University of Nevada, Reno

Analysis of the Mars Northern Seasonal Polar Cap Asymmetry in Conjunction with

Recession

A thesis submitted in partial fulfillment of the requirements for the degree of

Bachelor of Science in Geophysics and the Honors Program

By

Victoria Auerbach

Dr. Wendy Calvin, Thesis Advisor

May, 2020 UNIVERSITY OF NEVADA THE HONORS PROGRAM RENO

We recommend that the thesis prepared under our supervision by

Victoria Auerbach

entitled

Analysis of the Mars Northern Seasonal Polar Cap Asymmetry in Conjunction with

Recession

be accepted in partial fulfillment of the requirements for the degree of

BACHELOR OF SCIENCE, GEOPHYSICS

______Wendy Calvin, Ph.D., Thesis Advisor

______Matthew Means, P.S., Director, Honors Program

May, 2020 i

Abstract

Mars’ seasonal polar caps undergo a constant cycling throughout a single Martian year. These processes are dynamic and important aspects that showcase interactions between Mars’ weather, atmosphere, and surface activity. The rate at which CO2 sublimates from the seasonal ice sheet and into the atmosphere has been seen to remain fairly consistent between a variety of Mars years through the creation of an inter-annual climatological model. The cap itself, however, has been observed to retreat in an asymmetric fashion. We plan to utilize Mars topography data collected from the Mars

Orbiter Laser Altimeter in order to find a link between the observed quicker or slower recession of the seasonal CO2 cap and the local elevation.

Acknowledgements

First and foremost, I would like to Dr. Wendy Calvin for her incredible guidance throughout my undergraduate career. This project would not have existed without her.

Thank you for inspiring me and making my dreams become reality.

Thank you to the Honors Program for allowing me to create this work as one of my first published scientific writings and for guidance provided throughout my undergraduate career.

Thank you to the Undergraduate Research Office for funding through the Honors

Undergraduate Research Award (HURA).

Finally, thank you to the many inspiring professors I have had the pleasure of learning from throughout my time as an undergraduate, and thank you to the University of Nevada, Reno for inspiring me to work hard and always continue learning. ii

Table of Contents Abstract ...... i Acknowledgements ...... i List of Figures ...... iii Lists and Tables ...... iv Introduction ...... 1 Literature Review ...... 6 Phase I – Determining the Inter-annual Recession Rate for MY 31-34 ...... 11 1. Determining Recession Rate ...... 11 2. Comparison of Techniques ...... 19 3. Upon Further Inspection ...... 21 Methodology ...... 23 Tie Point and MATLAB Compilation Procedure ...... 23 Determining How to Section the ROIs ...... 25 Sectioning the ROIs ...... 29 Results ...... 30 Discussion and Conclusions ...... 42 Interpretations ...... 42 Sources of Error ...... 44 Future Work ...... 46 References ...... 48 Appendix A ...... 51

iii

List of Figures

Figure 1: MY 34 Recession Images ...... 15 Figure 2: Code Used to Translate ROI Data into Average Latitude ...... 16 Figure 3: ROI Sketch ...... 17 Figure 4: Recession Rates ...... 18 Figure 5: Climatological Model ...... 20 Figure 6: Longitude Separation ...... 26 Figure 7: Mars Latitude and Longitude Orientations ...... 28 Figure 8: MY 31, Ls 55...... 32 Figure 9: MY 31, Ls 60...... 33 Figure 10: MY 31, Ls 65...... 34 Figure 11: MY 31, Ls 70...... 35 Figure 12: MY 31, Ls 75...... 36 Figure 13: MY 31, Ls 80...... 37 Figure 14: Ls 55 Histogram ...... 38 Figure 15: Ls 60 Histogram ...... 39 Figure 16: Ls 65 Histogram ...... 39 Figure 17: Ls 70 Histogram ...... 40 Figure 18: Ls 75 Histogram ...... 40 Figure 19: Ls 80 Histogram ...... 41 Figure 20: Altitude vs. Temperature Comparison ...... 43 Figure 21: Ls 55 Section 1 Histogram ...... 51 Figure 22: Ls 55 Section 2 Histogram ...... 51 Figure 23: Ls 55 Section 3 Histogram ...... 51 Figure 24: Ls 60 Section 1 Histogram ...... 52 Figure 25: Ls 60 Section 2 Histogram ...... 52 Figure 26: Ls 60 Section 3 Histogram ...... 52 Figure 27: Ls 65 Section 1 Histogram ...... 53 Figure 28: Ls 65 Section 2 Histogram ...... 53 Figure 29: Ls 65 Section 3 Histogram ...... 53 Figure 30: Ls 70 Section 1 Histogram ...... 54 Figure 31: Ls 70 Section 2 Histogram ...... 54 Figure 32: Ls 70 Section 3 Histogram ...... 54 Figure 33: Ls 75 Section 1 Histogram ...... 55 Figure 34: Ls 75 Section 2 Histogram ...... 55 Figure 35: Ls 75 Section 3 Histogram ...... 55 Figure 36: Ls 80 Section 1 Histogram ...... 56 Figure 37: Ls 80 Section 2 Histogram ...... 56 Figure 38: Ls 80 Section 3 Histogram ...... 56

iv

Lists and Tables

List 1: Ls of images observed for each MY in Phase I…………………………………13 Table 1: Elevation data results………………………………………………………….31

1

Introduction

Fascination with planetary bodies and luminescent stars has persisted for centuries. Humanity’s curiosity for what lies past Earth’s confines has allowed for the development of innovative technologies and methods for understanding planetary processes that were once deemed outside of our grasp. Our interest in other planets goes far past our own solar system; however, we must begin our exploration somewhere.

Apart from Earth, Mars is one of the most studied planets in our solar system. Mars has an extremely thin atmosphere (about 1% of Earth’s), a rocky surface composed of basalt

(an igneous rock commonly seen on Earth’s surface), and conditions that make visual and physical observation of the planet’s surface manageable. Mars, having numerous similarities to Earth in size, tilt, and composition, proves an exceptional place to start.

Mars is currently under constant observation through various spacecrafts and rovers. Mars’ first up-close image was taken by Mariner 4 in 1965 (Williams and

Friedlander, 2015). Our understanding of the planet has consistently increased as we moved into the 21st century, allowing the number of studies and observations to grow exponentially. Multiple spacecrafts, including Mars Odyssey and the Mars

Reconnaissance Orbiter (MRO), are still active, and the latter is the source of data utilized in this study. These spacecrafts are vital in visually and analytically observing the planet’s polar caps. The north and south ice caps on Mars are the third and fourth largest ice sheets in the solar system, respectively. Mars presently has an obliquity, or axial tilt, of about 25°, very comparable to Earth’s tilt of 23.5°. This tilt allows the planet’s northern and southern hemispheres to have alternating summer/winter and fall/spring 2 seasons – meaning that when the northern hemisphere is experiencing summer, the southern hemisphere is in winter – in the same way we see the four seasons on Earth. The change in season allows for the growth and recession of the CO2 ice caps, described as

“seasonal” caps, in both the north and south. We focus primarily on the recession of the northern seasonal cap in this thesis. These seasonal caps are formed by direct condensation of atmospheric CO2 gas onto the surface as the temperature moves below the condensation line of the vapor pressure curve. This process is similar to water condensing to a solid at 32°F at atmospheric pressure on Earth, except here, CO2 goes straight from a gas to a solid.

Mars’ atmosphere has been a focal point for research due to its composition, thickness, and interaction with the surface. The Martian atmosphere is composed of approximately 95% CO2, which plays a major role in creating and removing both the northern and southern seasonal ice caps. The consistent condensation and sublimation of

CO2 throughout the year is a main driver of the Martian climate and atmospheric conditions (James, Keiffer, and Paige, 1992). Between one-fourth and one-third of the atmospheric carbon-dioxide is cycled through the atmosphere and seasonal cap during a given year; this interaction between the atmosphere and surface gives insight to Martian weather processes (Tillman et al., 1993).

On Earth, we see snowfall in winter months and melting as temperatures rise.

This is akin to the growth and recession of the seasonal caps on Mars. From this, we must distinguish between Mars’ seasonal and residual caps. The seasonal caps grow and recede throughout a Martian year, whereas the residual caps remain stable consistently. The northern seasonal cap, our main focus, is composed of CO2 ice, which sublimates and 3

condenses over time, whereas the northern residual cap is made of water (H2O) ice and remains over a Martian year.

Data collection for the surface conditions of Mars, such as the growth and recession of the seasonal caps, has been expansive and plentiful. Daily global maps of the planet have been created using the Mars Color Imager (MARCI) camera on MRO since its orbit began in 2006 (Malin Space Science Systems). We now have over six Mars years of daily data from which we are able to monitor the seasonal caps’ annual growth and recession. The community of researchers interested in seasonal phenomena developed a set of standards to reduce discrepancies and miscommunications when analyzing these processes. One of these standards includes the definition of solar longitude; particular times in a Martian year are given by solar longitude, or Ls (“ell-sub s”), values. These values range from 0 to 360, with Ls 0 being the onset of northern spring and continuing with each season broken into 90-degree intervals. I will utilize this Ls time-notation throughout this study. The northern seasonal cap recession period defines the range of Ls values where the cap undergoes recession. This time span is slightly variable; however, for the purposes of this analysis, I will define this range from Ls 350, which is the end of northern winter, to about Ls 80, which is the end of northern spring. It is important to note that the full extent of the recession period can range from Ls 280 to Ls 90, though we found Ls 350 to Ls 80 to be sufficient for the purposes of determining recession rate

(Piqueux et al., 2015).

Another standard definition is provided for Mars years (MY). A Mars year is comparable to an Earth year, meaning it is defined by the amount of time required to travel once in its elliptical path around the sun. Mars year enumeration is completely 4 described in Piqueux et al. 2015b, allowing for consistency among publications. MY 1 is defined as April 11, 1955 at Ls 0.0 (Piqueux et al., 2015b). The definition of a Mars year is pointed out to be distinct from the more commonly known Earth year, as Mars takes approximately 687 Earth days to complete a full rotation around the sun. This is vital in understanding how an Ls value corresponds to Earth days; though not exact, one Earth day translates to approximately 0.5 degrees of Ls. This is useful in calculating the Ls of images based on the Earth date they were taken.

The inter-annual recession of the northern seasonal cap is the primary interest in this study. Research surrounding the recession rate over time has been conducted with varying methodology, including spectral, thermal, and visual observation. Since MY 25, data analysis applying these multiple techniques has been performed utilizing imaging technology from MARCI on MRO and the thermal infrared data from the Thermal

Emission Spectrometer (TES) on Mars Global Surveyor (MGS) and the Mars Climate

Sounder (MCS) on MRO. Many previous studies focus on utilizing the data gathered from these orbiters in order to determine the following information: the inter-annual recession rate of the seasonal cap, an accepted method to define the seasonal boundary at any given point in the recession season, and the average latitude boundary of the seasonal cap throughout the recession season.

My research began with utilization of the visual observation technique of the northern seasonal cap using MARCI imagery in order to measure the correspondence of the four most recent Mars Years’ recession rates with one another. This study revealed a clear correlation of the recession rates, and the results were comparable to those obtained through other methodologies, such as using thermal data. While conducting this study, 5 however, we identified new processes that have not previously been described in the literature. The seasonal cap, originally a near-perfect circle around the northern hemisphere of the planet, became asymmetric as the recession season neared its end. The asymmetry of the cap begged the following questions: why is the cap’s edge receding with varying rates? Is the side further receded at the end of the season retreating faster, or are other portions retreating slower? Our initial hypothesis introduces the idea that local elevation affects recession of the seasonal cap – some sections retreat slower due to local elevation, and others retreat quicker in relation to their corresponding topographical features. This topic is not well documented in the literature, and may influence other climate related processes, such as long-term preservation of ice and evolution of water ice in the residual cap over spring and summer seasons. I introduce this study as a way to provide background on the recession of the northern seasonal polar cap and potentially allow for a more detailed understanding of the cap’s yearly alterations.

6

Literature Review

Work in the field of Martian exploration through observational, experimental, and spectral/thermal data collection has been extensive over the last few decades, going as far back as James’ study using Viking orbiter observations in 1979 and Iwasaki and Saito’s observations published in 1982 (James, 1979 and Iwasaki and Saito, 1982). I focus primarily on papers that look specifically at the northern seasonal cap, as this is my targeted interest and a focal point for observation. Determination of the optimal way to approximate the seasonal cap boundary edge has included a variety of techniques in order to create a general consensus of this boundary definition. While a multitude of methods have been utilized to study the entirety of the cap boundary at a given time, few studies analyze the differences in the location of the cap’s edge as it retreats. This review mainly focuses on the previously documented determinations of the northern seasonal cap’s edge to provide a basis of understanding of this process as seen in the literature. The asymmetry of the cap during this recession is also discussed in two studies, which establishes a foundation from which our new research question stems.

In Appéré et al.’s paper from 2011, the temporal and spatial distributions of the

CO2 and H2O ices from the seasonal and residual caps during the MY 28 recession are presented through spectral analysis (Appéré et al., 2011). Appéré’s study also discusses the relationship this recession process has with the Martian climate. This investigation of the boundary is performed utilizing albedo (reflectivity), CO2 ice, and H2O ice spectroscopy and imaging in order to distinguish the CO2 seasonal cap from the H2O residual cap, as well as from any extraneous substances that appear visually similar to the high-albedo materials. This is done through comparison of the Mars Express 7

Spectrometer Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA,

Infrared Mineralogical Mapping Spectrometer) observations during MY 28, as well as the techniques applied to data acquired from the Mars Orbiter Camera (MOC), TES, and

Thermal Emission Imaging System (THEMIS). The OMEGA observations were used to analyze the albedo of the surface and to monitor the seasonal deposits at the caps. This analysis was performed for Ls 280 in MY 27 through Ls 95 of MY 28, resulting in a reasonable understanding of this Mars year’s seasonal cap recession.

In slight contrast to Appéré’s technique, Sylvain Piqueux opts for focusing on thermal infrared analysis to create this distinction (Piqueux et al., 2015). Piqueux chose to analyze eight Mars years of thermal infrared data from TES aboard MGS and MCS aboard MRO. The northern seasonal cap was defined at regions where “diurnal radiometric temperature variations at ~32 [micrometers] wavelength do not exceed 5 K”

(Piqueux et al., 2015). The technique adequately defined the cap for the purposes of tracking recession, as well as growth, of the north and south caps – though for our purposes, we focus on the recession of the north cap. In addition to this, thermal emission spectra from MCS on MRO was collected to compare the temperature data with absorption band spectral data and make accurate conclusions. Corrections to this spectroscopy data were also applied in order to correct for the phase function of CO2 ice

(Piqueux et al., 2015).

While spectral and thermal techniques are prevalent, visual observation has remained another useful technique for observing the Martian poles. James and Cantor’s

2000 Mars Orbiter Camera (MOC) study analyzes the recession of Mars’ northern seasonal cap in MY 25. MOC, aboard MGS, provided images of the northern 8 hemisphere, allowing the visual observation and tracking of the seasonal cap’s recession, just as MARCI does today. In this study, the cap’s latitudinal extent was measured for every 10 degrees of Ls between Ls 340 and Ls 90 (James and Cantor, 2001). This visual method required the ability to analyze different high-albedo substances, which proved difficult, especially earlier in the recession season. A linear fit was applied to the data to determine the northern seasonal cap’s recession rate. Conclusions discussed the visibility of the recession through these images, as well as changes in the cap’s albedo as a function of insolation (James and Cantor, 2001).

This technique has been adapted in later studies too, such as Calvin et al.’s in

2016, in order to continue this visual investigation of the seasonal cap. Observation of the cap’s recession is completed through visual tracking of the boundary utilizing MARCI images from MRO (Calvin et al., 2016). Further details of this technique are described in the methodology section of this paper. This technique is of particular importance because the data is readily available, accessible to those with limited experience in spectroscopy – like myself – and clearly showcases the boundary’s edge through the images themselves.

Presenting the data through the medium of direct images is useful in explaining to a broad community of scientists why this research is important and clearly observable.

Additional studies include Cantor et al.’s analysis in 2002, Jenson and James’ in

2005, and Kieffer and Titus’ in 2001. The sheer number of studies conducted clearly emphasizes the amount of attention given to the seasonal caps on Mars. In supplement to this, other studies, such as Haberle et al.’s publication in 2008, explain the relationship between recession and Mars’ overall weather patterns, atmospheric circulation, and contributions to the annual processes seen on the planet. Yet, there still remains a lack of 9 research on the asymmetry of the cap during recession. Fishbaugh et al.’s research in

2000 discusses the variation in topography within the northern polar region and its significance (Fishbaugh et al., 2000). This study primarily focuses on the geologic and greater-picture context of the northern polar region in relation to topography. This is useful to us in understanding how elevation varies throughout the northern hemisphere, particularly where the seasonal cap would be during the recession season. Fishbaugh utilizes Mars Orbiter Laser Altimeter (MOLA) data to understand this regional elevation variation and provides a topographic map of the northern hemisphere extending from 90° to 55° latitude in a polar stereographic view.

One study that did emerge and discussed asymmetric polar cap recession was

Giuranna et al. in 2007. This paper analyzes the southern seasonal cap rather than the north, but the methodology and theories used are still relevant. The study’s original purpose was to measure the southern seasonal cap recession utilizing thermal techniques in order to differentiate CO2 ice from low-albedo terrain (Giuranna et al., 2007). The data was obtained from Mars Express, and the analysis focused on MY 27. Upon conducting this study, asymmetric cap recession was noted; partial pressure measurements were used to relate topographic data to the cap boundary in order to determine if cap recession asymmetries were related to local elevations. Through the use of the Clausisus-Clapeyron equation, an indirect correlation between surface temperature (which directly relates to pressure) and altitude was obtained (Giuranna et al., 2007). Giuranna et al.’s study will prove important in interpreting the results of this thesis work.

The clear regional difference in topography (with the lowest portion relating to the region of quicker retreat) provides a foundation from which the relationship between 10 these elevation differences and the seasonal cap edge can be compared. Through this relationship, we intend to highlight the importance of understanding the reasoning behind this irregularity in the cap edge’s location over time, as well as how we can better denote the average latitude of the cap edge to incorporate asymmetry in the future.

11

Phase I – Determining the Inter-annual Recession Rate for MY 31-34

In the initial stages of this project, the objectives were threefold:

1. To determine the inter-annual recession rate of the northern seasonal cap from

MY 31-34

2. Compare the method of determining this rate to thermal analysis in order to

confirm the validity of observational data

3. Analyze images of the cap to make determinations about how the cap recedes

within a year and between years (i.e. does the cap recede symmetrically? Does

recession look different in different places? Etc.)

I will therefore construct this section into three respective subsections.

1. Determining Recession Rate

As described previously, the CO2 seasonal cap sublimates into the atmosphere each year. The time period during which this occurs is denoted as the recession season.

By observing the location of the cap boundary’s latitudinal value over time, I am able to track the rate at which the CO2 is sublimating. By utilizing the same Ls time-stamped images for each Mars year in this study (MY 31-34), I am able to track the recession rate for each year and compare them; hence, I obtain an inter-annual recession rate.

MRO remains in a sun-synchronous orbit around Mars; this means that as the planet rotates on its own axis under the orbiting spacecraft, the longitude at which the spacecraft crosses the equator changes for each orbit. The lighting of the sun allows the

MARCI camera to take images of the surface. Each Earth day, MARCI takes and sends back approximately 13 image strips. This data is recorded and reconfigured into a polar 12 stereographic projection, dubbed a mosaic. Each daily mosaic represents approximately

0.5 Ls in time, providing a number of images to analyze throughout the recession season.

The camera shifts with the sun-lit surface in order to exclude data collection during times at which the pole is dark (not sun-lit).

The spacecraft obtains northern cap recession data from approximately Ls 280 until Ls 100 of the next Mars year. We find that the period of Ls 350 to Ls 80 encompasses the majority of the cap’s recession, so we define this as the recession period for this study. The imaging of the recession season, this Ls 350 to Ls 80, is maintained annually, meaning the period of visibility remains consistent each year. When looking between Ls 350 and Ls 80, we have a total of about 180 images to utilize for analysis in that given Mars year. In order to reduce redundancy, since the cap’s recession is indistinguishable between just 0.5 Ls, I looked at one image for every 5 degrees of Ls during this Ls 350 to Ls 80 period. Remembering that Ls values stop at 360 and begin again at 0, this gives a total of 19 mosaics that were analyzed for each Mars year, or 76 mosaics in total.

Since this analysis is observational, attempting to distinguish the difference between the seasonal cap and other high-albedo (highly reflective) materials, such as clouds, becomes difficult. In order to combat this obstacle, movies were created to easily flip between 0.5 Ls-step mosaics. If a portion of the cap changed drastically from one mosaic to the next, this section was determined to have a high-albedo obstruction and was discounted in boundary analysis. While this technique is certainly subjective, the data was highly repeatable between the four Mars years. The movies were simple .mov files, essentially with the mosaics running back to back every 0.5 Ls, each with a one 13 second delay. These movies also contained both the Ls time stamp, as well as the corresponding Earth day, month, and year.

The 76 images that were predetermined to be the observational mosaics were approximately the same in Ls for each Mars year investigated in this study. The following images were included:

Ls 351.4 Ls 15.1 Ls 40.1 Ls 65.7

Ls 355.5 Ls 19.4 Ls 45.0 Ls 70.5

Ls 0.5 Ls 24.1 Ls 50.3 Ls 74.8

Ls 5.4 Ls 30.5 Ls 55.2 Ls 80.1

Ls 10.3 Ls 35.1 Ls 60.0

List 1: Ls value images analyzed in Phase I of this study. Representative for each Mars year (MY 31-34), with slight variations of ± 0.4 These mosaics were chosen based on the visibility of the cap, proximity of 5 degrees of

Ls from the preceding and following mosaics, and full polar projection. It is important to note that not all mosaics were projected well; some projections contained warped image strips, making that day’s mosaic unusable for this analysis.

Each mosaic was opened one by one in ENVI Classic software. Within this program, the Region of Interest (ROI) tool allowed me to hand trace the seasonal cap boundary directly onto the image. In order to do this, the mosaic was loaded in as a 2312 x 2312-pixel image and opened in RGB (red-green-blue) color.* Three image windows

* The second dimension, which represents the maximum y-coordinate value, varied between 2312 and 2327 for each mosaic that was analyzed. This discrepancy was not enough to skew the data collected and discussed here, but the resizing of these images to match the 2312 x 2312 dimensions would have been ideal. This is further discussed in the Error section. 14 appeared at this time, providing varying levels of zoom. The first was the full cap mosaic, which gave me a point of reference as I worked my way around the cap boundary. The second was a further zoomed-in section of the cap; this image was where I would draw the ROI. The third was a detailed, considerably further zoomed-in image of the exact pixels that I was drawing on, providing greater precision during this process. In addition to these three opened windows, I also kept the mosaic’s respective MY movie open on the screen. This allowed me to easily flip to the previous and next image, assisting me in removing obstacles from my data collection.

I utilized the distinct difference in albedo between the seasonal cap edge and the basaltic, red-brown colored sand surrounding the cap in order to draw the ROIs as accurately as possible. A clear visual of the change in the northern seasonal cap extent is shown in Figure 1. The ROI tool was set to polyline, meaning that the tool would allow the user to draw in straight lines until they clicked the screen, which would then place a point and allow a new line to begin within the same ROI dataset. Each ROI, 76 in total for the respective mosaics, retained between 5000-7000-pixel coordinate points along the boundary. These pixel coordinate values were then saved in ASCII text files, allowing a full dataset for each ROI and the respective mosaic’s cap boundary to be saved numerically. 15

Figure 1:Image showing recession from MY 34. Images from left to right are of Ls 0.5, 60.0, and 80.5 Each X-Y coordinate point within the ASCII text file then needed to be translated into a latitudinal value, in order to compare the average latitude with the mosaic’s corresponding Ls value. I wrote a few small lines of code, shown in Figure 2, in order to translate each cartesian point into a latitude value. Each of these values for the entire ROI were then averaged in order to find a final average latitude for the seasonal cap at the given Ls. The code lines were written utilizing the knowledge that the center of the mosaic, or the cartesian point (1156, 1156) represented 90° latitude, and the cap’s edge on the image represented 55° latitude. Figure 3 further shows a sketch of a point on the

ROI within the image. 16

Figure 2:Description of code used to translate ROI data into average latitude

17

Figure 3: Sketch of a point on an ROI. Image dimensions are shown with the pixel coordinate point (0,0) in the top left and (2312,2312) on the bottom right. Latitude extent is 55° with 90° latitude in the center Once each of the mosaic’s average latitude values were obtained, the recession rate was then plotted. Figure 4 represents the preliminary recession data as an Average

Latitude vs. Ls plot for MY 31-34, with the inclusion of a few other previous Mars years for comparison (James and Cantor, 2001 and Calvin et al., 2016). A linear fit was then applied to these data points, providing a slope, maximum latitude, and minimum latitude for that Mars year’s recession. As seen in Figure 4, these linear fits plotted almost right on top of each other, with similar maximum and minimum extents. This is conclusive evidence that the average cap recession rate is consistent between years. The resulting 18 data also helps to prove that even with the subjective nature of this method, the data is compatible with past results and repeatable.

Figure 4: Recession rates for MY 31-34. Data for MY 25, 29, 30 and 31, collected from previous studies, is also included for comparison (James and Cantor, 2001 and Calvin et al., 2016). Note that “BFL” stands for “Best Fit Line,” which represents the linear fit applied to each data set The data remained consistent for these extra MY 25, 29, 30, and 31 data values as well, with a single exception – MY 25. MY 29-31 utilized the same technique, and this was detailed in Calvin et al., 2016. The data for MY 25, analyzed in James and Cantor,

2001, is found using a slightly different technique. Here, best fit circles were used to obtain the average latitude of the cap. My mentor and I agreed that these values be included in this analysis as well, despite the difference in methodology. The reasoning behind this was that there had been a global dust storm in MY 25, and we wanted to see if there was an extreme variation in data compared to non-dusty Mars years. While there was some variation clearly seen, we ended up deciding that the variation was not enough 19 to fully conclude that dust storm years had different recession rates, mainly due to the fact that this data was not directly comparable with the data for MY 29-34.

While it would be a simple conclusion to also state that the recession rate can be defined as linear in nature, this average does not account for the spatial variability of the cap.

The next subsection details the reasoning behind the inaccuracy of this claim and describes a potentially more appropriate fit.

2. Comparison of Techniques

After the average latitude values were obtained and the recession rates were plotted, I created a climatological model to describe the cap’s average behavior for all four Mars years. This climatological model, shown as the red line in Figure 5, then required comparison to determine if observation is a viable method for analyzing the cap boundary. I compared my method with a thermal technique used in Piqueux et al., 2015, shown as the blue line in this same Figure. Though the models are not too varied, they are clearly distinct. The larger data set, when plotted, proved a parabolic fit was more appropriate to model the cap’s growth and recession. Since I did not have the growth data, my linear fit worked well for the recession section of the parabola. 20

Figure 5: Climatological model of inter-annual recession rate. Red line represents observation data, the blue line represents thermal data presented in Piqueux et al., 2015. Though the linear fit was not ideal in the larger picture, the method still works reasonably well for both datasets. The distinction in fit techniques (parabolic vs. linear) provides some evidence as to why the two climatological models are slightly varied.

Even with this difference, however, we can clearly see that the recession rates are very comparable, proving that observation is a viable method for completing this analysis. The intention behind proving the validity of this technique comes from access to data; while some researchers may be able to access certain datasets, such as thermal data, few are specialists in this field. The observational technique is considerably more accessible to 21 scientists and researchers interested in this recession, and the methodology is fairly simple to repeat.

This method is particularly useful in visualizing how the cap recedes as opposed to only measuring the recession rate numerically. The ability to visually observe where the boundary is physically located at any given time is helpful in making further observations about recession. We can overlay different ROIs, within a single Mars year or between multiple years, and we are able to check quantitative values for validity, limiting error and confusion. The clarity obtained with the visual analysis is a benefit to utilizing this technique, and it provided me with the ability to ask new questions about the recession.

3. Upon Further Inspection

Near the end of the initial stages of my research, I had looked at the same 76 mosaics for over two months. The repeated analysis of these cap boundaries led me to make important observations, one of which became the main focus of this thesis. As recession progressed over time, the edge of the cap transformed from a near-perfect circle to a clearly asymmetric one. This observation begged the question concerning the reasoning for this change in the cap’s appearance. Upon examining the literature, finding no studies that directly observe this phenomenon, and also speaking with my mentor, we determined that the reasoning was currently unknown and of interest. We hypothesize that elevation plays a major role in this advancement from a symmetric to an asymmetric cap. We aim to analyze how local elevation plays a role, which would consequently imply other influences, such as the amount of insolation (heating from the sun) that 22 reaches the cap at a given point and the amount of pressure – and by relation, temperature

– at said location.

23

Methodology

In order to directly relate a given Ls image’s cap boundary location with the associated topography, I required the local elevation of the northern pole. The Mars

Orbiter Laser Altimeter (MOLA) instrument aboard the MGS spacecraft collected altimetry data – the height of Mars’ surface features –from March of 1998 to June of

2001 (Neumann, 2007). The MOLA data accumulated includes a full elevation map of the northern polar region, which is the section we are interested in for the purposes of this study.

Tie Point and MATLAB Compilation Procedure

In order to understand how topography may influence the seasonal cap’s recession, we first required a technique to capture the relevant elevation data corresponding to a particular image’s drawn ROI boundary. The technique needed to be applied to the later season ROIs from Phase I of this study, including Ls 55, 60, 65, 70,

75, and 80 (each ± 0.4 degrees of Ls). This period of the recession, about the last third of the recession season, is where the cap clearly transitions from being symmetric to asymmetric. Through iteration, the procedure for capturing the elevation data was established by combining MOLA and MARCI images using tie points and using a

MATLAB compilation code to capture the relevant topography data. I utilized both methods sequentially in order to capture the appropriate topography data for each Ls value listed above.

The ENVI software package has a tool programed in that allows a user to create tie points, or matching points, by hand on two images, and then warp one image onto the 24 other. By loading the MOLA and MARCI images into the ENVI displays and loading this tool, I was able to move cross hares to exact pixels of locations that matched on each image. I placed the tie points at clearly defined locations, such as craters or distinctively shaped features. I chose to select ten tie points for each image pair. Choosing too few points does not give the software enough information to match the images appropriately yet choosing too many points will distort the image; therefore, through trial and error and guidance, I determined that ten points was an appropriate number to select.

After saving the ten tie points as a PTS file, I utilized the warp tool, also in ENVI, to combine the data from both images. I used the MARCI image as the base and warped the MOLA image onto it since the original ROI recession analysis was conducted on the

MARCI images. The new, combined image was then resized to match the original

MARCI image’s dimensions, and the resized image was then be loaded onto the display.

As long as the combined image had the same pixel dimensions as the MARCI image which that Ls’ ROI was drawn on, the original ROI could then be loaded directly onto the

MOLA-MARCI image. Visual observation of the ROI on this resized MOLA-MARCI image allowed for a further understanding of how topography may play a role in longitude-variant recession rates. I was able to see where the cap’s boundary was located and if there were any significant local topographical features. I will further explain my findings and inferences from this analysis in the discussion section.

In MATLAB, I then uploaded the new resized image’s topography data into a

2312 x 2312 array. With this data uploaded into a single variable, I needed to select only the elevation data from all coordinate points on a particular ROI boundary, and then put the x and y coordinate data and that point’s corresponding elevation into a new variable. 25

This method required some dialogue in order to ensure the image data was oriented properly and loaded in the correct data type (float32 for MOLA data), but otherwise required few lines of code. The resulting data array essentially associated the related elevation data to the original ROI points. This procedure was conducted for each Ls analyzed in this study.

Determining How to Section the ROIs

The next step in this process was determining how to divide the cap into sections in order to study the elevation locations that observationally recede quicker or slower. I chose to divide the cap into three sections:

• Section 1, which is in upper right quadrant of the image, visually receded slower

than the rest

• Section 2, which appeared consistent in recession, was the average of Sections 1

and 3

• Section 3, the left side of the image, was consistently receding quicker than the

rest of the cap, in an extremely asymmetric fashion

Sections 1 and 3 were my primary interests, with Section 2 used as a control or average comparison to use against the others. Section 3 has a large chasm near the center of the image that spans between approximately 270 and 330° longitude, and Section 1 has a large dune field in between the residual cap and the further extended ice sheet.

I made the decision of where to divide these sections somewhat subjectively in the beginning, by choosing points where the cap drastically shifted in terms of how much ice remained. The points I selected to divide the cap were chosen on Ls 80, the most 26 asymmetric image. They include the points (1062, 870), dividing Sections 1 and 3, (1663,

1181), dividing Sections 1 and 2, and (1122, 1541), dividing sections 2 and 3. Figure 6 visually represents these points and the divisions they make. It is important to remember that these cartesian coordinates are in relation to the top left corner representing the point

(0,0) and the bottom right corner being (2312, 2312). This concept is visually represented in Figure 3 shown previously.

1

3 2

Figure 6: Image of MY 31, Ls 80 denoting the longitudes drawn to separate Sections 1, 2, and 3. Each section is shown through its corresponding number within the image. Longitude lines are colored magenta. 27

Though this initial selection was arguably arbitrary, I maintained consistency between different Ls images by applying, what I call, the longitudinal method. The longitudinal method takes a point from a particular ROI, say for Ls 80, and finds the corresponding point along the same longitude line on a new ROI, say for Ls 75. In order to conduct this process, I first needed to find the longitude lines along which my initial division points were chosen. By uploading the Ls 80 image back into ENVI and using the

ROI polyline tool, I was able to draw a line from the point (1156, 1156), the center of the image, out to each of the three chosen points individually. I saved this linear ROI data as an ASCII text file, which contained all points along this longitude line for the Ls 80 image. I then plotted the data into MATLAB, applied a linear fit, and copied the equation that was produced. This equation represented an approximate line of longitude along which my initial points lay. I also used trigonometric functions to determine these lines of longitude for reference: The Section 1 / 3 division is along 198° longitude, the Section 1 /

2 division is along 87° longitude, and the Section 2 / 3 division is along 354° longitude.

Figure 7 shows Mars’ north pole longitude orientation to clarify these longitude bearings

(Lopes and Solomonidou, 2014). Figure 6 also demonstrates these longitude lines on the image and the corresponding sections they divide. 28

Figure 7: Polar and cartesian views of Mars’ surface. North polar region (top right image) shows longitude orientations used in this study. Image from Lopes and Solomonidou, 2014 I repeated this process for each of the five remaining Ls images utilized in this study. Occasionally, I did not obtain a point (likely due to rounding of the linear fit equation) for a new image. To manually find the point, I created a new variable to store the difference between each coordinate point’s actual y-value and the y-value obtained from the linear fit equation. I then scrolled through all of the points and searched for one that was only one or two pixels off, likely due to rounding error from the equation’s creation. Though I could have implemented code to do this for me, the y-value differences followed a pattern, and it was generally easy to discover the missing point. In 29 the end, I successfully obtained three section-separation points for each of the six images using this longitude application technique.

Sectioning the ROIs

Once the three section-division points were established for each image, I then utilized the intersect tool to divide the original ROI into the three sections. I first drew a polygon ROI from one boundary division point to the other. For the Ls 80 example,

Section 1’s polygon intersected the original ROI at the points (1062, 870) and

(1663,1181), with the polygon overlapping all original ROI points in between. I then used the intersect tool and selected the original ROI data and the new polygon data to find all points that were contained in Section 1. I repeated this process for Sections 2 and 3 on the same image, and then again for all three sections of the remaining five images. I will note that for the next sections, I changed the x or y-value by 1 (meaning I used the point

(1663,1182) for the Section 2 beginning point) in order to eliminate repetition of coordinate points between sections. Figures 8-13 show the divisions of each of the six images, with the blue ROI corresponding to Section 1, the red ROI corresponding to

Section 2, and the yellow ROI corresponding to Section 3.

I saved these sectioned ROIs as ASCII text files, which contained all of the x-y coordinate points contained in that section’s new ROI. I then uploaded each point into

MATLAB and matched the x-y coordinate points to that in the full ROI saved with elevation data. This allowed me to compile each section’s elevation data for all six images into individual arrays.

30

Results

My analysis of data specifically looked at MY 31. I began with this Mars year, and I worked under the assumption that data collected from this study would be applicable to MY 32-34 as well. From Phase I results, MY 31-34 maintained consistent recession rates with one another. With this in mind, I thoroughly investigated the progression of asymmetry throughout one recession season, instead of analyzing the latest image for each different Mars year. Though I would have preferred to expand this study to include MY 32-34 for confirmation of this assumption, time did not allow.

I analyzed six images, approximately Ls 55, 60, 65, 70, 75, and 80, from MY 31. Each image was divided into three sections (described in the Methodology section), and the elevation data for each was analyzed to see if there were any distinctions. I chose to look at the average, maximum, and minimum extents of the seasonal cap at the corresponding

Ls, as well as the standard deviation of the elevation data and the number of points in each section’s ROI. The resulting data is shown below in Table 1 (Note that the northern region of Mars is low in elevation compared to the rest of the planet’s surface, giving values in the negative thousands of meters from the defined zero elevation level):

31

Number of Average Maximum Minimum Standard Section Points in [m] [m] [m] Deviation ROI

1 -4330.4 -3869.5 -4819.0 221.88 1262

Ls 55 2 -4421.5 -3964.3 -4902.0 226.11 1041

3 -4656.2 -3786.3 -5248.5 422.12 1732

1 -4368.1 -3655.3 -5325.0 267.59 1180

Ls 60 2 -4426.7 -3992.3 -4893.5 234.54 993

3 -4747.9 -3799.3 -5229.8 371.48 1881

1 -4428.8 -3436.0 -5683.5 305.29 1209

Ls 65 2 -4442.5 -4072.0 -4913.3 218.21 959

3 -4880.3 -4273.3 -5253.3 258.54 1764

1 -4478.0 -3722.5 -5729.8 279.42 1697

Ls 70 2 -4504.6 -4080.5 -4918.0 220.66 1078

3 -4913.9 -4382.0 -5235.0 215.25 2755

1 -4448.8 -3880.0 -5649.3 283.32 1512

Ls 75 2 -4545.8 -4072.0 -4892.5 219.02 1215

3 -4871.9 -4293.8 -5216.8 228.03 2594

1 -4492.1 -3900.5 -5170.8 288.75 1651

Ls 80 2 -4535.8 -4090.9 -4891.6 212.15 855

3 -4800.1 -4284.0 -5288.7 217.20 2452

Table 1: Elevation Data results divided by section and Ls 32

The following listed Figures correspond to each ROI and are color coded by section, with blue corresponding to Section 1, red corresponding to Section 2, and yellow corresponding to Section 3:

Figure 8: MY 31, Ls 55

33

Figure 9: MY 31, Ls 60

34

Figure 10: MY 31, Ls 65

35

Figure 11: MY 31, Ls 70

36

Figure 12: MY 31, Ls 75

37

Figure 13: MY 31, Ls 80

I also plotted the histograms to visually represent the spread of these data sets.

The three sections’ combined histograms are shown in Figures 14-19 below, with each color corresponding to the respective section shown on the ROI images. The individual sections’ histograms can be found in Appendix A. Each histogram was separated into 10 bins in order to maintain consistent visuals. Discussion of these results, as well as their 38 potential consequences for the seasonal cap, are detailed in the following Discussion section.

Figure 14: Ls 55 Histogram

39

Figure 15: Ls 60 Histogram

Figure 16: Ls 65 Histogram 40

Figure 17: Ls 70 Histogram

Figure 18: Ls 75 Histogram 41

Figure 19: Ls 80 Histogram

These histograms (Figures 14-19) particularly show the changes in elevation trends. The first couple of histograms show section data bunched together, overlapping considerably. As time progresses, a clear separation becomes apparent, with the blue

(Section 1) data representing locally higher elevations and the yellow (Section 3) data representing locally lower elevations. This distinction leads to further interpretations discussed below. For full statistic calculations of the data produced, Section 1’s overall average elevation was -4424.4 m, Section 2’s average was -4479.5 m, and Section 3’s average was -4811.7 m.

42

Discussion and Conclusions

Interpretations

As clearly seen in Table 1 and each histogram in the above Results section,

Section 1 data tends to be higher in elevation, and Section 3 tends to be lower in elevation. We can also visually observe in Figures 8-13 that Section 1 remains further extended in the late season (slower retreat) while Section 3 recedes quicker. The correlation between higher elevation and slower retreat (or lower elevation and quicker retreat) helps to prove our hypothesis that elevation affects recession rates. While it would be incorrect to simply say that these factors each occur so they are naturally related, we can use the argument of local pressure to confirm this relationship.

Giuranna et al., 2007, described previously, is a study that looks at the recession of the southern seasonal cap during MY 27. Though this analysis is not exactly the same as mine, which looks at the northern seasonal cap, he does utilize partial pressure relations to explain potential asymmetries in the cap boundary’s recession. The explanation in this study discusses that pressure, which is directly related to temperature through the Ideal Gas Law, can affect how quickly the CO2 ice sublimates (Giuranna et al., 2007). Essentially, we can relate condensation temperature to local elevation; if local temperatures are higher (or elevation is lower), the triple point at which CO2 sublimates can be crossed earlier than if the local temperature is lower (or elevation is higher). In addition to this, higher elevations generally have lower temperatures already due to adiabatic lapse, and vice versa for lower elevations retaining higher temperatures. This furthers the argument that we see more stable CO2 conditions at higher elevations, 43

whereas CO2 is able to sublimate quicker at lower elevations. Figure 20, from Giuranna et al., 2007, shows an example image from this paper’s work to relate altitude (elevation) and temperature. Here, the red curve is altitude over the south cap, and the black curve is surface temperature. The indirect relationship between altitude and temperature can clearly be seen here.

Figure 20: Figure from Giuranna et al., 2007. The red curve represents altitude in kilometers and the black curve represents temperature in Kelvin. The indirect relationship helps to demonstrate my conclusive results’ relationships Though this exact data is not relevant to my study, the conclusions I draw are demonstrated through this relationship. When local elevation is lower, the partial pressure at the surface is higher, and the surface temperature is also higher. This means that sublimation can occur more often or quicker at these locations than at lower locations along the cap boundary. This conclusion is extremely interesting, and it is well represented in the data found from my analysis with Section 1 averaging an elevation of -

4424.4 m and Section 3 averaging an elevation of -4811.7 m. However, due to the clear overlapping seen in the earlier Ls data from this study, it is clear that elevation is likely 44 not the only factor leading to variation in recession. It is certainly possible, and likely, that insolation variations, winds, and shading also contribute to this later season asymmetry. These concepts are potentially worth pursuing in the future. While our original hypotheses were confirmed, there is much more to observe and analyze.

Sources of Error

With many steps in translating these data sets throughout this analysis, there are various potential sources of error. The main sources that I will discuss here include sizes and resizing of images, error occurrences from the intersection of ROI polygons with original Ls ROIs, Phase I observations, and the tie point procedure. While each of these error sources are certainly worth mentioning, I do not believe they significantly impact my results in a way that could reverse or damage the conclusions stated.

One source of error is tedious, but of importance. Each MARCI image that the original Phase I ROIs were drawn on were not each of dimensions 2312 x 2312, but of a slightly varied second dimensional size. The y-values’ maximum extent for the first 76 images observed ranged from 2312-2327, which is not a large distinction from the 2312 value used, but significant enough to potentially alter one or two points throughout this analysis. The resized MOLA data required a square dimensional shape, meaning we had to use 2312 x 2312 pixels for this image in order to at least preserve the x-value dimension. This distinction is likely not the source of any major errors, but it is certainly an inconsistency that we would have preferred to eliminate. The ROI data collection had been conducted considerably before this study, meaning that the resizing of each image would have also required redoing each ROI and the entire analysis from Phase I. This 45 was not likely enough of an error source to warrant this restart, but in future work, it would be beneficial to maintain consistency in image sizing.

The main source of error originates from the sectioning of each ROI. During this process of creating a polygon over the desired section and intersecting it with the original

ROI, pixel-coordinate points were lost. Approximately 300 points were dropped from the conversion of the original ROI into three sections, though none should have been. I believe that potential reasonings for this error come from the different sizing of images, or the reduction of redundancy from original point repetition. The aforementioned image dimension problem could potentially affect the loss of these points, though I would estimate this error in the range of 10 points or less rather than around 300. The redundancy source of error originates from my tracking of the original ROIs. Each original ROI contains some points that were repeated, likely from my drawing of the

ROIs going over the same point twice to recover missed CO2 frost during Phase I. This repetition was likely dropped during the intersection of the polygon and the original ROI, maintaining only a single copy of said point. While this would technically be helpful in reducing the repetition of points unnecessarily, it is still producing an error that is not transparently explainable.

The results for this study work under the assumption that the recession rate for

MY 31-34 is consistent. From the full recession rate graph, seen in Figure 4, this is not a completely valid claim. There is slight variety between each of these four Mars years, and the conclusions presented here would greatly benefit from a thorough analysis of all four

Mars years. These conclusions could also be supported by a complete analysis of elevation relationships throughout the entire Ls 350 to Ls 80 recession period, rather than 46 only the last third of the season. Though it is worth mentioning these factors that could prospectively induce slight variances in future observations of the more complete data set, we still stand by the fact that the conclusions drawn in this study are applicable to

MY 32-34.

Though providing a useful visual aid, the tie point procedure is likely a main source of error. The warping of the MOLA image onto the MARCI image for each Ls in this study stretched the data, and the placement of tie points was very subjective. Though

I attempted to match significantly distinct features, the images were vastly different in dimensional size, making it difficult to distinguish nearby, small craters from one another. The choice of using ten points also may have introduced error by warping the image too much or not providing enough data to make an accurate combined image.

It is important to note these sources of error, not to discredit the work that has been done, but to denote places to improve in future projects. These errors are minimal in the grand scheme of this study, and they do not include some of the finer details of this project. While there are likely other unknown sources of error, I believe these to be the main errors that occurred throughout this study.

Future Work

In future investigations, it may be useful to take another look at the local topography more than just quantitatively. Intricacies from the dune fields and high mountains, as well as low basins and chasms around the northern polar cap may further affect local recession rates. The slopes of elevated terrain may induce wind and/or inhibit insolation, which could significantly impact the recession rate of the local cap boundary. 47

In addition, the tilt of the planet may also affect certain longitudinal regions, where one side retains more heat from insolation than others. These are certainly areas to be explored, all with the goal of refining the definitions of Mars’ northern seasonal polar cap recession. The thorough understanding of this process leads to implications regarding

Mars’ atmospheric cycling processes, weather patterns, and possibly dust storm patterns.

All of these topics are of great interest to research scientists, as our journey of exploring

Mars has only just begun.

48

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Appendix A

Figure 21: Ls 55 Section 1 Histogram Figure 22: Ls 55 Section 2 Histogram

Figure 23: Ls 55 Section 3 Histogram 52

Figure 24: Ls 60 Section 1 Histogram Figure 25: Ls 60 Section 2 Histogram

Figure 26: Ls 60 Section 3 Histogram 53

Figure 27: Ls 65 Section 1 Histogram Figure 28: Ls 65 Section 2 Histogram

Figure 29: Ls 65 Section 3 Histogram 54

Figure 30: Ls 70 Section 1 Histogram Figure 31: Ls 70 Section 2 Histogram

Figure 32: Ls 70 Section 3 Histogram

55

Figure 33: Ls 75 Section 1 Histogram Figure 34: Ls 75 Section 2 Histogram

Figure 35: Ls 75 Section 3 Histogram 56

Figure 36: Ls 80 Section 1 Histogram Figure 37: Ls 80 Section 2 Histogram

Figure 38: Ls 80 Section 3 Histogram