace, personal communication - 2017). This is suggested by the analyses of variation in δ, given by Orion, of two stars with low proper motions like Deneb and Mintaka (see Tab. 2, 3 and 4). While from 2500 BC to 4500 BC it has been registered a variation roughly equal to 1.2° in 2000 years for 7070 Deneb, in the same time interval it can be noticed a variation of approximately 11° for Mintaka. Moreover, from 4500 BC to 6000 BC (i.e. a lapse of time equal to 1500 years), the difference is on the order of about 3° for Deneb and 8.5° for Mintaka. Between 6000 BC and 8000 BC (i.e. in 2000 years), the two stars show a variation of 6.5° and 10° respectively and, finally, the difference is of 10° between 8000 BC and 10000 BC (i.e. in about 2000 years) for Deneb and 5.3° for Mintaka. 7075 These examples also indicate that the effects of the precessional phenomenon upon stellar coordinates are not constant over time. Ultimately, one may argue that, in the determination of stellar position, the way in which the approximation of precession is evaluated plays a more fundamental role compared to the estimation of proper motion, except for the case of “fast” moving stars, such as Sirius, Arcturus, and especially Toliman (see next subsection), which deeply influence, for example, the output of CyberSky 7080 and Stellarium. This is confirmed by the analysis of the trends of δ over time obtained with Orion, for stars with high proper motion like Toliman (Fig. 2) and a star with low proper motion such as Mintaka (Fig. 3). For Mintaka, proper motion components do not affect the δ trends, and thus the registered differences among the different approximations of precession are all due to the polynomial or periodic process employed to reproduce the phenomenon. On the contrary, by observing the trend of δ for 7085 Toliman, the deviations seen are noticeable because the star is characterized by high proper motion, and thus influence the behaviour of δ. 9.4 The special case of Toliman Toliman (or Rigil Kentaurus), the brightest star of the Centaurus constellation, is, among all the stars of the sample considered, the one that presents, in most of the analyzed programs, the highest deviations in δ 7090 from the results predicted by Orion. Its case needs, therefore, further discussion. This star is a system of three components, named A, B and C, with the latter, much fainter than the first two, which is invisible to the naked eye. This multiple star is the closest to Earth and, mainly for this reason, it shows the highest proper motion of the whole sample. Usually in the text, when we refer to Toliman, we intend the A component. This because most of the studied software consider, as initial 7095 parameters of this stellar system at J2000 (both in position and proper motions), values that are very closer to those of the component A. Consequently, the comparison we performed for this star between Orion and the other seven software packages follows this choice in order to compare data as homogeneous as possible. We recall, however, we do not know exactly which initial values of the stellar parameters are actually used by these programs in their calculations since, in alternative to the initial data

221 7100 of the component A, also the average position and proper motions of the system A + B can be reasonably used. Obviously this double possibility can be a further cause of discrepancy with respect to Orion output. We also recall that, for instance, we made this second choice in the reconstruction of the position of Toliman over a period of precession (see Section 9.1) where we used, as starting parameters the mean values (both in position and proper motions) of the two components A and B instead of those of the 7105 component A only. According to SIMBAD, the average values of μα and μδ for the system A and B are, respectively, -3608 mas/yr and 686 mas/yr. We preferred to use these values for the precessional analysis because the mean value of V of the star considered as a combination of the two components is coherent with the selection criteria exposed in Section 5. In any case, this choice does not influence the results obtained in the above-mentioned Section. 7110 Let us discuss the deviations observed for Toliman. From Tab. 2-4, it is immediately evident that, even in 2500 BC, the deviations in δ for this star are already above the resolving power of the human eye for four of the programs under analysis. The differences tend to increase notably going further back in time. The worst situation concerns Stellarium. Even if the program uses the same approximation for precession of Orion (Stellarium User Guide, 2017) the differences registered are very large, ranging from 3.5° and 9° 7115 about. It is difficult to understand the reason of these so large discrepancies. In any case, the program does not correctly take into account proper motion effects on stellar positioning, as reported by Stellarium User Guide (2017), which are relevant when the star investigated is very fast as Toliman. For Starry Night Pro and CyberSky the cause of the discrepancy are most likely due, respectively, to the not adequate evaluation of proper motion and, in the second case, also of precession for very remote 7120 epochs. Finally, as reported before, we can hypothesize that the large deviations registered for Toliman could be due, in addition to the causes discussed in the previous subsections, also to the different initial parameters (both in position and proper motions) adopted by the various routines. In other words, the choice of using as initial values of the stellar parameters those of the first component, or the average ones of the system A 7125 + B, can have important impact on the final results of the calculations, especially when extremely high proper motions are involved.

9.5 Use of old releases of the software programs The evidence reported in the previous Sections about the way by which the analyzed software products 7130 evaluate stellar position concerns the most recent releases of these programs. It is common to find, in the literature, papers carried out by means of not updated versions of the above-mentioned software packages. Apart from minor bugs related to graphical purposes, these old releases very often do not contain the essential last updates regarding the parameterizations of precession and the inclusion of proper motion (and, in particular, radial velocity) effects in the calculations. We will briefly show how the 7135 use of such not-updated programs could bring to relevant errors in the evaluation of star positions, especially in the remote past. Let us consider two astronomical programs recently updated: Stellarium and TheSky. In Fig. 4 we report the deviations observed, with respect to Orion output, for the five epochs analyzed and the same sample of stars, regarding the last versions of the two software products (Stellarium 0.16.2 and TheSky 10.5) and 7140 the previous ones (Stellarium 0.13.2 and TheSky 10.2). What emerges is the great improvements that both the programs gain from the old version to the last updated. In the case of Stellarium, an evident decrease of the average differences with Orion can be observed passing from version 0.13.2 to the last one 0.16.2. Even though in the last release, in all the epochs, the differences are well above the resolving power of human eye, these are much lower than the previous version of the program. In the old version the cause of 7145 the differences is the incorrect parameterization of precession, which was not that by Vondrák et al., (2011), but one which takes into account only the short-term effects. The deviations still remains appreciable also in the new release because, as evidenced in Section 9.2, the program does not adequately take into account proper motions effects on stellar positioning. At this purpose in fact, in the user guide of the program, it is claimed that the software product does not take into account radial velocity in stellar 7150 positioning evaluations, but are considered only the current shift rates of proper motions in right

222 ascension and declination (see Section 2). As a consequence, the authors warn that the results in very far epochs should be seen only as approximations (Stellarium User Guide, 2017). Also in the case of TheSky the updates installed in the new release positively influence its output. In fact, in the only two epoch analyzable, we can observe that the deviations pass from an average of about 0.5° 7155 for the old release to a negligible value of 0.01° - 0.02° for the most recent one. This happens because, in the last release, precession is adequately reproduced by means of Vondrák et al. (2011) parameterization and, in addition, the effects of proper motion on stellar position are introduced in the code. The need to apply updated versions for archaeoastronomical studies will clearly emerge in Section 10.1.

7160

7165

7170

7175

7180

7185 Figure 4: Mean deviations in δ, with respect to Orion output, for the various epoch, obtained for the last two versions of the programs Stellarium (ST 0.13.2 and ST 0.16.2) and TheSky (TS 10.2 and TS 10.5).

10. An archaeoastronomical application of stellar simulation software programs

The analysis herein presented can immediately find application by reviewing several studies about 7190 alignments towards stars proposed by various authors in the literature, aimed at explaining the disposition of some megalithic structures build up across the globe. We will present an example which will highlight how the use of programs that are not so precise in the evaluation of stellar positions can lead to misleading results for the purposes of Archaeoastronomy. In the literature there are numerous works that examine the possible orientations that some ancient monuments may present towards the brightest stars in 7195 the sky, one of the main purposes of Archaeoastronomy. The goal is to try to understand the message that the ancient civilizations wished to leave by building these constructions on the ground. In these kind of archaeoastronomical works, very frequently different simulation software programs have been used to evaluate the position of celestial objects, in order to reproduce the skies observed by ancient civilizations. The aims of these efforts were to target celestial reference objects: the Moon (Thom, 1967; 7200 Ruggles, 1985; Magli, 2009; De Lorenzis & Orofino, 2015), the Sun (Calledda & Proverbio, 2004; Magli, 2009; De Lorenzis & Orofino, 2015), the brightest stars (North, 1996; Calledda & Proverbio, 2004; Zedda & Belmonte, 2004; Magli, 2009; Bauval et al., 2011; Collins, 2013; De Lorenzis & Orofino, 2015)

223 with their heliacal risings (Lockyer, 1894; Aveni, 1972; Schaefer, 1987; Galal & Rashed, 2012). Clearly, the more accurate is the way in which the program evaluates the stellar position, the more reliable are the 7205 conclusions that can be obtained at the end of the work. At this purpose, essential is the way by which the program chosen for the study approximates the position in the remote past and how it evaluates the two phenomena which most affect the conclusions acquired: precession of the equinoxes and proper motion of the stars. The differences emerged in the present work among the various astronomical software programs imply that, depending on the simulation program used, the conclusions to which one may arrive could 7210 diverge, especially when the investigating alignments are related to archeological sites that are dated back thousands of years ago. In the following, we have briefly considered some alignments, in particular those proposed for the most ancient megalithic site in the world: Göbekli Tepe. It will be showed how, in some cases, the use of software that is not updated and/or not so precise in mapping stellar positioning at the time of presumed 7215 construction of a megalithic complex, may lead to inaccurate results. 10.1 Gӧbekli Tepe (Turkey) and the alignments towards Deneb (α Cyg) About 13 km from the Turkish city of Şanliurfa, in the southeast of Anatolia, there is the most ancient religious structure in the world, Gӧbekli Tepe. Most likely constructed during the 10th millennium BC, during the Pre-Pottery Neolithic A (9800 – 8700 BC: Dietrich, 2011), the sanctuary was built many 7220 thousands of years before Stonehenge and the Egyptian pyramids. The archeological site consists of a series of rings or enclosures (around 20). The most interesting among them are denoted by the letters A, B, C and D, according to the date of their discovery. The main characteristic linking them is that, at the center of each, there are two large monolithic T-shaped pillars, with height varying between three and six meters, surrounded by other pillars of the same shape, but lower, located around the circling barriers. 7225 In the literature, many hypotheses have been advanced to explain the orientation of the central pillars of the enclosures, which should be a sort of astronomical markers (Collins, 2013). For example, it has been proposed that the pillars reflect the disposition of the Taurus constellation, or that of Orion or of the asterism of the Pleiades. However, these, as well as other interpretations (for example Magli, 2013) had been discredited over the course of time (Collins, 2013). In particular, Collins (2013), using an in situ 7230 survey, proposed Deneb as possible celestial target of the pillars of enclosures D, E, C and B. In a recent paper, De Lorenzis & Orofino (2015) have shown that the data proposed by Collins for the rising azimuth of the star do not coincide with the epoch indicated by the author. This is because the version of Stellarium used by Collins (2013) at that time was not sufficiently precise in the reproduction of stellar positions in very remote epochs of the past, thus negatively influencing the results obtained (see 7235 Section 9.5). In fact, until version v0.14.0 (2017), Stellarium did not implement the long-time precession parameterization of Vondrák et al. (2011) – see Stellarium User Guide (2017) - but probably a polynomial one which, as observed in Section 3, is not sufficiently precise to evaluate precession especially in very remote epochs. The deviations obtained in that case are summed up in Tab. 6.

7240 Table 6: Data relative to the four central pillars of enclosures D, E, C and B of Göbekli Tepe oriented towards the setting point Deneb. In the second column, we find the orientation azimuth of the central pillars according to Collins (2013); in the third, the date of the presumed construction of the enclosures proposed by Collins (2013); in the fourth, the alternative dating proposed; in the fifth, the difference between the two previous datings. Source: De Lorenzis & Orofino (2015). AZIMUTH COLLINS YEAR COLLINS YEAR CDC Δ ENCLOSURE (°) (BC) (BC) (YEARS) D 353 9400 9590 190 E 350 9290 9463 173 C 345 8980 9156 176 B 337 8245 8409 164 7245

224 De Lorenzis & Orofino (2015) used, instead, Cartes du Ciel that, as shown in Sections 8 and 9, is the best program among the commercial software currently available to reproduce stars positions, as it is able to reproduce contemporaneously both precession and proper motions effects correctly. The differences between the two proposed datings are approximately equal to 160-200 years. Such deviations are 7250 certainly not negligible in absolute terms, even if they are not dramatically large, when compared with the very ancient age of the buildings under study (about 12000 years). Among the alternative interpretations to the one herein presented, we examined the one proposed by Magli (2013) regarding the possible dispositions of the central pillars of the enclosures D, C and B towards Sirius. Using the astronomical program Starry Night Pro, Magli (2013) obtained for these 7255 enclosures the dating reported in Tab. 7. In order to verify this hypothesis of alignment, we decided to check if the dating of the rising azimuth provided by Magli was compatible with the proposed dates. The results are reported in Tab. 7.

Table 7: Dates of the alignments towards the rising point of Sirius of the enclosures D, C and B as found by 7260 Magli and by us. t’ is the epoch at which Magli (2013) obtained, with Starry Night Pro, a rising azimuth of Sirius equal to A, the azimuth of the central pillars. A’ denotes Sirius’ azimuths at the epoch t’, according to Cartes du Ciel. t is the epoch at which, always using this program, it was possible to see Sirius rise with an azimuth equal to A. Finally, Δt is the difference between t and t’.

A t’ A’ t Δt ENCLOSURE (°) (BC) (°) (BC) (years) D 172 9100 170 9200 100 C 165 8750 164 8830 80 B 159 8300 158 8370 70 7265 As it can be seen from that table, the hypothesis proposed by Magli seems to be less precise than that obtained by us. In fact, as shown from the check carried out with Cartes Du Ciel, there is no correspondence between the dating proposed and the values of rising azimuth that Magli assumed to be accurate. This is principally due to the use of Starry Night Pro to estimate the position of Sirius. This 7270 program, as seen in Sections 8 and 9, does not accurately evaluate the effects of proper motion and precession of the equinoxes on stellar positioning in very remote epochs in the past. Also in this case, however, it must be remembered that such deviations (few hundred over thousands of years), although relevant in absolute term, are not so large when are referred to very remote epochs like those here considered. 7275 11. Conclusions In the present work we tested and compared the outputs generated by some commercially available software programs that reproduce stellar positions in very remote past epochs. In particular, we tested if the astronomical programs are able to properly evaluate the effects, upon stellar coordinates, of two important phenomena that characterize celestial mechanics and influence their long-term assessment, i.e. 7280 proper motions of the stars and the precession of the equinoxes. The inaccurate estimations of these two effects can lead to reach misleading results, especially for very remote epochs in the past. This turns out to be a great limitation when one uses these programs in the archaeoastronomical field, particularly in cases where the differences observed for a stellar parameter (for example: right ascension, declination, rising azimuth, height of culmination) exceed the resolving power of the human eye (typically 0.05°, that 7285 is three arcmin, in favorable conditions – Hermann, 1975; Gribbin & Gribbin, 1996). A supposed alignment proposed for an archeological structure oriented towards a star, according to the output of an astronomical program that poorly evaluated the two previously cited effects, could bring a researcher to presume of have finding an explanation for the disposition of the investigated archeological site. But, most likely, the data obtained with this inadequate program are not precise enough and could lead to 7290 wrong conclusions.

225 There are many examples that can be found in the literature that are illustrative of the improper use of such programs. Often the disagreement between distinct hypotheses is due to the collection of information carried on by the researchers, which turns out to be profoundly divergent (even for the same data examined) just because the programs used are different. 7295 We decided, therefore, to test the ability of some astronomical software products in the reproduction of the position of stars that populate the ancient sky and to highlight certain critical issues. More specifically, a comparison was done between the outputs generated by some stellar plotting products and Orion, a routine specifically created to carry out comparisons between commercial software products that accurately evaluate both proper motions of the star and the precession phenomenon, according to the 7300 parametrization of Vondrák et al. (2011). In detail, deviations in declination (δ) from Orion output were collected for the most popular programs, such as Cartes du Ciel, Star Calc, Starry Night Pro, Stellarium, CyberSky, SkyMap Pro and TheSky, taken as representative of the astronomical simulation programs actually available. The sample on which the programs were evaluated consists of 24 stars, the first 16 brightest stars (V ≤ 1.0) of the sky, plus others chosen for their archaeoastronomical and historical 7305 importance (see Section 5). The epochs analyzed were: 2500 BC, 4500 BC, 6000 BC, 8000 BC and 10000 BC. The obtained deviations between the reference routine Orion and the commercial programs analyzed (Tab. 2-4) showed notable deviations in δ in the various epochs that exceed the resolving power of the human eye, even 10 to 15 times this limit (see Tab. 2-4). The POA between Orion and these programs are presented in Tab. 5. 7310 As noted in Section 8 and evidenced in Tab. 5, the POA results to be satisfactory for almost all the programs up to around 4500 BC. Going further back in the past, instead, the accordance rapidly decreases due to the not adequate evaluation of the proper motion of the stars and, above all, of the precessional phenomenon. This is mainly due to the use of a short-term polynomial expression to approximate the precession of equinoxes instead of a periodic long-term approximation, like that by Vondrák et al. (2011), 7315 implemented in Orion. This leads, for very remote epochs in the past (see Section 3), to very significant deviations, a degree or more (see Sections 8 and 9). To investigate the origin of the differences observed, the principal sources of these deviations have been analyzed individually: the approximation of precession (Section 9.1) and that of the proper motions (Section 9.2) In Section 9.1, the analysis has been focused on the way by which it is possible to represent precession. 7320 The Vondrák et al. (2011) model is that best reproduces this periodic movement, and which can also respect the periodicity with which the phenomenon repeats (approximately 26000 years – see De Lorenzis, 2011). The other methods of precession taken into consideration (IAU 1976, IAU 2000 and IAU 2006), as deduced by Fig. 2 and Fig. 3, are characterized by trends that move away notably from the reference one for very remote epochs in the past. This is the principal reason of the deviations in 7325 declination observed between Orion and the commercial products: very likely, these programs use approximations like these herein analyzed which generate outputs tending to diverge from the reference output in the remote past. Next to these effects, also the contribution due to the estimation of proper motion upon stellar positioning must be considered. As expected (see Section 9.2), the fastest moving stars present even higher deviations in the furthest epochs when compared to stars with low or 7330 intermediate proper motions. This behavior can be due to the fact that only short term effects are considered in the evaluation of the proper motions, neglecting the contribution of the radial velocity and parallax in such calculations (see for example Stellarium). Among the 24 star of the chosen sample a special object is Toliman (see Section 9.4), since for this star the deviations from Orion obtained by most of the analyzed software are by far the largest in the whole 7335 sample (see Tab. 2-4). Apart from the usual causes (precession and proper motions), these deviations could be also due to the different initial parameters (both in position and proper motions) adopted by the various routines, depending of their choice of using as initial values of the stellar parameters those of component A, or the average ones of the system A + B. The evidence from this work, by investigating some of the most used astronomical software programs 7340 that reproduce the ancient skies, must be taken into consideration when using such programs for scientific purposes. The lacking precision with which some commercial programs evaluate stellar positioning in the very remote past, in fact, may lead to completely misleading conclusions, especially in the field of

226 Archaeoastronomy. In the literature, there are works in which presumed alignments are proposed for some megalithic structures dispersed around the world, but which actually were oriented and built to 7345 indicate other stars from those proposed in these hypotheses. These wrong conclusions are not always due to the archaeological or historical considerations presented to support the thesis, but to the usage of astronomical programs that do not adequately reproduce the celestial positions of the stars admired by humans in the past. From this study, the following results for each program emerged: 7350  Cartes du Ciel is, among the seven software products here compared, the program that presents the best POA with respect to Orion data. This program correctly calculates stellar position even for very remote past epochs;  CyberSky presents the highest deviations from Orion, already at 6000 BC, with POA progressively deteriorating with time. The reason for why this happens is due to the evaluation of 7355 both proper motion and precession;  Star Calc gives outputs that are in accordance with that of Orion for all sampled stars, except in 10000 BC. The differences observed are most likely due to the way in which the program treats proper motions;  SkyMap Pro determines stellar positions until 4700 BC. Only for two stars we observed 7360 deviations beyond the resolving power of human eye at this date. No definitive conclusion can be drawn regarding the way in which the program approximates precession, even if it can be said that it adequately determine stellar positions in not so far epochs;  Stellarium gives outputs that are in a moderate POA (on average about 67%) with those of Orion. Even though, the program presents very large deviations for stars with high proper motions (see 7365 the case of Toliman) and, also, for intermediate ones (see the case of Dubhe) already at 2500 BC (see Tab. 2). The reason is the inadequate evaluation of proper motions, principally caused by the exclusion of the radial velocity contribution on the equations used to reproduce these effects (see Sections 2);  Starry Night Pro presents a very good agreement with Orion up to 6000 BC, then the accordance 7370 deeply deteriorates for remote epochs. The reason for these differences is due to the approximation used to reproduce precession, mixed with an incorrect evaluation of proper motion effects;  TheSky adequately reproduces precession and proper motion effects upon stellar positions in the two epochs analyzable, with the only exception of Toliman in 2500 BC. 7375 Summarizing, the outputs of the analyzed astronomical programs come to be reliable enough in relatively recent epochs (back to around 4500 BC), even if, for all of the software, the reliability progressively decreases in more remote epochs, mainly due to the inaccurate parameterization of precession (see Tab. 5). Thus, if the epochs to be investigated are not too remote (in the future or past), using any of those 7380 herein presented programs is equivalent (exceptions made for those which poorly evaluate proper motion, like CyberSky and Stellarium for very fast and moderately fast stars  see Section 9.2). However, if one needs to go further back in time, the only truly reliable programs are those that, like Cartes du Ciel, correctly evaluate both proper motion and precession effects.

7385 As a possible application of the present work, in Section 10, we have presented a brief discussion regarding the case of Gӧbekli Tepe, Turkey, the most ancient megalithic site in the world. A few alignment hypotheses have been advanced over the years by several authors to explain the disposition of some T-shaped pillars that characterize the enclosures present in the plan and that were rapidly examined there. Many authors, for their investigations, used different astronomical software programs to reproduce 7390 the ancient sky observed by the ancient populations of Anatolia. Collins (2013) for example, using Stellarium (an old release of this software that did not implement the Vondrák et al. (2011) parameterization for precession – see Sections 9.5 and 10.1), has proposed certain alignments of some pillars towards Deneb that seem not to be compatible with some datings (see De Lorenzis & Orofino, 2015). Magli (2013), by using Starry Night Pro, claimed instead that these buildings were oriented

227 7395 towards Sirius in epochs which, as seen in Section 10.1, differ from those obtained in the present work with Orion. The emerged differences on the date of the alignments (of about 160-200 years with respect Collins’ estimations and of 70-100 years with respect Magli’s calculations, see Tab. 6) are certainly not large when compared with the very ancient age of the monument considered (about 12000 years), but are indisputably relevant in absolute terms. 7400 In conclusion, to verify and study the possible alignments that some ancient monuments may present towards some specific celestial targets for archaeoastronomical (and other) purposes, it must be used an updated astronomical software that is able to take into account, correctly and simultaneously, both precession and proper motion effects. Actually, the most appropriate commercial software available that best reproduce stellar positions over the time is Cartes du Ciel as demonstrated in this paper. 7405 Acknowledgements The authors warmly thank to Patrick Wallace of STFC Rutherford Appleton Laboratory, UK for having specially written the Orion program used in this investigation. Vincenzo Orofino acknowledges the TAsP and Euclid INFN projects. 7410

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