The Attributes and Formation Mechanisms of Kallistos Vallis, Venus

by

Derek A. Berman, B.S.

A Thesis

In

Geosciences

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

Approved

David W. Leverington, Ph.D. Chair of Committee

Haraldur R. Karlsson, Ph.D.

Harold Gurrola, Ph.D.

Dr. Mark Sheridan Dean of the Graduate School

December, 2020

Copyright 2020, Derek A. Berman

Texas Tech University, Derek A. Berman, December 2020

ACKNOWLEDGMENTS I would like give my heartfelt gratitude and thanks to all my committee members. I would like to thank Dr. David Leverington for working with me these past years to accomplish this research and further my knowledge of planetary geology, geomorphology, and remote sensing. I hope this will be just the start to future collaborations, and that in 20 years we can still consider each other friends and colleagues in science. Thank you to Dr. Hal Karlsson for all your thoughtful comments and feedback on my thesis and a thank you to Dr. Harold Gurrola for serving on my thesis committee. I would also like to thank Lucia Barbato, Cameron Griffith, and Dr. Callum Hetherington for all the thoughtful advice, mentoring, and academic training. The three of you definitely helped to enrich my academic experience at TTU.

The past several years have represented a huge personal growth period, full of challenges and triumphs. I want to thank all my friends and family members who lent me their undying support and motivation. I especially want to thank my sister Nicole, who was with me through the toughest of times, and my friends Giovanni, Luka, and Matteo, as well as all the members of the “Italian Club”, for your camaraderie and kind words of encouragement.

Finally, I would like to thank the Texas Tech University Department of Geosciences and Texas Tech University Graduate School for all of the additional financial support that was provided over these last few years. Without this support I would have never been able to commit the necessary time required to complete the research that has led to my successful thesis defense.

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TABLE OF CONTENTS ACKNOWLEDGMENTS...... ii

ABSTRACT...... v

LIST OF TABLES ...... vii

LIST OF FIGURES ...... viii

I. INTRODUCTION...... 1

1.1 General Overview ...... 1 1.2 Previous Studies ...... 2 1.3 Purpose of Study ...... 2 II. BACKGROUND ...... 4

2.1 Overview of Early Historical Observations ...... 4 2.2 Modern Obsrvations and Magellan Overview ...... 5 2.3 Venusian Geological and Physiographic Units ...... 7 2.4 Geologic Time Periods ...... 9 2.5 Analog Channel Systems on Mercury, Earth, and the Moon ...... 11 2.5.1. Mercurian Channels ...... 13 2.5.2. Lunar Channels ...... 16 2.5.3. Terrestrial Channels ...... 19 2.6 Channel Systems on Venus ...... 21 2.6.1. Compound and Complex Channels ...... 22 2.6.2. Canali ...... 23 2.6.3. Sinuous Rilles ...... 24 2.7 Regional Geologic Setting of Kallistos Vallis ...... 25 2.8 Overview of Kallistos Vallis ...... 30 III. MORPHOLOGICAL CHARACTERIZATION OF KALLISTOS VALLIS ...... 40

3.1 Overview of Methodology ...... 40 3.2 Data Acquisition ...... 40 3.3 Topographic Overview ...... 41 3.4 Cross-sectional Profiles ...... 42

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3.5 Longitudinal Profiles ...... 52 3.6 Channel Area Measurements ...... 58 IV. ESTIMATION OF FLOW CONDITIONS AND INCISION RATES ....61

4.1 Mechanical Incision Parameters ...... 61 4.2 Thermal Incision Parameters...... 64 4.3 Estimates of Flow Conditions ...... 68 4.3.1. Flow Velocity Estimates ...... 68 4.3.2. Total Discharge Estimates ...... 69 4.3.3. Reynolds Number Estimates ...... 70 4.4 Estimates of Mechanical and Thermal Incision ...... 71 4.4.1. Mechanical Calculations ...... 71 4.4.2. Thermal Calculations ...... 72 4.4.3. Dynamic Viscosity Parameter Space Calculations ...... 73 V. ESTIMATION OF MINIMUM LAVA VOLUMES REQUIRED FOR FORMATION OF KALLISTOS VALLIS ...... 75

5.1 Elementary Thermal Determination of Minimum Lava Volume Effused at Kallistos Vallis ...... 76 5.2 Discharge-Related Determination of Minimum Lava Effused at Kallistos Vallis ...... 79 VI. DISCUSSION ...... 81

VII. CONCLUSIONS ...... 90

BIBLIOGRAPHY ...... 92

APPENDICES

A. SOURCE CODE FOR THE ITERATIVE CALCULATION OF MECHANICAL INCISION RATES ...... 107

B. SOURCE CODE FOR THE ITERATIVE CALCULATION OF THERMAL INCISION RATES ...... 111

C. SOURCE CODE FOR AREA CALCULATIONS ...... 116

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ABSTRACT Kallistos Vallis is a large volcanic channel system located in the Ammavaru volcanic province of Venus. The system extends more than 1200 km downslope from a complex topographic depression, terminating at distal plains characterized by distributary channels that emplaced extensive volcanic flows with estimated total volumes of thousands of cubic kilometers. Some channel reaches of Kallistos Vallis are as wide as 30 km and are in places characterized by the presence of prominent streamlined erosional residuals about which the system anastomoses. Cross-sectional and longitudinal profiles generated for Kallistos Vallis using low-resolution Magellan altimetry data do not constrain the form of the system effectively, beyond demonstrating that topographic relief across channels is generally at least tens of meters, and the kilometer-scale longitudinal slopes that characterize the system are generally well below 1°. The main Kallistos Vallis system has a surface area of ~41,000 km2, roughly 20% of which is comprised of the channel reaches that form the westernmost and central parts of the system, and 80% of which forms the eastern volcanic plains and related distributary channel reaches. The head depression of Kallistos Vallis is interpreted as the surface expression of a deeply-rooted igneous plumbing system that conveyed large volumes of mafic or ultramafic magma to the surface from subcrustal depths. The flow conditions potentially associated with development of the channel system were estimated on the basis of known constraints of the Venusian environment and the nature of volcanic analogs of the inner solar system. Flows with depths of 5 m and 20 m and viscosities of 1 Pa s would have been fully turbulent on essentially all channel slopes, and could have reached velocities of tens of meters per second and discharges of up to ~107 m3/s on longitudinal slopes no greater than 1°. Flows with viscosities of 1 Pa s are expected to have had a ready capacity for thermomechanical incision of at least meters per day, facilitated by the relatively high gravity and hot surface temperatures of Venus, and could have developed the channel system in as little as tens of days. System development by multiple discrete eruptive episodes separated by geological time is also possible. The

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volumes of effused lava most likely to have been required for development of Kallistos Vallis range from thousands to tens of thousands of cubic kilometers. The eruptive and flow conditions estimated for Kallistos Vallis agree with those previously determined for large ancient volcanic channels of other rocky bodies of the inner solar system, and attest to the remarkable differences between the predominant character of volcanism on modern Earth and that which prevailed on numerous rocky bodies during earlier episodes of solar system history.

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LIST OF TABLES 3.1 Estimated minimum channel depth ...... 46 3.2 Vertical exaggerations for individual cross-sectional profiles ...... 49 3.3 Distance, average slope, and vertical exaggeration calculations ...... 57 4.1 List of constants ...... 67

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LIST OF FIGURES 2.1 Angkor Vallis ...... 15 2.2 Oblique view of Vallis Schroteri ...... 17 2.3 Two westernmost channels of Rimae Prinz sinuous rille system ...... 18 2.4 Rimae Krieger ...... 19 2.5 Meandering lava channel exploration model for the Raglan Belt ...... 20 2.6 Conditions for genesis of komatiite-hosted Ni-Cu-(PGE) ores ...... 21 2.7 Large Venusian complex volcanic channel system ...... 23 2.8 Kinsei Vallis ...... 24 2.9 Venusian sinuous rill located within Lo Shen Valles ...... 25 2.10 Venus photomosaic ...... 26 2.11 Regional view of Kallistos Vallis ...... 27 2.12 Local view of Kallistos Vallis ...... 32 2.13 Kallistos Vallis sourcs regions ...... 33 2.14 Two channels flowing southeast of source region ...... 34 2.15 First anastomosing reach of Kallistos Vallis ...... 35 2.16 Second anastomosing reach of Kallistos Vallis ...... 35 2.17 Third anastomosing reach of Kallistos Vallis ...... 36 2.18 Distributary reach of Kallistos Vallis ...... 36 2.19 Distal reach of Kallistos Vallis ...... 37 3.1 Topographic overview of Kallistos Vallis ...... 42 3.2 Cross-sectional transects of Kallistos Vallis ...... 44 3.3 Cross-sectional profiles of Kallistos Vallis ...... 47 3.4 Radar vs. altimetry image of pixels with islands and shorelines ...... 51 3.5 Radar vs. altimetry image of pixels with adjacent shorelines ...... 53 3.6 Radar vs. altimetry image of pixels with streamlined islands ...... 54 3.7 Longitudinal segments of Kalistos Vallis ...... 55 3.8 Longitudinal profiles of Kallistos Vallis ...... 56 3.9 The area mask of Kallistos Vallis ...... 59 3.10 Kallistos Vallis bitmap for area calculations ...... 60

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4.1 Flow velocity rates ...... 68 4.2 Discharge rates ...... 69 4.3 Reynolds Numbers ...... 70 4.4 Mechanical incision rates ...... 71 4.5 Thermal incision rates ...... 73 4.6 Dynamic viscosity plots for mechanical/thermal incision rates ...... 74

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CHAPTER I

INTRODUCTION 1.1 General Overview Kallistos Vallis is one of the most complex and geologically important compound channels on Venus. Compound channels are characterized by both simple and complex segments (Baker et al., 1992). Previous studies of this system include those of Parker et al., (1991), Baker et al. (1992, 1997), Komatsu et al. (1993), Komatsu and Baker, (1996), Bougher et al. (1997), Bridges and McGill, (2002), and Komatsu, G, (2007). Although some argue there is scientific plausibility that some or all channels on Venus may be fluvial in origin (Jones and Pickering, 2003), it is widely accepted on the basis of the nature of the Venusian environment (in modern times and in the more distant geological past) that Venusian channels were formed through volcanic processes in exceedingly hot and dry environments (Parker et al., 1991; Baker et al., 1992; Komatsu et al., 1993; Komatsu and Baker, 1996; Bougher et al., 1997; Bridges and McGill, 2002; Komatsu, G, 2007). Observations of the channel show that it is characterized by many of the same types of geologic features, such as streamlined erosional residuals and complex anastomosing reaches, found in channels accepted by most to be of fluvial origin, including late-glacial diluvial systems on Earth and many of the Martian outflow channels (Baker et al., 1992; Bougher et al., 1997; alternative volcanic origins for the latter are discussed by e.g. Leverington, 2004, 2011, 2014, 2018, 2019ab, 2020; Baker, 2009; Hopper and Leverington, 2014; Baumgartner et al., 2015, 2017; Keszthelyi et al., 2017; Leone, 2017; Vetere et al., 2019). The further investigation of Kallistos Vallis has the potential to help us better understand how separate channel systems on different worlds can be formed through completely different mechanisms (volcanic vs. fluvial), yet still share many of the same types of morphological features. Investigation of large volcanic channels on Venus can additionally assist in shedding new light on the nature of past volcanic processes that have operated on Venus and within the inner solar system.

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1.2 Previous Studies Early work involving Magellan data included the preliminary identification and analysis of over 200 different valleys and channels on Venus (Head et al., 1991; Baker et al., 1992). This included the study of Kallistos Vallis, which at the time was not yet named, and only given the moniker of “The Outflow Channel” due to its similarity in appearance to many of the Martian outflow channels, including the presence of streamlined erosional residuals and complex anastomosing reaches (Baker, 1982). The results of Baker et al. (1992) provided an early geomorphologic description of the channel and surrounding region and initial inferences regarding the flow conditions and fluid compositions that might have been involved in channel development. The study of Baker et al., (1997) utilized low-resolution topography from the Magellan radar altimeter and high-resolution stereo radar images to generate cross-sectional and longitudinal profiles. Additionally, that study attempted to explain genetic processes involved in channel evolution including calculations of volcanic flow parameters. A detailed map of the Kaiwan Fluctus quadrangle, published by Bridges and McGill in 2002, includes a sub-section of the text focused on Kallistos Vallis, which helps to place this system into a greater regional context.

1.3 Purpose of Study The overarching scientific goals of this study are as follows: 1) to better characterize the basic morphological features and attributes of the Kallistos Vallis channel system; 2) to generate cross-sectional and longitudinal profiles of the system, and to determine the surface area of key parts of the system; 3) to use morphological information to better constrain possible eruptive and flow conditions involved in the formation of this system; and 4) to use these results to better understand and conceptualize the broader context and relevance of the Kallistos Vallis system within the inner solar system. Chapter 2 reviews the history of Venusian research, including an overview of early historical through modern-day observations. Also presented is an overview of

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past studies of Kallistos Vallis and associated regional geology. Analog channel systems of the inner solar system are also discussed. Chapter 3 explores the morphological charactistics of the Kallistos Vallis system, including cross-sectional profiles, longitudinal profiles, and surface area data. Chapter 4 presents inferences of the flow conditions and incision rates that may have been involved in the development of Kallistos Vallis. Chapter 5 gives crude estimates of the total volumes of lava that may have been required for formation of this channel system. Chapter 6 places the results of the present study in the context of previous studies of large volcanic channels of the inner solar system, and outlines possible routes for future research. Chapter 7 concludes by summarizing the key findings of this study.

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CHAPTER II

BACKGROUND 2.1 Overview of Early Historical Observations The first recorded observations of Venus were by the ancient Sumerians, who saw Venus as a single astronomical object and recorded its motion through the sky (Cooley, 2008). The planet was associated with a female deity known as Inanna (Black and Green, 1992; Nejat and Rhea, 1998; Cooley, 2008). The ancient Babylonians also observed Venus and viewed it as a single object which was supported by detailed astronomical observations (van der Waerden, 1974). The Greeks originally believed Venus to be two separate objects known as Phosphorus and Hesperus, and Pliny the Elder credited Pythagoras with the discovery that Venus was a single object (Healy, 1991). Conversely, Diogenes Laertius (a biographer of Greek philosophers), credited Parmenides as probably being responsible for the discovery (Burkert, 1972). In the second century, Ptolemy theorized that Venus was located between the Earth and the Sun (Goldstein, 1972). In the 11th-century, the transit of Venus was claimed to have been observed by the Persian astronomer Avicenna. Astronomers later considered this a confirmation of Ptolemy's theory. In the early 17th century Galileo Galilei observed Venus and found it showed phases like the Earth’s moon. This could only be possible if Venus orbited the sun, and this was a clear contradiction of Ptolemy’s geocentric model of the solar system (Palmieri, 2001). Jeremiah Horrocks accurately predicted and observed the 1639 transit of Venus (Kollerstrom, 2004). In 1761, the Venusian atmosphere was discovered by Russian scientist Mikhail Lomonosov (Marov, 2004). It was later observed in 1790, by the German astronomer Johann Schroter, who observed that when the planet was viewed as a thin crescent, the cusps extended beyond 180 degrees. This, he correctly postulated, would only be possible if sunlight was scattering through a dense atmosphere. This was further

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supported when American astronomer Chester Lyman observed a ring that encircled the dark side of Venus when it was at inferior conjunction (Russell, 1899). In the 20th century, spectroscopic, radar, and ultraviolet observations made it possible to probe different aspects of Venus that were previously hidden; these included atmospheric composition, planetary rotation rate, and the nature of the Venusian surface. In the 1920s, Frank E. Ross conducted the first ultraviolet observations of Venus. These observations made it possible to see cloud features that were not observable in the visible or infrared portion of the electromagnetic spectrum. Ross postulated these details resulted from of a dense, yellow lower atmosphere with high cirrus clouds circulating from above (Ross, 1928). Vesto Slipher conducted spectroscopic observations in the early 1900s. His goal was to measure Doppler shifts to determine the planet’s rate of rotation. Unfortunately, he was unable to detect any rotation and surmised the rotation period must be much longer than previously thought (Slipher, 1903). It was not until the 1950s that Venus was shown to have retrograde rotation. Finally, in the 1960s, the sidereal rotation period was determined via the use of radar observations (Goldstein and Carpenter, 1963). This measured value was close to the modern value of 243.025 Earth days (Williams, 2005), a value greater than the Venusian year (~225 days. As detailed in Section 2.2, it was not until the 1970s that ground-based radar was able to finally reveal geological features of the planet’s surface.

2.2 Modern Observations and Magellan Overview Beginning in the 1960s, Earth-based telescopes such as Haystack (Massachusetts), Goldstone (California), and Arecibo (Puerto Rico), were used to make radar observations of the Venusian surface. This produced primarily low- resolution images between 1-20 km/pixel as well as data pertaining to the scattering properties of the Venusian surface (Ford et al.,1993). Between 1978 and 1981, the U.S. Pioneer-Venus orbiter obtained radar images of the surface with a resolution of 30 km/pixel, and altimetry data with a footprint size of 100 km with an altitude

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accuracy of 100 m (Pettengill et al., 1980). Even though these observations did not cover the entirety of Venus (the poles were poorly covered), the data showed that the surface consists of approximately 8% highlands, 27% lowlands, and 65% rolling plains (Masursky et al., 1980). These data, combined with surface sample data, provided by Soviet landers Venera 8, 10, 13, and 14, were used to gain a better understanding of Venusian surface properties, topography, and tectonic evolution (McGill et al., 1983). Orbital Synthetic Aperture Radar (SAR) images of the Venusian surface were obtained between 1983 and 1984 by the Soviet Venera 15 and 16 spacecraft. This provided an image resolution of 1-2 km/pixel, covering approximately 25% of the planet’s surface. The corresponding altimeter footprint was 40-50 km with an accuracy of 50 m (Barsukov et al., 1986; Ford et al.,1993). These data revealed a variety of tectonic features including ridge-belts, domical uplifts, pronounced circular features (coronae), heavily deformed terrain (tesserae), and a variety of impact craters and plains (Barsukov et al., 1986). The results of these orbital-mapping, Earth-based imaging, and radar-altimetry observations clearly showed the need for near-global radar-altimeter coverage of the surface of Venus, at a resolution that was orders of magnitude greater than previously observed (Ford et al.,1993). This directly influenced planning for the Magellan mission by helping to determine not only the mission objectives, but also in the planning of mission operations and the type of onboard sensor systems required (Ford et al.,1993). On May 4th, 1989, the Magellan mission was launched aboard the Space Shuttle Atlantis, from Cape Canaveral, Florida. On August 10, 1990, the spacecraft entered a near-polar elliptical orbit around Venus. Magellan instruments began mapping the Venusian surface on September 15, 1990. The main goals of the mission were to image a minimum of 70% of the planet’s surface at a resolution of <300 m/pixel (Saunders et al.,1992) and to ascertain global topographic relief at a horizontal resolution of approximately 10 km/pixel, with a vertical accuracy of ≤ 80 m (Ford and Pettengill, 1992). Obtaining data at these resolutions makes it possible to facilitate the in-depth analysis of volcanic, tectonic, impact, and eolian features (Ford et al.,1993).

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The scientific objectives of the Magellan mission were to 1) understand and distinguish impact processes, 2) model the interior density distribution of the planet, 3) provide a global characterization of tectonic features and landforms, and 4) to explain and define deposition, erosion, and chemical processes (Ford et al.,1993). Magellan mission cycles 1, 2, and 3, which took place from September 1990 to September 1992, involved collection of data covering ~98% of the Venusian surface. This included detection of passive microwave thermal emissions, generation of SAR images, and measurement of backscatter power at small angles of incidence (Kumar and Head, 2013). Magellan mission cycles 4, 5, and 6, which took place between September 1992 and October 1994, involved collection of high-resolution gravity measurements. Operating at a wavelength of 12.6 cm (S-band), the SAR instrument used horizontal transmit and receive polarization to penetrate the Venusian cloud cover, thereby revealing wavelength-scale surface roughness (Kumar and Head, 2013). The catalogue of SAR image data and interpretation methods are given by both Ford et al., (1993) and Wall et al., (1995).

2.3 Venusian Geological and Physiographic Units The surface of Venus is characterized by regions of highlands and other topographic rises, separated by extensive lowlands characterized mainly by plains (Head et al., 1992; Ivanov and Head, 2011). Uplands of various types exist in places and consist of fold belts and related features, highland plateaus, and volcanic rises (Ivanov and Head, 2011). A large system of extensional chasmata exists on Venus (Ivanov and Head, 2011). The chasmata are large areas of young extensional structures that were formed after development of the regional and shield plains (Ivanov and Head, 2011). Volcanic landforms include small to large cones, including shields with sizes similar to those of the largest shields on Earth (Aubele and Slyuta, 1990; Guest et al., 1992; Head et al., 1992; Ivanov and Head, 2011; Ivanov and Head, 2013). The abundance of small volcanic cones ( ~100,000) greatly exceeds that of the larger of these features (~150) (Head et al., 1992).

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There are four different classes of Venusian volcano-tectonic landforms: coronae, arachnoids, novae, and calderas (Crumpler and Aubele, 2000; Ivanov and Head, 2013). Coronae, the most abundant volcano-tectonic features on Venus, are landforms that appear to have formed in direct association with mantle plumes; these features have dimensions of hundreds of kilometers, and are defined by extensional features of both radial and annular geometries (Barsukov et al., 1986; Pronin and Stofan, 1990; Head et al., 1992; Stofan et al., 1992; Crumpler and Aubele, 2000; Grinrod and Hoogenboom, 2006; Ivanov and Head, 2011; Ivanov and Head, 2013). Arachnoids are features outlined by broad, low topographic rims, and paired systems of structural lineaments that extend radially in opposite directions (Barsukov et al., 1986; Aittola and Kostama, 2000; Ivanov and Head, 2013). Novae are characterized by abundant radially-oriented tectonic structures, whose volcanic components are either absent or subdued (Krassilnikov and Head, 2003; Ivanov and Head, 2013). Venusian calderas are characterized by shallow, broad, topographic depressions that are encircled by concentric fractures (Crumpler and Aubele, 2000; Ivanov and Head, 2013). Vast expanses of volcanic plains exist on Venus (Ivanov and Head, 2011). Though regions of crustal shortening and extension/rifting exist, Venus lacks evidence for the past operation of Earth-like plate tectonics, and instead is viewed as a single- plate planet that has experienced its own style of global tectonics (Ivanov and Head, 2011). The aqueous and biological processes that have locked up substantial amounts of carbon in rocks on Earth have not operated on Venus, leading to the high CO2 content of the Venusian atmosphere (Ivanov and Head, 2011). In the absence of extensive and widespread information on Venusian lithologies and rock ages, geological units on Venus are mainly defined on the basis of physiographic properties, and the relative ages of units are determined on the basis of superposition and cross-cutting relationships (Ivanov and Head, 2011). Plains units are subdivided into lineated plains (dissected by numerous narrow lineaments), ridged plains (crossed by linear and curvilinear ridges), shield plains (characterized by the

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presence of numerous small volcanic shields with diameters of up to ~10 km) (Aubele and Slyuta, 1990; Guest et al., 1992; Head et al., 1992; Ivanov and Head, 2011), regional plains (smooth and homogeneous plains typically deformed by wrinkle ridges; these are the most wide-spread material units on Venus) (Bilotti and Suppe, 1999), smooth plains (featureless and tectonically undisturbed plains typically characterized by low levels of radar backscatter), and lobate plains (plains characterized by the presence of flow-like features that can be distinguished from each other on the basis of variations in radar albedo) (Ivanov and Head, 2011). Mountain belts are associated with the Lakshmi Planum region of Ishtar Terra, and consist of ridges that are densely packed, up to 15 km wide, and up to several hundred km long (Masursky et al., 1980; Pettengill et al., 1980; Barsukov et al., 1986; Head, 1990; Pronin, 1992; Ivanov and Head, 2011). Mountain belts resemble ridge belts, but with dissimilar topographic characteristics (e.g., mountain belts tend to be characterized by greater topographic relief than ridge belts) (Ivanov and Head, 2011). Groove belts consist of systems of extensional structures most typically composed of fractures and grabens (Wilhelms, 1990; Ivanov and Head, 2011). Tesserae are upland regions that show evidence of substantial tectonic disruption, including a minimum of two sets of intersecting structures (Barsukov et al., 1986; Bindschadler and Head, 1991; Sukhanov, 1992; Ivanov and Head, 2011). They are highly tectonically deformed terrain containing both extensional (fractures and grabens) and contractional (ridges) features (Ivanov and Head, 2011). Rift zones are characterized by dense zones of extensional structures associated with fissures and flat-floored troughs (Ivanov and Head, 2011). They can be up to tens of kilometers wide and up to several hundred kilometers long (Ivanov and Head, 2011).

2.4 Geologic Time Periods The geological history of Venus is divided into four periods of relative time: The Pre-Fortunian, Fortunian, Guineverian, and Atlian (Ivanov and Head, 2011). The cratering record of Venus indicates that the planet has been resurfaced in the last ~1

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Ga, either due to a geologically sudden set of catastrophic events of global extent, or a series of many smaller events that have cumulatively affected the entire surface (Romeo and Turcotte, 2010). This global resurfacing post-dates the Pre-Fortunian period, therefore making it impossible with the current datasets to discern past surface features and stratigraphic units. The observable history of Venus is confined to the Fortunian, Guineverian, and Atlian periods only. As documented in Ivanov and Head (2011), the observable geological periods of Venus are described as follows:

Fortunian Period The earliest phase of Venus’ observable history is marked by intense deformation and construction of regions of thicker crust (tesserae). The lower stratigraphic boundary is yet to be determined.

Guineverian Period This period is divided into two parts. The first part is characterized by the formation of regional interconnected groove belts, mountain belts, distributed deformed plains, and most of the coronae. The second part saw the global emplacement of wide-spread, mildly deformed, volcanic plains. This was followed by a period of global wrinkle ridge formation. It is estimated that 70% of the exposed Venusian surface was resurfaced during this time.

Atlian Period This period saw the construction of prominent rift zones and fields of lava flows. These lava flows show no modification by wrinkle ridges that are often associated with earlier formed coronae and/or large shield volcanoes. It is estimated that 16% of the exposed Venusian surface was resurfaced during this period. According to absolute age models, it is estimated the Atlian Period was twice as long as the Guineverian period. However, this period experienced significantly reduced rates of tectonic activity and volcanism. It is hypothesized that this volcanism may still be occurring today.

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2.5 Analog Channel Systems on Mercury, Earth, and the Moon Lava incision is not typically observed in modern terrestrial volcanic environments, and most modern volcanic channels on Earth are instead primarily constructional in nature however, under appropriate conditions, lava can incise into substrates through both thermal and mechanical processes to form erosional channel systems of various sizes and morphologies (Hulme, 1973, 1982; Greeley et al., 1998; Williams et al., 1998, 2001, 2004, 2011; Wilson and Mouginis-Mark, 2001; Leverington, 2004, 2011, 2014, 2018, 2019ab, 2020, in press; Hurwitz et al., 2010, 2012; Hopper and Leverington 2014; Vetere et al., 2017, 2019; Gallant et al., 2020). As indicated by geochemical data collected from the Russian Vega and Venera landers, the surface of Venus is anhydrous in nature (Surkov, 1983; Kargel et al., 1993, 1994). This, and the extraordinarily hot conditions that have likely dominated on Venus over extended geological timescales, would preclude Venusian channel formation by any means other than volcanism, except possibly during the earliest history of the planet (a time frame that is not represented in the preserved geological record of the planet). It is thus generally accepted that channels on Venus were formed via volcanic (not fluvial) mechanisms. To better understand the nature of channel development, and to thereby illuminate important aspects of the general characteristics of Venusian volcanism, it is important to explore the physical parameters and conditions that might have been required for channel incision. To do so, we first look to other analog systems within the inner solar system for physical clues to what these erosional processes involved. The most important properties used to determine the capacity of lavas to incise include the following: 1) the physical nature of the lava, including its viscosity, temperature, chemical composition, crystal content, volatile content and yield strength; 2) the temperature and composition of the underlying substrate; 3) the turbulence of the flow (Reynolds number); 4) the slope (gradient) of the flow downstream from the channel source; 5) the rates of effusion and the total volume of erupted material; and 6) the nature of the flow cover, including the presence or absence of an overlying crust (Hulme,1973; Williams et al., 1998; Leverington

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2007, 2011; Hurwitz et al., 2010, 2012; Jaeger et al., 2010; Hopper and Leverington, 2014; Leverington 2014, 2018, 2019ab, 2020, in press). Generally, a lava’s ability to incise will increase with higher temperatures, higher turbulence, lower viscosities, steeper topographic gradients, and higher rates of discharge (Hulme, 1973, 1982; Pinkerton et al., 1975; Hulme and Fielder, 1977, Bussey et al., 1995; Williams et al., 1998; Hurwitz et al., 2010, 2012; Leverington, 2011, 2018, 2019ab, 2020, in press; Hopper and Leverington, 2014). Flows with Reynolds numbers below 1000 are generally characterized by laminar flow conditions, and will exhibit lower velocities and higher viscosities; however, it’s not unusual for the dividing line between laminar and turbulent flow to more conservatively be treated as falling between ~2000 and 15000 (Hulme, 1973; Williams et al., 1998; Hurwitz et al., 2010; Hurwitz and Head, 2012). It is therefore expected that Reynolds numbers associated with vigorous lava incision will be in the tens of thousands to millions, which indicate fully turbulent flow. Flows characterized by turbulence levels capable of promoting vigorous incision are expected to have higher velocities and lower viscosities (Hulme, 1973; Williams et al., 1998; Hurwitz et al., 2010, 2012). The most common lava types found within the inner solar system that are capable of highly turbulent flows are those that possess mafic to ultramafic chemistries (Murase and McBirney, 1970; Hulme, 1973; Huppert et al., 1984; Head and Wilson, 1992; Williams et al., 1998; Keszthelyi et al., 2006; Chevrel et al., 2013, 2014; Hurwitz et al., 2013ab; Leverington, 2014; Vetere et al., 2017, 2019; Peplowski and Stockstill-Cahill, 2019). Carbonatite lavas, with lower eruption temperatures of only ~500 C, can have viscosities that are several orders of magnitude lower than modern terrestrial basalts (Zimbelman and Gregg, 2000). However, carbonatites are relatively rare and thus not typical of most volcanic eruptions that have occurred within the inner solar system, and are unlikely to have caused volcanic incision on planet-wide scales. By studying the morphologies of terrestrial, Martian, Mercurian and lunar analog systems, we can indirectly discern aspects of the physical conditions most likely to have been responsible for volcanic incision on these bodies. Furthermore,

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remote sensing data and the in situ sampling of geological units can provide direct information on the type(s) of lava extruded during channel formation on these bodies. This morphological and compositional information can help to guide aspects of quantitative modeling of channel development in the inner solar system. Figures 2.1 - 2.6 depict channels located on Earth, Mercury and the Moon that are widely interpreted to have formed via the eruption of low-viscosity magmas (Oberleck et al., 1969; Greeley, 1971; Cruikshank and Wood, 1972; Schultz, 1976; Wilhelms, 1987; Bougher et al., 1997; Head et al., 2011; Williams et al., 2011; Gallant et al., 2020). Surface conditions present on the Moon and Mercury throughout most of our solar system’s history are very likely to have been incompatible with aqueous flow (Baker et al., 1992; Papike et al., 1991; Wilhelms, 1997; Head et al., 2011). Both Mercury and the Moon lack meaningful atmospheres today, and are very unlikely to have had substantial atmospheres over most of their histories, creating surface environments that would have caused liquid water to quickly boil. Long-term dry conditions on the Moon have resulted in the near absence of aqueous minerals such as clays, gypsum, or amphiboles in lunar geological samples (Papike et al., 1991). Orbital data from Mercury MESSENGER (the MErcury Surface, Space ENvironment, GEochemistry, and Ranging mission) similarly indicate the widespread presence of pristine anhydrous materials (Head et al., 2011; Peplowski and Stockstill-Cahill, 2019; Thomas and Rothery, 2019).

2.5.1. Mercurian Channels Angkor Vallis (Figure 2.1) is one of ten large volcanic channel systems located in Mercury’s high northern latitudes. This system is approximately 85 km in length and exceeds 30 km in width at what appears to be the mouth of the system. This is similar in width to multiple other Mercurian systems, such as Paestum Vallis (~20 km) and Timgad Vallis (~25 km) (Byrne et al., 2013). It exhibits morphologies similar to those seen at channels of the Moon and Venus, including streamlined islands, and a depositional plain comprised of smooth plains materials comprised of lava flows that

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embay pre-existing topography (Head et al., 2011). Impact craters that are covered but can still be identified as a result of later lava subsidence, also known as “ghost craters”, have properties suggesting multiple phases of emplacement by volcanic plains materials (Head et al., 2011). This is evidenced by the appearance of smaller ghost craters found within the interior of the smooth plains that are believed to have post-dated the initial phases of flooding (which buried older craters), then were buried by later stage flooding (Head et al., 2011). Morphometric relations between ghost craters and mantling lava flows indicate that plains units should have local thicknesses in excess of 1 km (Head et al., 2011). MESSENGER X-ray spectrometer (XRS) data indicate that mafic and ultramafic compositions are very common at the surface of Mercury (Head et al., 2011). Such compositions are broadly consistent with inferences of channel formation by low-viscosity flood lavas through thermomechanical processes (Head et al., 2011; Byrne et al., 2013; Hurwitz et al., 2013b; Sehlke and Whittington, 2016; Vetere et al., 2017; Peplowski and Stockstill-Cahill, 2019; Thomas and Rothery, 2019).

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Figure 2.1 The Angkor Vallis channel system of Mercury is approximately 85 km in length and has a maximum width that exceeds 30 km. The channel apparently flowed from northwest to southeast, connecting low-relief lava plains that mantle impact basins including the Kofi Basin in the southeast (Head et al., 2011; Byrne et al., 2013; Hurwitz et al., 2013b). It is estimated that maximum lava effusion rates of at least were involved in channel development (Byrne et al., 2013). White arrows mark elongate hills whose orientations suggest possible formation as erosional residuals (Head et al., 2011). The above image is a mosaic of images EW0261568757G, EW0246417788G, and EW0231221923G, all acquired by the Wide Angle Camera onboard the Mercury MESSENGER spacecraft. Figure is centered at 57.7 N, 113.8 E, with illumination from the right.

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2.5.2. Lunar Channels The majority of the more than 200 lunar volcanic channel systems are characterized by sinuous conduits that flow downslope from topographic depressions (source regions), and empty into flat-floored basins that are mantled by ridged volcanic units (Gornitz, 1973; Guest and Murray, 1976; Head, 1976; Schultz, 1976; Wilhelms, 1987; McEwen et al., 1994; Hurwitz et al., 2010, 2013a). The largest of these systems are located in the Aristarchus region, which includes the Aristarchus Plateau, a raised ~170  200 km plateau located near the southwestern margin of the Mare Imbrium basin and residing inside the easternmost reaches of Oceanus Procellarum (Shultz, 1976; Wilhelms, 1987; McEwen et al., 1994). Common morphological attributes of lunar volcanic outflow systems include the following: 1) low channel order or a complete absence of tributaries; 2) inner channels; 3) streamlined erosional residuals; 4) anastomosing reaches; and 5) reaches containing chemical and morphological properties consistent with thermal and mechanical erosion by lava (Howard et al., 1972; Gornitz, 1973; Carr, 1974; Schultz, 1976; Strain and El-Baz, 1977; Wilhelms, 1987, Leverington 2004, 2009, 2011; Bleacher et al., 2010). Three examples of the channel systems associated with the Aristarchus Plateau region include Vallis Schröteri (Figure 2.2), Rimae Prinz (Figure 2.3), and Rimae Krieger (Figure 2.4). Vallis Schröteri, at 4.3 km wide, is the widest recognized lunar volcanic channel. The source region of this channel system is a topographic depression located north of crater Herodotus (Leverington, 2011; Hurwitz et al., 2013). The main channel extends northward, turns west, and then turns southwest, and is apparently incised into the Aristarchus Plateau (Wilhelms, 1987; Garry and Bleacher, 2011; Hurwitz et al., 2013). The inner channel, whose average depth is ~120 m below adjacent uplands, is highly sinuous, and extends beyond the walls of the main outer valley and fades into the volcanic plains of Oceanus Procellarum (Garry and Bleacher, 2011; Hurwitz et al., 2013).

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Figure 2.2 Oblique view of Vallis Schröteri, the widest and deepest sinuous rille on the Moon, has a width of ~4.3 km, an average depth of ~534 m below the adjacent uplands, and length of ~150 km (Hurwitz et al., 2013). The source region (S) is a topographic depression located north of Herodotus, a 35 km diameter crater (Leverington, 2011). Apollo 15 Metric camera image (AS15-M-2612) centered at 25.5 N, 51.5 W. Illumination is from the left.

Rimae Prinz, at an average width (per channel) of ~3 km, is a four-channel system located northeast of the Aristarchus Plateau and north of crater Prinz. Morphologically, the individual channels comprising the system are similar to Vallis Schröteri, but smaller. Running from west to east, the second channel in the system incises across a hill feature (H) (Figure 2.3) which indicates topographic (possibly structural) control of channel position, or an incision process that began before the regional subsidence of related mare materials.

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Figure 2.3 The two westernmost channels of the four-channel Rimae Prinz sinuous rille system. These channels have source regions (S) that are marked by topographic depressions, and the channels extend from these sources to the west before they turn southward. The easternmost of these two channels incises across a hill feature (H), which suggests topographic (and possibly structural) control of channel position, or an incision process that began before the regional subsidence of related mare materials (Greeley and Spudis, 1978; Leverington, 2004). Apollo 15 Hasselblad frame (AS15- 9312608) centered at ~27 N, 44 W. Illumination is from the left.

Rimae Krieger is a lunar sinuous rille located north of the Aristarchus Plateau that extends westward from a breach in the wall of Krieger crater. It is an example of a lunar volcanic channel that contains streamlined islands, a type of morphological feature normally considered to be indicative of the past action of fluvial or diluvial

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processes. Each of the two observed islands have long-axis dimensions of ~1-2 km (Leverington, 2004).

Figure 2.4 Rimae Krieger is a lunar sinuous rille that extends westward from a breach in the wall of Krieger crater, located in lowlands adjacent to the Aristarchus Plateau region (Carr, 1974). Arrows indicate streamlined islands located within the main channel (Leverington, 2004). Apollo 15 panoramic frame (324), centered at ~29 30 N, 46 30 W. Illumination is from the right.

2.5.3. Terrestrial Channels The Proterozoic-aged Cape Smith Belt and Archean-aged Perseverance ultramafic complex of Western Australia are examples of areas where submarine volcanic channel systems formed via the eruption of ultramafic (komatiitic basalt) lavas with initial eruption temperatures as great as ~1400 to ~1600C, minimum viscosities of 0.1 to 1 Pa s, peak discharges approaching or in excess of 106m3/s, and highly turbulent flow conditions (Williams et al., 1998, 2001, 2011). These channel systems, whose individual properties and sizes are similar to those of lunar rilles, are closely associated with some of the largest Ni-Cu-(PGE) deposits on Earth (Williams et al., 1998, 2001, 2011). A prime example is found at the Katinniq member of the

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Raglan Formation, at the base of the Chukotat group, Cape Smith Belt, Quebec, Canada (Figure 2.5) (Williams et al., 2011).

Figure 2.5 Meandering lava channel exploration model for the Raglan Belt ores, taken from Green and Dupras (1999), Lesher (2007), and Williams et al., (2011).

The lavas here had an especially high capacity for thermomechanical incision, thereby allowing for assimilation of both substrate materials (at channels) and materials adjacent to intrusions (within plumbing systems) (e.g., Huppert and Sparks, 1985b; Williams et al., 1998; Stone and Stone, 2000; Fiorentini et al., 2007; Ding et al., 2012; Barnes et al., 2018; Jaroka et al., 2019; Vetere et al., 2019). Sulfides contained in assimilated materials reacted with metals in the channelized lavas to produce the Ni- Cu-(PGE) ore deposits that we see today (e.g., Huppert and Sparks, 1985a; Groves et al., 1986; Lesher and Campbell, 1993; Williams et al., 2001, 2011; Arndt et al., 2005; Barnes, 2006; Baumgartner et al., 2015, 2017; Barnes et al., 2016; Le Vaillant et al., 2016; Barnes and Robertson, 2019) (Figure 2.6).

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Figure 2.6 Schematic illustration (Leverington, in press; after Le Vaillant et al., 2016), that shows the conditions and processes inferred to have been involved in the genesis of komatiite-hosted Ni-Cu-(PGE) deposits at large terrestrial volcanic channels of the Archean and Paleoproterozoic. Turbulently flowing komatiite lava assimilates sulfide-rich substrates, resulting in the creation of sulfide mineral ore deposits (e.g., pentlandite) at the base of associated channels.

2.6 Channel Systems on Venus As with bodies such as Mercury and the Moon, Venus is associated with numerous examples of channel systems believed to have formed via thermal and mechanical incision by low-viscosity lavas (Hess and Head, 1990; Baker et al., 1992, 1997; Head et al., 1992; Komatsu et al., 1993; Komatsu and Baker, 1994; Basilevsky and Head, 1996; Komatsu, 2007; Leftwich et al., 1999; Oshigami and Namiki, 2007). Many of these channel systems have morphological traits comparable to multiple types of observed lunar and Mercurian systems. The Venusian channel systems include complex channels (Figure 2.7), the canali (Figure 2.8) and sinuous rills (Figure

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2.9). The associated traits of Venusian channels include: 1) inferred mafic to ultra- mafic lava composition, though more exotic fluids such as carbonatites and liquid sulfur have also been previously hypothesized; 2) typical channel lengths of tens to thousands of kilometers, with channel widths up to several tens of kilometers; 3) source regions defined by prominent topographic depressions; 4) typical presence of simple meandering low-order trunk channels; 5) presence of streamlined erosional residuals at some systems; 6) presence of complex anastomosing reaches at some systems; 7) channel termini at depositional plains apparently mantled by lava flows; and 8) apparent evidence for at least partial channel development via substantial erosional processes (Hess and Head, 1990; Baker et al., 1992, 1997; Head et al., 1992; Kargel et al., 1993, 1994; Komatsu et al., 1993; Komatsu and Baker, 1994).

2.6.1. Compound and Complex Channels The most important channel systems on Venus, from the perspective of this study, are the large compound and complex channels, which are (in part) morphologically similar to both Kallistos Vallis (a compound channel), and the Martian outflow channels. These channels share characteristics such as the following: 1) source regions defined by large collapse features and chaotic terrain; 2) channel widths  30 km; 3) medium to large streamlined islands separated by complexly anastomosing sub-channels and reaches; 4) system mouths terminating at extensive volcanic depositional plains; and 5) (for compound channels) segment that share morphologies found in simple channel systems (Baker et al., 1992; Komatsu et al., 1993). One such Venusian system, (Figure 2.7) is a large complex system located northeast of Ozza Mons in Aphrodite Terra. It exhibits both the streamlined erosional residuals and the anastomosing reaches typical of compound systems such as Kallistos Vallis, but without the presence of simple segments. The long-axis dimensions of some of the streamlined residuals exceed ~25 km, with maximum residual widths at least as great as 15 km (Komatsu et al., 1993; Leverington, 2007; Leverington, 2011).

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Figure 2.7 Large Venusian complex volcanic channel system located northeast of Ozza Mons, in eastern Aphrodite Terra (Komatsu et al., 1993; Leverington, 2007). Flow along the central part of the depicted system is northward. The system exhibits an anastomosing character that is associated with numerous streamlined islands. Channel segments are variously radar-smooth (dark) and radar rough (bright). Image is a Magellan FMAP left-look SAR mosaic. Radar illumination is from the left. Imaged area is centered at 11.6 N, 211.6 E.

2.6.2. Canali The Venusian canali, which are typically > 500 km in length (Baker et al., 2000) are relatively simple channels, morphologically similar to many lunar systems, but are characterized in some cases by extreme lengths. These systems exist almost entirely on broad mare-like volcanic plains (Baker et al., 1992, 1997; Head et al., 1992). A prime example of this is Baltis Vallis, which at 6800 km is the longest known channel of any kind in the solar system (Baker et al., 1992; Basilevsky and Head, 1996; Leftwich et al., 1999; Oshigami and Namiki, 2007; Komatsu, 2007).

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Figure 2.8 Kinsei Vallis is a Venusian canali-type channel. Channel width is ~10 km, which is unusually wide for a volcanic channel of this type. Wide canali do not typically show observable depth, but do retain the same regional distribution as many of the narrower types (Komatsu et al., 1993). Radar illumination is from the left. Imaged area is located between 12-16 N and 137-143 E.

2.6.3. Sinuous Rilles Sinuous rilles are the most abundant and widely distributed type of channel on Venus and share morphological characteristics with sinuous rilles found on the Moon (Baker et al., 1992, 1997; Oshigami et al., 2009). The morphological characteristics of Venusian rilles include the following: 1) source depressions; 2) narrow sinuous reaches with total lengths ranging from tens of kilometers to several hundred kilometers; 3) often occur in close proximity to, or connection with, Venusian valley networks (integrated networks forming a complex system of first and second order branching valleys); 4) channel floors that are clearly at a lower elevation than surrounding plains, suggesting in some cases (but not all) possible erosional origins, especially where channels cross upland terrain; and 5) decreasing depth trends towards channel termini, that are in agreement with laboratory and theoretical models for thermal erosion (Oshigami et al., 2009).

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Figure 2.9 Venusian sinuous rille that forms part of Lo Shen Valles, a system of channels and collapsed source areas. Parts of this channel cut across tesserae terrain of Aphrodite Terra (Komatsu and Baker, 1994). Channel morphologies here suggest the past operation of volcanic erosional processes, at least where the channel crosses tessera uplands. Radar illumination is from the left. Imaged area is centered at 13 S, 89 W.

2.7 Regional Geologic Setting of Kallistos Vallis Kallistos Vallis is located within two separate mapped Venusian quadrangles and lies just adjacent to a third (Figures 2.10 and 2.11). The northernmost section containing the source or head of the channel is in the Kaiwan Fluctus Quadrangle (V- 44) (Bridges and McGill, 2002), whereas the southern anastomosing reaches and channel terminus lies in the Lada Terra Quadrangle (V-56) (Kumar and Head, 2013). Agnesi Quadrangle (V-45) (Hansen and Tharalson, 2014), which lies east of Kaiwan

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Fluctus Quadrangle and north of Lada Terra Quadrangle, is included for regional context.

Figure 2.10 Venus photomosaic modified from Kumar and Head (2013) and showing the location of relevant quadrangles (highlighted in blue) encompassing Kallistos Vallis and the surrounding region. Map scale is 1:5,000,000.

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Figure 2.11 Regional view encompassing the Kallistos Vallis outflow channel (Magellan FMAP left-look SAR mosaic). SAR illumination is from the left and centered on Kallistos Vallis at 50°S, 21°E (main channel is marked with white arrows). The mapped area extends from -40˚S to -60˚S and 6˚E to 36˚E. As a part of the volcanic province of Ammavaru, Kallistos Vallis is located in both the Kaiwan Fluctus (Bridges and McGill, 2002) and Lada Terra Quadrangles (Kumar and Head, 2013). The system is located near four coronae; Derceto Corona to the north, Otygen Corona to the southeast, and Sarpanitum Corona and Eithinoha Corona to the southwest. To the northeast corner of the regional map, between -40˚S to -50˚S and 30˚E to 36˚E, lies the Agnesi Quadrangle (Hansen and Tharalson, 2014). Although there are no reaches of Kallistos Vallis that extend into Agnesi Quadrangle, it is close enough to be included for regional context. The source (S) marks the head of Kallistos Vallis. The channel terminus is widely mantled by extensive radar-rough lava flows (F) (Baker et al., 1992; Leverington, 2011). Rectangular coordinate system.

The Kaiwan Fluctus Quadrangle is located between 25° to 50° S latitude and 0° to 30° E longitude. It is bordered by Lada Terra Quadrangle (V-56) in the south and Agnesi Quadrangle (V-45) in the east. The material units found within Kaiwan Fluctus Quadrangle are separated into five groupings of geological features that are all defined

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as relative age related structures: 1) flow materials; 2) volcanic construct materials; 3) plains materials; 4) belt and tessera materials; and 5) materials of impact craters (Bridges and McGill, 2002). The northwestern section is dominated by Alpha Regio, an approximately Greenland-sized block of tessera with pronounced topography rising 3 km above the surrounding plains (Bindschadler et al., 1992). The southeastern to south-central section contains Astkhik Planum, which rises a few hundred meters above the adjacent plains (Baer et al., 1994) and whose southwest margin is bounded by tessera material. The northern and eastern edges of Astkhik are surrounded by a belt of troughs and ridges whose slope is oriented away from the plateau into a topographic moat (Bridges and McGill, 2002). There is a total of seven coronae within the Kaiwan Fluctus Quadrangle, of these, five are part of a larger extensional belt that continues southward into Lada Terra Quadrangle: Derceto, Carpo, Eve, Selu and Tamfana (Baer et al., 1994). Within Kaiwan Fluctus, lineated regional plains material surrounds Kallistos Vallis (Bridges and McGill, 2002). The northern ~250 km section of Kallistos Vallis begins in the south-central region of Kaiwan Fluctus Quadrangle at 47.5° S. and southward, 19° to 20° E. It consists of a collapse pit at its head, south of which runs an apparently structurally-controlled and deep trough. This trough consists of straight segments that parallel regional structural trends along Astkhik Planum’s margin (Bridges and McGill, 2002). The Lada Terra Quadrangle is located between 50° to 70° S. latitude and 0° to 60° E. longitude (Kumar and Head, 2013). It is bordered in the north by both Kaiwan Fluctus (V-44) (Bridges and McGill, 2002) and Agnesi (V–45) (Hansen and Tharalson, 2014). The material units found within the Lada Terra Quadrangle are separated into three groupings of relative-age-related structures: 1) heavily deformed materials such as tesserae, tessera-like terrain, or densely lineated terrain; 2) wrinkle ridged and regional plains; and 3) volcanic plains materials originating from coronae or shield structures (Kumar and Head, 2013). Located at high southern latitudes, Lada Terra Quadrangle is a wide region of terrain of moderate elevation situated 0 to 2 km above mean planetary radius (MPR). Its western area is dominated by a dome shaped

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structure that is ~2000 km across (Kumar and Head, 2013). Surrounding the western section of Lada Terra Quadrangle lies a vast lowland that is ~1 to 1.5 km below MPR known as Lavinia Planitia (Kumar and Head, 2013). Lada Terra Quadrangle contains numerous coronae including Quetzalpetlatl, one of the largest coronae on Venus (Stofan et al., 1992); these coronae are connected via a series of belts of fractures and grabens (Baer et al., 1994). Some of the most stunning morphological features of Lada Terra Quadrangle are the large complexes of lava flows that emanate from the various coronae. These coronae include the following: 1) Quetzalpetlatl, Sarpantium, and Eithinoha (concentric coronae); 2) Otogen (double ringed corona); 3) seven asymmetric coronae including Derceto, Toyo-uke, and Demvamvit; and 4) Loo-Wit Mons (an astra-like structure) (Stofan et al., 1992). The southern reaches of Kallistos Vallis located within the Lada Terra Quadrangle run for ~950 km. The system lies northwest of Otygen Corona and northeast of Eithinoha Corona (Hopper and Leverington, 2014). Agnesi Quadrangle is located between -40˚ to -50˚S latitude and 30˚ to 36˚E longitude. It is bordered in the west by Kaiwan Fluctus Quadrangle (V-44) (Bridges and McGill, 2002) and in the south by Lada Terra Quadrangle (V-56) (Kumar and Head, 2013). The material units found within Agnesi Quadrangle are separated into three groupings of geological features that are all defined as relative-age related structures: 1) crater material; 2) flow and deposit material; and 3) ribbon tessera terrain material and related units (Hansen and Tharalson, 2014). The region, which is named for the centrally located Agnesi crater, has an average altitude of ~6,052 km, which is approximately equivalent to MPR (Hansen and Tharalson, 2014). Agnesi Quadrangle lies in a lowland region situated between the highlands of Alpha Regio in the west, and Ovda Regio in the northeast (Hansen and Tharalson, 2014). Agnesi Quadrangle contains a wide variety of features to include 13 perfectly preserved impact craters, 10 lowland coronae, 2 montes, small to large arcuate exposures of ribbon-tessera terrain, and long localized volcanic flows that originate in Kaiwan Fluctus to the west (Hansen and Willis, 1998; Hansen, 2005). Shield terrain is

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commonplace across most of Agnesi Quadrangle (Hansen, 2005). Since Agnesi Quadrangle is in the topographic lowlands, it contains only one large plains region, which is known as Fonueha Planitia (Hansen, 2005). As detailed in Hansen and Tharalson (2014), the geologic mapping of the Agnesi Quadrangle was useful in helping to understand the nature of lowland vs. highland ribbon tessera terrain, as well as understanding the history and nature of lowland montes and coronae. This was also helpful in evaluating hypotheses for not only the evolution of these features, but for hypotheses related to instances of global catastrophic resurfacing. Since Agnesi Quadrangle lies in such close proximity to Kallistos Vallis, its geology may have had some influence in the geological formation of the channel system. This influence is still yet unknown an may require future missions and acquired datasets to discern.

2.8 Overview of Kallistos Vallis Kallistos Vallis is a Venusian compound channel that is ~1200 km in length and up to ~30 km in width (Figure 2.12). Located within the Ammavaru volcanic province, it is widely accepted to be of volcanic origin (Parker et al., 1991; Baker et al., 1992; Komatsu et al., 1993; Komatsu and Baker, 1996; Bougher et al., 1997; Bridges and McGill, 2002; Komatsu, G, 2007), although, aqueous origins cannot strictly be ruled out based on channel morphology alone (Baker et al., 1992; Jones and Pickering, 2003). Centered at 49°14′ S, 22°20′ E, the system is located within two separate mapped Venusian quadrangles; Kaiwan Fluctus, which encompasses its northernmost reaches (Bridges and McGill, 2002), and Lada Terra in the south (Kumar and Head, 2013). Early observations and analyses of Magellan radar data, documented in Parker et al. (1991), Baker et al. (1992), and Baker et al. (1997), show Kallistos Vallis to be smaller but morphologically similar to the Martian outflow channels. Kallistos Vallis can be separated into three separate sections or reaches: 1) a source reach comprised of a collapse pit (chaotic terrain) and a structurally-controlled trough; 2) a middle anastomosing reach; and 3) a distal distributary reach. The source

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of the channel is located on the southwest flank of a volcanic complex near Derceto Corona, and is marked by a collapse feature approximately 17.5 km wide, 31.3 km long, and over 400 m in depth relative to adjacent terrain (Figure 2.13). This collapse feature has similar morphologies to the collapsed terrains that exist at the heads of numerous Martian outflow channels. A deep and possibly structurally-controlled trough, 380 km long, 4 km wide, and over 600 m in depth, extends from the collapse pit and might have contained most of the channelized fluid flow for the first 275 km, where it then branched off into a second channel that transmitted a portion of the initial flow. This second channel is roughly parallel to the main channel and is both shallower and mostly narrower than the main flow. This reach is located to the east of the trough, is approximately 300 km long and 1 km wide (Figure 2.14), and is morphologically similar to Venusian canali. The second reach of Kallistos Vallis is 300 km in length and exhibits morphologies such as anastomosing reaches and streamlined erosional residuals of the types typically associated with terrestrial fluvial channel systems (Figures 2.15 - 2.17). The floors of this reach show variations in roughness evidenced by radar brightness ranging from dark to light. The third reach of the channel system is intersected by a ridge known as Vaidilute Rupes that trends from north to south (Figures 2.18 and 2.19). To the west of the ridge, the channel separates, spreading out into three main “finger like” series of distributary channels with radar bright lobate margins (Figure 2.18). These lobate deposits appear to have spread laterally on both sides of each distributary channel. The main channel continues for several hundred more kilometers until it terminates at Ubastet Fluctus, a depositional plain located to the east of the Vaidilute Rupes ridge (Figures 2.18 and 2.19).

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Figure 2.12 The Kallistos Vallis system (white arrows) is a ~1200 km long Venusian outflow channel (figure from Hopper and Leverington, 2014; see also Baker et al., 1992; Leverington, 2009). The source of the system (S) is marked by an area of chaotic terrain that collectively forms a large topographic depression. It is from this depression that the channel extends southward and then eastward to its lower reaches. Along its middle reaches, the channel system widens and complexly anastomoses about numerous streamlined erosional residuals (R) (Baker et al., 1992; Leverington, 2011). The channel system terminates in extensive lava flows, some of which are radar-rough (F). Magellan FMAP left-look SAR mosaic. SAR illumination is from the left. Figure is centered at 49°14′ S, 22°20′ E.

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Figure 2.13 The Kallistos Vallis source regions (S) can be subdivided into two main parts: the first northernmost source is marked by an area of chaotic terrain that collectively forms a large topographic depression. It is a collapse feature ~17.5 km wide, ~31.3 km long, and ~400 m deep (Baker et al., 1992). The second source area lies to the southwest and is the northernmost section of the main trough. It is connected to the chaotic terrain source and may have acted as an initial and/or additional flow source (Baker et al., 1992). Magellan FMAP (full-resolution map) left- look SAR mosaic. SAR illumination is from the left.

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Figure 2.14 Two separate channel reaches flowing in a southeasterly direction from the Kallistos Vallis source region (S). The primary channel (white arrows) appears to be a structurally controlled trough that is ~380 km long, ~4 km wide and over 600 m in depth (Baker et al., 1992). To the northeast of the primary channel lies a secondary channel (red arrows), that is ~300 km long and ~1 km wide (Baker et al., 1992). It terminates downstream, failing to reconnect with the primary channel. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

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Figure 2.15 The first segment of the anastomosing reach of Kallistos Vallis. Here it widens and complexly anastomoses about numerous streamlined erosional residuals (R) (Baker et al., 1992). Variations in roughness are suggested by variations in radar brightness. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

Figure 2.16 The second segment of the anastomosing reach of Kallistos Vallis (streamlined erosional residuals are designated R) (Baker et al., 1992). White arrows indicate the eastward flow path of the primary channel. Red arrows indicate the path of a secondary channel which splits off of the primary channel and extends to the southeast. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

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Figure 2.17 The third segment of the anastomosing reach of Kallistos Vallis. White arrows indicate path of primary channel. Red arrow show path of secondary channel as it turns to the northeast linking back up with the primary flow. Streamlined erosional residuals are designated with R. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

Figure 2.18 The distributary reach of Kallistos Vallis, where the channel separates into three prominent distributary channels. Associated with these channels are lava flows (F) that in places are distinctly radar bright and that possess in places sharp lobate margins. These flows appear to expand laterally where a north-south ridge was encountered (Baker et al., 1992). One of the distributary channels (black arrows) continues northeastward for several hundred kilometers (Figure 2.19). Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

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Figure 2.19 The most distant reach of Kallistos Vallis extends across a low point in the north-south oriented ridge component of Vaidilute Rupes and disappears into a depositional plain located immediately east of the ridge. The lava flows of this region form part of the broader Ubastet Fluctus unit. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left.

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The morphology of Kallistos Vallis is strongly suggestive of channel formation as a result of past voluminous effusions of low-viscosity fluids (Baker et al., 1992, 1997, 2000; Kargel et al., 1994; Parker et al. 1995; Komatsu and Baker, 1996; Komatsu, 2007). Thus, the study of Kallistos Vallis is of considerable importance as it has the potential to shed light on numerous aspects of Venusian volcanism, and broader aspects of volcanism in the inner solar system. Since there are no mineralogical data specifically available for Kallistos Vallis, the nature and rheology of the flows involved in the development of this system must be crudely inferred based on the morphologies of local channel landforms, the mineralogy of sites located elsewhere on Venus, and the nature of materials associated with analog volcanic systems on other rocky bodies (Hess and Head, 1990; Baker et al., 1992; Kargel et al., 1993; Hurwitz et al., 2010, 2012; Leverington, 2014; Ashley and Ramsey, 2019). The results of numerous previous studies of large volcanic flows and channels of the inner solar system (e.g., Hulme,1973, 1982; Hulme and Fielder, 1977; Kargel et al., 1993; Williams 2001, 2011; Hurwitz et al., 2010, 2012; Ivanov and Head, 2013; Chevrel et al., 2014; Dundas and Keszthelyi, 2014; Baumgartner 2017; Leverington, 2018, 2019ab; Ashley and Ramsey, 2019; Dundas et al., 2019) are available for use in the inference of flow properties most likely involved in the development of Kallistos Vallis. Sites examined by the Vega and Venera programs were found to be characterized by anhydrous mafic materials (Surkov, 1983; Kargel et al., 1993; Hurwitz et al., 2010, 2012; Ashley and Ramsey, 2019). Previous studies have suggested that the Venusian channels could conceivably have formed as a result of the flow of lavas or liquids including tholeiite, olivine nephelenite, komatiite, sulfur, or carbonatite (e.g., Baker et al., 1992; Komatsu et al., 1992; Gregg and Greeley, 1993; Kargel et al., 1994; Lang and Hansen, 2006). Flows comprised of sulfur or carbonatites are relatively rare and are considered here to be unlikely to have formed Venusian systems such as Kallistos Vallis. Flows of mafic to ultramafic origins could easily form channels such as those observed on Venus, or other planets of the inner solar system. Relevant examples of flow types capable of forming large channel

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systems include Fe-rich lunar flows (i.e., Murase and McBirney, 1970; Hulme, 1973; Head, 1976; Head et al., 1978; Head and Wilson, 1992; Williams et al., 2000), Mg- rich Mercurian flows (i.e., Head et al., 2011; Byrne et al., 2013; Hurwitz et al., 2013b; Vetere et al., 2017; Peplowski and Stockstill-Cahill, 2019; Thomas and Rothery, 2019), mafic and ultramafic flows such as those observed at Mars’ Gusev crater at the mouth of Ma’adim Vallis (i.e., Gellert et al., 2004; Squyres et al., 2004; Leverington, 2020, in press), and terrestrial komatiite flows with their own specific sets of geochemistries (i.e., Huppert et al., 1984; Hill, 1985; Hess and Head, 1990; Williams et al., 1998, 2001, 2011b; Grove and Parman, 2004; Barnes, 2006; Houle et al., 2012; Staude et al., 2017).

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CHAPTER III

MORPHOLOGICAL CHARACTERIZATION OF KALLISTOS VALLIS 3.1 Overview of Methodology The overarching purpose of this study was to better characterize the basic nature of the Kallistos Vallis system and associated features found in the Ammavaru volcanic province, and to better understand the flow mechanisms and conditions that may have been involved in the development of channel features. This involved the use of Magellan SAR and elevation data to better characterize the morphology of the system, the estimation of flow conditions likely to have existed during system development, the estimation of rates of thermal and mechanical incision under different flow conditions, and the estimation of minimum volumes of effused lavas required for system development. Analog channel systems located on several bodies of the inner solar system provided context for key aspects of this study.

3.2 Data Acquisition The primary data sources used in this thesis originated from observations taken by the radar onboard the Magellan spacecraft. The Magellan Radar Sensor (RDRS) consisted primarily of low, medium, and high-gain antennas, and a small nadir- directed altimeter horn antenna (ALTA). The device operated and collected radar data in three modes: Synthetic Aperture Radar (SAR), Altimetry (ALT), and Radiometry (RAD). In SAR mode, it imaged at no better than 75 m resolution. In ALT mode, it imaged with a resolution of approximately 10 to 30 km. The RDSR was the only imaging device on Magellan (Ford, et al., 1993). RDRS data used in this study are publicly available and were downloaded from the USGS Astrogeology website, Map- a-Planet 2 (https://astrocloud.wr.usgs.gov/index.php?view=map2).

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3.3 Topographic Overview In order to characterize the morphological nature of the Kallistos Vallis system, two separate databases were downloaded from the USGS website Map-A- Planet 2. The first database is a Magellan Synthetic Aperture Radar (SAR) FMAP (full-resolution map) left-look global mosaic with a resolution of 75 meters/pixel. The database has a simple cylindrical projection, and consists of 8-bit data in geotiff format with a 1%-saturated linear contrast stretch. The database is centered at 21 E. longitude, with extents ranging from 18 to 28 E. longitude and 47 to 52 S. latitude. The second database is a Magellan altimetry image with a spatial resolution of 4641 meters/pixel. The data are downgraded from 16-bit format to 8-bit format, and were downloaded as a simple cylindrical geotiff with a 1% contrast stretch. As with the first database, it is centered at 23 E longitude, with extents ranging from 18 to 28 E. longitude and 47 to 52 S. latitude. Pixel sizes have fixed angular sizes and will technically vary slightly across the study area with regard to their actual surface dimensions; pixel dimensions are constant in the vertical direction (i.e., the north- south direction) for all pixels, and vary in the horizontal direction (i.e., the east-west direction); pixel dimensions would be constant in both vertical and horizontal directions for pixels located along the equator (though the equator does not fall within the extent of the database). Both databases were georeferenced using the datum “Venus 2000” and were co-registered (i.e., layered one on top of the other, with essentially identical overall spatial extents and coordinate systems but with different angular pixel sizes). Figure 3.1 depicts the altimetry and SAR data together (generated using ArcGIS 10 software), with the top altimetry layer assigned a 60% transparency in order to show critical aspects of the underlying SAR layer. This figure shows the channel and its immediate vicinity to range in elevation from 360 to 1767 m in relation to the mean planetary radius, with a calculated mean elevation in this area of ~1094 m and a standard deviation of 176 m. Kallistos Vallis itself ranges in elevation from ~1300 m at its source to ~925 m along its eastern distal reaches.

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Figure 3.1 Topographic overview of Kallistos Vallis, depicting combined Magellan left-look SAR and altimetry data. Terrain in the depicted area ranges in elevation from 360 to 1767 m relative to the mean planetary radius (MPR). The channel source (S) is located at an elevation of ~1300 m above MPR. Black arrows indicate the path of the channel system. Three separate distributary channels and associated radar-bright lava flows (F) form part of the distal reaches of the system. The channel is centered at 23 E longitude. The mapped area extends from 47˚ S to 52˚ S latitude and 18˚ E to 28˚ E longitude. The original spatial resolution of the top layer altimetry database is 4641 meters/pixel, and the original spatial resolution of the bottom layer SAR database is 75 meters/pixel.

3.4 Cross-Sectional Profiles Cross-sectional topographic profiles of the Kallistos Vallis channel system were generated in order to characterize the form of the channel floor and its relationship with adjacent uplands. Due to the low spatial resolution of the Magellan altimetry data, channel floors of individual channel segments at Kallistos Vallis can generally be represented by no more than 1-3 pixels in cross-sectional profiles (not including overflow areas and flow margins, parallel channel segments, or adjacent uplands), which potentially allows for the determination of minimum channel depths

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but otherwise limits the utility of these elevation data. In order to work with straight transects not characterized by unwanted zig-zag patterns, elevations were sampled along south-north, west-east, northwest-southeast, and southwest-northeast directions (Figure 3.2). The ArcGIS “Raster to Point Conversion Tool” was used to draw points in the center of each individual pixel within a given transect, and then snap the line to the centers of the individual pixels within the altimetry database. This allows for simplified calculations by working directly with original database elevations and thus avoiding the need for resampling. The higher-resolution radar (SAR) image was used to select channel reaches of greatest interest, and the altimetry layers’ pixels were used for the actual snapping process. Transects were drawn in order to sample both channel floors and immediately-adjacent uplands. After activating both image layers within ArcGIS 10, the “Create Features” function was used in conjunction with the “Raster to Point Conversion Tool” within an edit session to create the required transects which were outputted as a cross-section feature class (Figure 3.2). Next the “Feature Vertices to Points Tool” was used to convert the vertices in the center of each pixel to actual points from which the latitude and longitude of each point can be determined and added to the map documents attribute table. Finally, the “Extract Values to Points Spatial Analyst Tool” was used to calculate the altitude (z-coordinate) of each point. Once this final step was completed, the latitude, longitude, and altitude of each point within the altimetry database was calculated and added to the map documents attribute table for later import into Excel for distance calculations and plotting. In total, 19 separate cross-sectional transects were generated for Kallistos Vallis, and each transect was characterized in terms of total profile length as well as the individual coordinates and altitudes associated with each pixel point within each transect. The precise length selected for each transect is arbitrary, and the key goal for each transect was to sample the full local width of the channel and immediately- adjacent uplands (which would ideally allow the position of channel floors to be clearly identified in the cross-sectional profiles) (Figure 3.3).

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Figure 3.2 Locations of all 19 numbered cross-sectional profiles beginning at 1, the northernmost part of the channel source and ending at 19, the furthest northern boundary of the depositional plain located west of the north-south ridge. Magellan FMAP left-look SAR mosaic. SAR illumination is from the left. The Magellan altimetry layer used in calculating the z-axis of each transect is not depicted here, in order to better show how transects were drawn in relation to the channel. In order to sample topographic data along perfectly straight lines connecting the centers of pixels within the altimetry database, transects were only drawn from west to east, south to north, northwest to southeast, and southwest to northeast.

To produce accurate cross-sectional transect plots, it was first necessary to use the angular coordinates of pixels to calculate point-to-point and cumulative distances within each transect. On Venus the length of one degree of longitude is given by:

L = cos(latitude) x 105.625 km. (3.1)

On the surface of Venus (just as on Earth), the actual length of one degree of latitude will vary slightly from the poles to the equator, due to the slightly oblate shape of the planet. Venus is the most spheroidal planet in the solar system, since it spins on its axis so slowly (~243 days for the sidereal day). The difference in one degree of

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latitude is thus quite small on Venus and is considered negligible for the purposes of this study. The length of one degree of longitude, however, will vary greatly with latitude, ranging from 105.625 km at the equator and to 0 km at the poles. To calculate the distance per degree of latitude on Venus the planetary circumference (~38,025 km) is divided by 360 degrees. This yields a measurement of 105.625 km per degree of latitude (at the equator). This measurement is then used in the calculation of angular distance (D) between two points, where:

퐶표푠(퐷) = [sin(푙푎푡 퐴) × sin(푙푎푡 퐵)] + [cos(푙푎푡 퐴) × cos(푙푎푡 퐵) × cos(푑𝑖푓푓푒푟푒푛푐푒 𝑖푛 푙표푛푔𝑖푡푢푑푒푠)] (3.2)

The angular distance D (in degrees) between any two pairs of latitude-longitude coordinates is determined by taking the arc-cosine of the result of the right-hand side of the above equation, which when multiplied by 105.625 km yields the corresponding great-circle distance in kilometers. The resulting calculations were used to generate line plots representing the nineteen cross-sectional profiles of the channel (Figure 3.3). Vertical exaggeration for each profile is listed in Table 3.2. The cross-sectional profiles suggest the floors of Kallistos Vallis are at least tens of meters below adjacent terrain. Due to the low resolution of the altimetry data, estimated minimum channel depths are determined for select cross-sectional profiles only. The approximations are as follows:

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Table 3.1: Estimated minimum channel depths associated with particular cross- sectional profiles

Cross-Sectional Profile 2 ~17 meters

Cross-Sectional Profile 12 ~20 meters

Cross-Sectional Profile 13 ~75 meters

Cross-Sectional Profile 14 ~60 meters

Cross-Sectional Profile 15 ~30 meters

Cross-Sectional Profile 19 ~50 meters

The minimum estimated channel depths given above do not account for any channel infilling that may have taken place due to constructive emplacement of later lava flows. It is possible that some amount of material partially infilled any given channel reach, obscuring the actual original amount of vertical topographic relief that may have once existed along a particular cross-section. Also, channel depths may not correspond at all to incision depth, as some reaches of the system may have developed without any amount of meaningful incision, yet the associated channel floors may nevertheless be noticeable lower in elevation than the adjacent uplands.

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Figure 3.3 The above 19 plots depict cross-sectional profiles for selected segments of Kallistos Vallis. Elevations are expressed in meters, and cross-sectional distances are expressed in kilometers. Red dots represent the location of the channel within a given cross-sectional profile, where each dot corresponds to a channel bank. The plots begin with profile 1, located along the northernmost extent of the source region and progress toward the south and east, where they finish at profile 19 (Figure 3.2). Profiles 1 and 2 cross chaotic terrain. Profiles where there is no clear representation of a channel conduit (i.e., Profiles 3, 4, 5, 6, 7, 8, 17, and 18) are in numerous cases associated either with channel islands or with altimetry pixels that extend beyond channel limits, reducing or eliminating apparent channel relief; such issues are directly a result of the low spatial resolution of the altimetry database Profile 16 crosses 3 separate channel segments located in the eastern part of the channel system.

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Table 3.2: Vertical exaggerations for individual cross-sectional profiles (Figure 3.3)

Profile Vertical Profile Vertical Profile Vertical Number Exaggeration Number Exaggeration Number Exaggeration 1 125 to 1 8 1176 to 1 15 216 to 1 2 350 to 1 9 43 to 1 16 1176 to 1 3 3030 to 1 10 145 to 1 17 61 to 1 4 333 to 1 11 445 to 1 18 125 to 1 5 272 to 1 12 563 to 1 19 250 to 1 6 44 to 1 13 346 to 1 푉푒푟푡𝑖푐푎푙 푆푐푎푙푒 푉퐸 = 7 23 to 1 14 108 to 1 퐻표푟𝑖푧표푛푡푎푙 푆푐푎푙푒

Some of the estimated minimum channel depths (i.e., cross-sectional profiles 15-19) are associated with transects that cross distal channel reaches that are closely associated with terminal volcanic plains and thus are more likely to have developed predominantly as a result of constructive processes rather than erosive, at least in the final stages of channel activity here. The difficulty in confidently determining original channel depth and topographic relief (i.e., channel shape) along Kallistos Vallis arises from the low spatial resolution of available elevation data (a secondary issue is the lack of in situ data as to how much subsequent infilling has taken place along particular channel floors). Where channel width is limited to only 1 to 3 pixels, the representativeness of channel profiles must be especially poor. Since the pixel sizes of elevation data are several kilometers in width, the area covered by a given pixel may encompass multiple landforms of differing height. Prime examples of this are depicted in Figure 3.4 (this section) and Figures 3.5 - 3.6 (from Section 3.5: Longitudinal Profiles), which include channel segments where there are streamlined island contained within a portion of the pixel, pixels that cover both the channel and the channels banks, and areas within the channel where damming has occurred (forcing lava to travel around the dam, partially overflowing channel banks). In cases where the channel is less than one pixel across, the channel itself may not even show up in cross-section (Figure 3.3, Profiles 4, 7, 8, 17, and 18). This is because the elevation of the pixel is a function of both the local channel floor and terrain features located adjacent to the channel. Profile 1 shows an

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increase in elevation as it runs from west to east. This is explained by the presence of chaotic terrain, where each pixels value does not represent an actual altitude, but is instead influenced by the presence of terrains of varying altitudes contained within the pixels boarders (as observed in the underlying SAR image layer). The average value (altitude) across each pixel of the transect itself is increasing, therefore, the expression of this within the plot is that of a slope that is gradually increasing in the easterly direction. This makes sense given the gradual increase in elevation moving east of the source region (as opposed to a decrease in the west) (Figure 3.1). The chaotic terrain combined with low-resolution altimetry data makes it difficult to detect where the source depression begins and ends. The most accurate measures of minimum estimated depth tend to be in areas of non-chaotic terrain, where the channel is at least 3 pixels across, the center pixel falls entirely within the channel, and the center pixel is not partially or completely occupied by a streamlined island.

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Figure 3.4 The above image pertains to cross-sectional profile 19 (Figure 3.2). The top half of the figure is a Magellan left-look SAR mosaic with a spatial resolution of 75 meters/pixel. The bottom half is the same image with a Magellan altimetry data layer (color) superposed on the SAR data (black and white). The resolution of the altimetry layer is 4641meters/pixel. The red line represents the path of the cross- sectional profile in the immediate vicinity of Kallistos Vallis. Along this reach, the channel falls within two separate altimetry pixels, and shares these pixels with other geomorphic features such as a streamlined island and uplands adjacent to the channel. Thus, elevation data here cannot precisely describe the cross-sectional form of the channel. The multi-colors used for each pixel in the altimetry layer are only there to visually aid in distinguishing one pixel from another and do not carry with them any specific values.

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3.5 Longitudinal Profiles Longitudinal profiles were generated for seven different channel segments, in order to better understand the nature of elevation changes in the downslope direction of different parts of the Kallistos Vallis system. These profiles were generated in the same manner as the cross-section profiles discussed above (Section 3.4). Channel Segment 1 begins in the channel source region, which appears to be a zone of collapse that marks the site of a caldera-like feature (Baker et al., 1992), and runs southward, intersecting with both Segments 2 and 6. Segment 6 runs southeasterly in parallel with the main channel (Segment 2) and terminates ~242 km from its origin at Segment 1. Segment 6 most likely acted as a conduit for a portion of the initial outflow (Baker et al., 1992) and for the purposes of this study is not considered a primary component of the Kallistos Vallis system, nor is it used in any calculations of channel length or area. Segment 2, which intersects with Segment 1, begins with a trough that appears to be connected to a source marked by collapsed terrain, and is likely to have served as an initial system conduit and has been associated with a second source of flows (Baker et al., 1992). The segment runs ~671.52 km and then connects with the central anastomosing reaches of the system. Segment 7 branches from Segment 2, running southeast of the main channel, then turning back toward the northeast toward Segment 2. As with Segment 6, Segment 7 is not considered to be a primary component of the Kallistos Vallis system and therefore has also been excluded from channel length and area calculations. Segments 3, 4, and 5 represent separate distributary channels that are radar dark and surrounded by radar bright lava flows with lobate margins (Baker et al., 1992). These segments extend eastward until they encounter a north-south oriented ridge belt, forming a depositional plain on both sides of this topographic feature (Baker et al., 1992) (Figure 3.4). The depositional plain to the east of the belt is not considered to be a part of the main channel system. Unlike the cross-sectional profiles, the paths traced out for the longitudinal profiles are not precisely linear in orientation, but instead “zig-zags” from pixel-to-

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pixel at the most local scales (Figure 3.5). Due to the low spatial resolution of available altimetry data, some of the pixels tracing out the channel overlap with channel banks (Figure 3.6), reducing the precision with which local channel topography is expressed.

Figure 3.5 The above image pertains to Segment 4 of this study’s longitudinal profiles (Figure 3.7). Top half of the figure is a Magellan left-look SAR mosaic with a resolution of 75 meters/pixel. The bottom half is the same image with a Magellan altimetry data layer (color) superposed on the SAR data (black and white). The top layer altimetry resolution is 4641meters/pixel. The purple line represents the path of the longitudinal profile in the immediate vicinity of Kallistos Vallis. It is drawn through the center of each pixel, where in certain areas the same pixel will overlap both the channel and its adjacent shoreline. Thus, elevation data here cannot precisely describe the longitudinal form of the channel. The multi-colors used for each pixel in the altimetry layer are only there to visually aid in distinguishing one pixel from another and do not carry with them any specific values.

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Figure 3.6 The above image pertains to Segment 2 of this study’s longitudinal profiles (Figure 3.7). Top half of the figure is a Magellan left-look SAR mosaic with a resolution of 75 meters/pixel. The bottom half is the same image with a Magellan altimetry data layer (color) superposed on the SAR data (black and white). The top layer altimetry resolution is 4641meters/pixel. The blue line represents the path of the longitudinal profile in the immediate vicinity of Kallistos Vallis. Near the center of the image the individual pixels encompass multiple geomorphic features such as a streamlined island, channel bed, and adjacent shoreline. Thus, elevation data here cannot precisely describe the longitudinal form of the channel. The multi-colors used for each pixel in the altimetry layer are only there to visually aid in distinguishing one pixel from another and do not carry with them any specific values.

A combination of Segment 1, Segment 2 (forward of where it intersects with Segment 1), and Segment 3 produces a composite profile that describes channel elevations along the approximate full length of the main Kallistos Vallis system

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(~1230 km). The difference in elevation from the starting point of Segment 1 and the end point of Segment 3 (involving a ~375 m drop in elevation) indicates an average down-channel slope of -0.30 m/km (only ~0.017 degrees), which is in general agreement with Baker et al. (1992). When calculating the total combined length and area of all system segments it is necessary to include all segments (primary components) of the system and not just the longest continuous segments. These include Segments 3, 4, and 5, the systems distributary reaches, and excludes Segments 6 and 7, which are considered failed system components. Though the actual length of the system is slightly in excess of 1200 km, the total combined length of the channel system (including parallel segments), with all components variously created via erosional and/or constructional processes, is calculated to be ~1750 km.

Figure 3.7 The above image shows the locations of all seven numbered longitudinal profile segments beginning at #1, the channel source, and ending at #3, the northern limit of the distributary channel that reaches the breach in the north-south oriented ridge. Magellan FMAP left-look SAR mosaic.

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Figure 3.8 Longitudinal profiles for selected segments of Kallistos Vallis. Profiles are numbered 1-7, beginning with 1 located in the northwestern source region and ending with 3 in the northeastern section of the depositional plain (Figure 3.7). Profile 1 represents the chaotic terrain of the main source region. Profiles 2-7 represent individual channel segments. The composite profile (“Longitudinal Profile Entire Channel”) is comprised of profiles 1,2, and 3 (not including the first part of profile 2), and collectively represents the longest continuous channel extent.

To calculate the average slope of each channel segment, F is defined on the closed interval [a,b], where the average slope of F between a and b is the quotient:

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[퐹(푏) − 퐹(푎)] 퐴푣푒푟푎푔푒 푆푙표푝푒 = (3.3) (푏 − 푎)

Where b is the total distance, a is the starting distance (equal to zero), F(b) is the end elevation, and F(a) is the starting elevation. The overall system slope of 0.3 m/km corresponds to a remarkably low average angular slope of only 0.017 degrees. Local channel slopes far in excess of this value are possible and are especially likely to have existed along some reaches earlier in the channel development process. Low longitudinal slopes (well under 1 degree) are typical of large volcanic channel systems of the inner solar system (e.g., Leverington, 2011, 2014), though sharp drops in elevation at local channel features such as cataracts (features formed in association with former “lava falls”) are known for some systems (e.g., Dundas and Keszthelyi, 2014).

Table 3.3: Total distance, average slope, and vertical exaggerations of longitudinal profiles. Measurements of average slope (Profiles 1-5) are in general agreement with previous calculations published in Baker et al., (1992).

Profile Number Total Distance Average Slope Vertical (km) (m/km) Exaggeration Profile 1 73.49 km -0.93 m/km 684 to 1 Profile 2 671.52 km -0.35 m/km 15 to 1 Profile 3 517.58 km -0.19 m/km 750 to 1 Profile 4 307.06 km -0.74 m/km 727 to 1 Profile 5 178.98 km +0.27 m/km 1497 to 1 Profile 6 242.85 km -0.63 m/km 1000 to 1 Profile 7 154.69 km -0.21 m/km 1476 to 1 Entire Channel 1234.61 km -0.30 m/km 750 to 1

As with the cross-sectional profiles discussed in Section 3.4, the elevations of the longitudinal profiles have been affected by the presence of streamlined islands, channel dams, and shorelines that are fully or partially contained within the large altimetry pixels. Major irregularities in the profiles given in Figure 3.8 could be a

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product of the multiple geomorphic features that fall within the boundaries of individual altimetry pixels. One especially notable anomaly is the abrupt 400 m drop in elevation depicted by Longitudinal Profile 3. Observations of the underlying radar image show no clear landforms associated with the location of this drop, but the topographic overview image (Figure 3.1) shows a very clear bowl-shaped depression that extends across the ridgeline to the east of the depositional plain. This local basin is expected to have developed after formation of Kallistos Vallis (had the depression existed before development of the channel, it would have been infilled in the same manner as the rest of the depositional plain).

3.6 Channel Area Measurements The total area of the main Kallistos Vallis system, including the overflow area of the portion of the depositional plain located on the west side of the north-south oriented ridge belt, was calculated by generating a mask on the basis of the system’s main outline in the FMAP left-look SAR database (Figure 3.6). Area measurements can be used to help estimate the total volume of material excavated during lava emplacement, and the amount of magma extruded onto the Venusian surface (Chapter 4). When making specific calculations of the amount of magma extruded, the overflow region located on the east side of the ridge belt (eastern portion of the depositional plain) should be considered, as some of this material is very likely to have originated from the Kallistos Vallis source region. Unlike with Magellan altimetry data, Magellan FMAP left-look SAR images are available at relatively high spatial resolution (75 meters/pixel), which allows for more accurate delineation of the channel system and thus more representative area measurements than if altimetry data were used. Channel area was determined through the processing of a bitmap of channel extent generated in ArcGIS, using the SAR image as a guide. The original mask of the channel system was generated by creating a feature (a polygon), and specifying the dimensions of this feature by tracing system margins by hand while zoomed into the SAR image at full spatial resolution.

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With the system mask in hand, a raster (bitmap) outlining the channel and its surrounding area was created such that every pixel within the channel had an assigned value of 1 and every pixel outside the channel had an assigned value of 0 (Figure 3.10). The bitmap was exported to a text file that was processed by software written by adviser Leverington (Appendix C). This software estimates the surface area of a bitmap, taking into account the changing surface area of individual pixels as a function of latitude. In total, the calculated channel area is 40,920 . This area estimation pertains to the main Kallistos Vallis channel system, and does not consider the volcanic plains located on the east side of the Vaidilute Rupes north-south trending ridge. If the east side of the Vaidilute Rupes ridge were to be included, then the total calculated channel area would be ~100,000 km2 (Baker et al., 1997).

Figure 3.9 Mask depicting the spatial extent of the main Kallistos Vallis channel system (blue area) located west of the north-south oriented ridge. This mask was generated by hand using the Magellan FMAP left-look SAR mosaic as a guide.

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Figure 3.10 Bitmap generated from the mask depicted in Figure 3.9. This raster mask of the main Kallistos Vallis system (white area) was used as a basis for area calculations. The total surface area of the region defined by the bitmap is 40,920 km2 The volcanic plains located east of the north-south oriented ridge are not included in the channel areas defined by this mask.

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CHAPTER IV

ESTIMATION OF FLOW CONDITIONS AND INCISION RATES The head depression of the Kallistos Vallis system is interpreted here as the surface expression of a deeply-rooted plumbing system of the type previously hypothesized for other large volcanic channel systems of the inner solar system (e.g., Wilson and Head, 2002, 2017ab; Leverington, 2011, 2019a). This plumbing system is correspondingly expected to have conveyed lavas from subcrustal depths to the Venusian surface in large volumes and at high rates of flow. The flow conditions and incision rates involved in the development of Kallistos Vallis can be crudely estimated on the basis of equations previously applied toward the study of other channels of the inner solar system, including those of the Earth, Moon, Mars, and Mercury (e.g., Hulme, 1973; Huppert and Sparks, 1985; Keszthelyi and Self, 1998; Williams et al., 1998, 2000; Sklar and Dietrich, 1998; Dundas and Keszthelyi, 2014; Cataldo et al., 2015; Baumgartner et al., 2017; Gasparri et al., 2020). The specific suite of equations utilized in this study was assembled by Hurwitz et al. (2010, 2012), and the software implementation of these equations has previously been applied to both Martian and terrestrial channel systems (Hopper and Leverington, 2014; Leverington, 2014, 2018, 2019ab, in press). These equations are functions of each other, and thus must be solved iteratively until stable solutions are found. As a result of current limitations in our general understanding of the manner in which lavas flow and incise, the utilized equations necessarily treat thermal and mechanical processes of incision as though they operate separately, which is not strictly the case.

4.1 Mechanical Incision Parameters When modeling the mechanical erosion of a solid substrate it is important to consider the region being eroded (Hurwitz et al., 2010, 2012). The velocity of the flow, the rate of discharge (푄푤) and total volume of the flow, are the primary factors influencing the amount of shear stress which is directed towards the underlying substrate (Sklar and Dietrich, 1998; Williams et al., 1998; Siewert and Ferlito, 2008).

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The mechanical incision rate for a low slope flow (<10°) (Sklar and Dietrich, 1998; Hurwitz et al., 2010, 2012) is given by:

d(푑chan) ( ) = 푘 휌 푔 푄w 푠𝑖푛훼 (4.1) d푡 mechanical where K is a constant of proportionality measured in units of Pa-1, which are representative of the erodibility of underlying substrates, ρ is lava density measured in 3 2 kg/m , g is gravitational acceleration (8.87 m/s for Venus), Qw is the average discharge of lava through the channel per unit width (given in m3/s), and α is the channel slope in degrees. The results calculated with Equation 4.1 should be treated with caution, as the physical processes involved in the mechanical erosion of lava are not yet well understood (Dundas and Keszthelyi, 2014). Most importantly, the range identifying appropriate values of K, the erodibility constant, are poorly constrained for lava, and it has not yet been clearly determined that the abrasion and plucking processes associated with both water and lava are similar enough to be able to be applied to the same form of the mechanical erosion law for the study of channelized lavas (Dundas and Keszthelyi, 2014). The flow velocity of lava (Sklar and Dietrich, 1998; Hurwitz et al., 2010, 2012) is given by:

2 푔 푑푙푎푣푎 푠𝑖푛훼 (푣푙푎푣푎) = (4.2) 퐶푓

2 where g is gravitational acceleration ( 8.87 m/s for Venus), dlava is lava depth, α is the channel slope in degrees, and Cf is the friction factor (Keszthelyi and Self, 1998), given by:

−2 2푅푒+800 0.92 1 [6.15 (( ) )]) 퐶푓 = ( ) (log10 41 (4.3) 32

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The associated Reynolds number (Re) is given by:

휌 푣 푑 푅푒 = 푙푎푣푎 (4.4) 휇 where ρ is the lava density (in kg/m3 ) , υ is the velocity of lava (calculated iteratively from Equations 4.2 and 4.3 in m/s), dlava is the lava depth, and µ is the dynamic viscosity of lava (in Pa s). As noted above, equations 4.2 – 4.4 are functions of each other and thus must be solved iteratively, beginning with seed values for key variables. In the above calculations, lava density is assumed to be 2800 kg/m3 (e.g., Mason and Melson, 1970; Schaber, 1973), and the favored dynamic viscosity is 1 Pa s. This dynamic viscosity is approximately typical of basalts that comprise the lunar maria (e.g., Mason and Melson, 1970; Schaber, 1973) and are believed to approximately characterize basalts that pooled inside Martian Gusev crater at the mouth of Ma’adim Vallis (Greeley et al., 2005; Chevrel et al., 2014). In this study, three primary viscosities were considered: 1, 7, and 44 Pa s. The favored viscosity of 1 Pa s is based on the 0.01 to 10 Pa s viscosities that are typical of lavas associated with the formation of large volcanic channels found on the Moon, Venus, Mercury, Mars, and early (Hadean-Paleoproterozoic) Earth (Hulme, 1973, 1982; Hulme and Fielder, 1977; Schonfeld, 1977a, b, 1979; Huppert et al., 1984; Huppert and Sparks, 1985; Williams et al., 1998, 2001, 2011; Leverington, 2004, 2007, 2009, 2011, 2014, 2018; Hurwitz et al., 2010, 2012; Jaeger et al., 2010; Byrne et al., 2013; Chevrel et al., 2014; Hopper and Leverington, 2014; Leone, 2014, 2017, 2018; Baumgartner et al., 2015, 2017; Vetere et al., 2017, 2019). A 7 Pa s flow is worthy of consideration on the basis of the 4.5 to 7.5 Pa s viscosity range estimated for fluids that formed the Venusian channels (Kargel et al., 1993). Finally, a lava viscosity of 44 Pa s flow is of interest as a viscosity of this approximate magnitude is suggested by the geochemical data obtained for basalts examined by the Venera 14 lander (assuming eruption temperatures of 1350°C) (Ashley and Ramsey, 2019). Though the Venera 14 landing site is not known to be associated with any type of large volcanic

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channel, it is associated with a broad basaltic plain that is likely to have been emplaced through the extrusion of flood basalts. On the basis of solar system analogs, viscosities ranging from ~7 Pa s to 44 Pa s are considered to be conservative estimates of Venusian lava viscosities, though these same viscosities are extraordinarily low by modern terrestrial standards (e.g., Leverington, 2014). Generally speaking, lavas with lower viscosities possess much greater potential for mechanical erosion than lavas with higher viscosities (e.g., Williams et al., 2001, 2011; Hurwitz et al., 2010, 2012; Jaeger et al., 2010; Leverington, 2014; Dundas and Keszthelyi, 2014; Hopper and Leverington, 2014; Cataldo et al., 2015; Baumgartner et al., 2017), though other factors such as rates of effusion and total erupted volumes are also important in this regard (e.g., Leverington, 2018, 2019ab). Importantly, the rheological properties of lavas should change with distance from eruptive centers: temperatures decrease, viscosities increase, and turbulence levels correspondingly decrease. Thus, the capacity for lavas to incise must also decrease with distance from erupted centers (e.g., Jaeger et al., 2010; Hurwitz et al., 2010, 2012; Leverington, 2014, 2018, 2019ab). The present study focuses on relatively hot lavas that are sufficiently insulated by fixed or mobile crusts to have not cooled to such an extent that their rheological properties have dramatically changed.

4.2 Thermal Incision Parameters The thermal incision rate for a volcanic flow (e.g., Hulme, 1973; Huppert and Sparks, 1985a; Williams et al., 1998, 2000; Hurwitz et al., 2012) is given by:

d(푑 ) ℎT(푇−푇mg) ( chan ) = (4.5) d푡 thermal 퐸mg

where hT is the heat transfer coefficient, T is the temperature of the lava (in C), Tmg is the melting temperature of the substrate materials (in C), and Emg is the energy that is

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required to melt the substrate materials (in J/kg) (Hulme, 1973; Huppert and Sparks, 1985a; Williams et al., 1998; 2000), given by:

퐸푚푔 = 휌g[푐g(푇mg − 푇g) + 푓mg 퐿g] (4.6)

3 where ρg is the density of the solid substrate materials (in kg/m ), cg is the specific J heat of the solid substrate materials (in /K), Tmg is the melting temperature of the kg substrate materials (in C), Tg is the initial temperature of the solid substrate materials

(470 C), fmg is the fraction of the solid substrate materials that must be melted prior to mobilization, Lg is the latent heat of fusion of the solid substrate materials (in J/kg), and hT is the heat transfer coefficient (Hulme, 1973), given by:

4 2 0.017 푘 푅푒5 푃푟5 ℎ푇 = (4.7) 푑푙푎푣푎 where k is the thermal conductivity of the lava [in W/(mK)] {[2.16 – (0.0013 T)]} (Williams et al., 1998), Re is the Reynolds number, Pr is the Prandtl number [a dimensionless number representing the ratio of kinematic viscosity to thermal diffusivity in (cgµ)/k], and dlava is the depth of the lava [in meters (m)]. A list of constants is given in Table 4.1. In the absence of clear information regarding the detailed properties of surface and near-surface geological units on Venus, as well as the nature of materials specifically at the Kallistos Vallis channel system, the magnitudes of these and related parameters have necessarily been derived mainly from information related to analogous units located on other bodies of the inner solar system. The assumed lava density is 2800 kg/m3 (e.g., Murase and McBirney, 1973; Sparks and Huppert, 1984; Williams et al., 2005; Hopper and Leverington, 2014; Leverington, 2018; Leverington, 2019ab). The assumed dynamic viscosity of lava was 1Pa s, which is typical of lunar mare basalts (e.g., Mason and

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Melson, 1970; Schaber, 1973). The value of K, the proportionality constant, is representative of an underlying substrates ability to erode, where lower values (10−9) represent better consolidated materials (such as bedrock) and higher values (10−7) represent less consolidated materials (such as regolith) (Hurwitz et al., 2010, 2012). A value of 10−9 was used here to reflect the probable low abundance of volcanoclastic units, ejecta materials, or regolith, and the presence of a strong bedrock substrate. The use of a lower K value of this magnitude makes it more difficult for the modeled substrate to be incised. The density of solid substrate used in the calculations is 2900 kg/m3 (e.g., Salisbury and Christensen, 1973; Moore, 2001; McSween, 2002; Hopper and Leverington, 2014; Leverington, 2018, 2019ab). Assumed lava depths of 5 and 20 m are meant to be conservative, and are in line with flow depths calculated for other analogous systems such as the Martian systems Hrad Vallis (Hopper and Leverington, 2014) and Athabasca Vallis (Jaeger et al., 2010) (perhaps the best analog for the Kallistos Vallis system). A channel slope of no greater than 1 degree is consistent with kilometer-scale longitudinal slopes along the Kallistos Vallis system as expressed in Magellan altimetry data, which on average are well under 0.l degrees. Software implementations of Equations 1 - 7, by adviser Leverington are given in Appendices A and B.

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Table 4.1: List of Constants

Symbol Parameter Value Units

Gravitational g acceleration of 8.87 m/s2 Venus Proportionality K 1 × 10−9 Pa−1 constant

 Density of lava 2800 kg/m3

Dynamic viscosity  1 (favored), 7, 44 Pa s of lava

T Temperature of lava 1350 C

풄 Specific heat of 1500 J/kg C 품 substrate

Latent heat of 푳 5.87 × 105 J/kg 품 fusion of substrate Fraction of 풇풎품 substrate melted 0.4 (40%) Dimensionless before movement Density of solid 흆 2900 kg/m3 품 substrate

푻 Initial temperature 470 C 품 of substrate Melting 푻풎품 temperature of the 1150 C substrate Thermal k 2.16 – (0.0013 T) W/(mK) conductivity

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4.3 Estimates of Flow Conditions

4.3.1. Flow Velocity Estimates Equations 4.2 - 4.4 were used to estimate velocities for lava flows with viscosities of 1, 7, and 44 Pa s, flowing on bedrock slopes of 0 to 1, involving lava depths of 5 and 20 m (Figure 4.1), and Venusian gravitational acceleration of 8.87 m/s2. On slopes of up to 1°, the calculated velocities are as great as ~55.28 m/s (1 Pa s), ~46.89 m/s (7 Pa s), and ~38.86 m/s (44 Pa s). As expected, velocity increases with slope and decreases as viscosity increases.

Figure 4.1 Flow velocity rates in meters per second for 5 (solid lines) and 20 (dashed lines) meter deep flows, with viscosities of 1 Pa s (red), 7 Pa s (blue), and 44 Pa s (green), Venus gravitational acceleration is 8.87 m/s2. Slopes range from 0 to 1 degree

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4.3.2. Total Discharge Estimates Total discharge (Q) is estimated for an assumed average channel width of 10 km, lava viscosities of 1, 7, and 44 Pa s, slopes of 0 to 1, and flow depths of 5 and 20 m (Figure 4.2). The calculated rates of discharge (Q) are as great as ~1.11 × 107m3/s (for a 1 Pa s flow), ~9.38 × 106m3/s (for a 7 Pa s flow), and ~7.77 × 106m3/s (for a 44 Pa s flow). Consistent with expectations, as flow depth and slope increase, total discharge increases. As viscosity increases, discharge decreases.

Figure 4.2 Discharge (Q) in m3/s for 5 (solid lines) and 20 (dashed lines) meter deep flows, with a 10 km wide reach, viscosities of 1 Pa s (red), 7 Pa s (blue), and 44 Pa s (green), and slopes of less than 1 degree

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4.3.3. Reynolds Number Estimates Equation 4.4 was used to estimate flow turbulence (Reynolds number), keeping in mind that a set of equations had to be solved iteratively in order to allow Equation 4.4 to be used in this manner. The magnitudes of Reynolds numbers estimated for Kallistos Vallis flows over the depths and slopes of interest (involving a minimum slope of only 0.01°) range from ~9.14 × 104 to ~3.10 × 106 (for a 1 Pa s flow), ~1.04 × 104 to 3.75 × 105 (for a 7 Pa s flow), and ~1.04 × 104 to ~3.75 × 105 (for a 44 Pa s flow). Reynolds numbers >2000 generally indicate a turbulent flow regime (e.g., Hurwitz et al., 2010). Therefore, the calculated values for Reynolds numbers here indicate fully turbulent lava flow for essentially all considered slope values apart from 0°.

Figure 4.3 Semi-log plot of Reynolds numbers for 5 (solid lines) and 20 (dashed lines) meter deep flows, with viscosities of 1 Pa s (red), 7 Pa s (blue), and 44 Pa s (green). Substrate density is 2900 kg/m3, and slopes of less than 1 degree are considered.

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4.4 Estimates of Mechanical and Thermal Incision This section explores estimates of the capacity of lava to have formed the Kallistos Vallis outflow system via mechanical and thermal erosion processes. Estimates are based on slopes no greater than 1 degree.

4.4.1. Mechanical Calculations Equations 4.1 - 4.4 were used to estimate the mechanical incision rates for lava with viscosities of 1, 7, and 44 Pa s, a lava density of 2800 kg/m3, slopes from 0 to 1, and flow depths of 5 and 20 m (Figure 4.4). The estimated rates of mechanical incision are as great as ~41.40 m/day (for a 1 Pa s flow), ~35.10 m/day (for a 7 Pa s flow), and ~29.10 m/day (for a 44 Pa s flow). As would be expected, mechanical incision rates increase with an increase in flow depth and slope. Mechanical incision decreases as viscosity increases.

Figure 4.4 Mechanical incision rates in meters per day for 5 (solid lines) and 20 (dashed lines) meter deep flows, with viscosities of 1 Pa s (red), 7 Pa s (blue), and 44 Pa s (green), and slopes ranging from 0 to 1 degree for a Venusian bedrock substrate and Venus gravitational acceleration of 8.87 푚/푠2.

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4.4.2. Thermal Calculations Equations 4.5 - 4.7 were used along with Equation 4.2 to estimate the thermal incision rate for a flows, with viscosities of 1, 7, and 44 Pa s, lava density of 2800 kg/m3, lava temperature of 1350C, initial substrate temperature of 470C, substrate melting temperature of 1150C, slopes from 0 to 1, and flow depths of 5 and 20 meters (Figure 4.5). The estimated rates of thermal incision are up to ~6.80 m/day (for a 1 Pa s flow), ~2.70 m/day (for a 7 Pa s flow), and ~1.10 m/day (for a 44 Pa s flow). As expected, the rate of thermal incision increases with steeper slopes, leveling out logarithmically as slope increases. Though rates of thermal incision decrease with shallowing slope, the relative importance of thermal incision – compared to that of mechanical incision – will increase with a decrease in slope (particularly at slopes closest to horizontal). Even though the absolute effects of thermal incision are greater for steeper slopes, it is at the point where the logarithmic thermal erosion curve crosses the exponential mechanical curve, that mechanical erosion takes over as the dominant source of channel incision.

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Figure 4.5 Thermal incision rates in meters per day for 5 (solid lines) and 20 (dashed lines) meter deep flows, with viscosities of 1 Pa s (red), 7 Pa s (blue), and 44 Pa s (green), and slopes ranging from 0 to 1 degree for a Venusian bedrock substrate under Venusian gravity.

4.4.3. Dynamic Viscosity Parameter Space Calculations The effects of differences or changes in lava flow viscosity are depicted for both mechanical and thermal incision in Figure 4.6. By exploring the viscosity parameter space more completely for 20-m-deep flows (i.e., going far beyond the three viscosity values considered above: 1, 7, and 44 Pa s), we are able to more clearly see the combined impacts of viscosity and slope on predicted incision rates. Again, as expected, the overall trend indicates that as viscosity increases, incision rates decrease for both mechanical and thermal processes. Furthermore, the rates of incision at lower viscosities and higher slopes can be considerably greater than the rates associated with much higher viscosities and lower slopes, especially for mechanical incision.

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A B

Figure 4.6 Estimated mechanical (A) and thermal (B) incision rates in meters per day for 20 meter deep flows, for a viscosity range of 1 to 10,000 Pa s, and a slope range of 0 to 1°, for a Venusian bedrock substrate and Venusian gravity.

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CHAPTER V

ESTIMATES OF MINIMUM LAVA VOLUMES REQUIRED FOR FORMATION OF KALLISTOS VALLIS What volume of effused lava might have been involved in the formation of Kallistos Vallis? Determination of even an order-of-magnitude estimate of this volume is of interest, as it can help to further illuminate the nature of the dynamics of past Venusian volcanic eruptions, and correspondingly has the potential to shed light on the manner in which all Venusian channel systems might have been formed. An improved understanding of the nature of volcanic channel development on Venus could ultimately help improve our understanding of fundamental processes involved in the development of volcanic channels and related features on large rocky bodies of the inner solar system, potentially shedding light on the nature of the interiors of these bodies. There are numerous factors that complicate our capacity to meaningfully estimate the total effused lava volume involved in the development of Kallistos Vallis. For example, little is known as to how much incision actually took place along this system. Though relatively deep channel incision at Kallistos Vallis appears likely to have occurred from the head of the system to the middle reaches (characterized by the presence of prominent streamlined erosional residuals), the exact amount of incision that took place at various points along the system cannot be readily determined from the available low-resolution topographic data (Sections 3.3 - 3.5). This is further complicated by an absence of clear information as to which channel reaches may have floors that are significantly mantled by later flows (potentially obscuring the amount of incision that took place over the history of the channel system). The easternmost reaches of the system are clearly mantled by lava flows, and it is not certain that these reaches experienced any substantial incision at all. Along volcanic channels, lava temperatures will be highest and viscosities will be lowest within reaches closest to volcanic sources. The cooling of lavas with increasing down-channel distance will increase lava viscosities and decrease capacities

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for incision into substrates. Overall, greater incision is expected along reaches located closer to volcanic sources and/or characterized by steeper longitudinal slopes (e.g., Williams et al., 2001, 2011; Jaeger et al., 2010; Hurwitz et al., 2012; Dundas and Keszthelyi, 2014; Hopper and Leverington, 2014; Cataldo et al., 2015; Baumgartner et al., 2017; Leverington 2014, 2018, 2019ab). In principle, efficiency in channel incision can be decreased by the periodic constructive emplacement of lava flows, which could result from: 1) lower-volume eruptions that cool and solidify before they can flow great distances; and/or 2) eruptions involving lavas that happen to be characterized by higher viscosities (e.g., Leverington, 2007; Leverington, 2018, 2019b). The minimum required volume of lava for formation of a given system should generally be easier to determine than the actual volume of lava involved in channel development, and among the techniques available for order-of-magnitude estimates of involved lava volumes are those based on crude thermal principles and those based on estimates of incision rates and lava discharge.

5.1 Elementary Thermal Determination of Minimum Lava Volume Effused at Kallistos Vallis One means by which the minimum effused lava volume can be very crudely determined for channels formed, at least in part by erosion, is to estimate the volume of material eroded during channel development. To accomplish this, we must determine what volume of lava at a particular temperature, that must be added to a volume of substrate at a particular temperature, in order to maintain an overall mixed temperature of 1150°C (a temperature considered a general lower limit for highly turbulent lava flows of mafic composition; e.g., Keszthelyi and Self, 1998). Focusing only on thermal mixing and neglecting the less important processes of phase changes involved in substrate melting and lava solidification, and assuming comparable densities and specific heat capacities for involved solid and liquid phases, this simple technique yields a basic order-of-magnitude thermal estimate of the minimum effused lava volume (e.g. Leverington, 2007, 2018, 2019ab; Cataldo et al., 2015).

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Assuming a Venusian substrate temperature of 470°C, a lava temperature of 1350°C, and a required minimum lava temperature of 1150°C, a minimum required lava:substrate ratio of 3.4:1 was determined strictly on the basis of thermal mixing (again, neglecting secondary factors such as phase changes, and any contributions to channel incision by purely mechanical processes). That is, where 푉푆푢푏 is the volume of 3 substrate lost and 푉퐿푎푣푎 is the lava volume, we have: [(470°C x 푉푆푢푏 km ) + (1350°C x 3 3 3 푉퐿푎푣푎 km ) = (1150°C) (푉푆푢푏 km + 푉퐿푎푣푎 km )], and 푉퐿푎푣푎/푉푆푢푏 = 3.4. This type of simplistic calculation implicitly involves numerous assumptions that are not strictly valid, such as the retention of a constant lava temperature along the length of a channel system. That being acknowledged, large volcanic channel systems are believed to have had extraordinary capacities to insulate flows through the formation of mobile or fixed crusts, and flow depths of tens of meters should have had much greater capacities to retain heat than much thinner flows of otherwise similar characteristics (e.g., Williams et al., 2001, 2011; Keszthelyi et al., 2006). For example, for Martian flows of only 20 to 30 m depth, decreases in lava temperature of only ~1°C / 30 km have previously been estimated (Keszthelyi et al., 2006). The extraordinary heat of the Venusian surface and near-surface would have also significantly reduced the rate at which lava temperatures at Kallistos Vallis decreased, even for well-exposed flows lacking insulating crusts. For an approximate total system area of 41,000 km2 and a hypothetical average incision depth of 50 m across the entire system, an overall volume of regolith removed of 2050 km3 is determined (average erosion depths of 10 m and 100 m instead suggest total regolith removal of 410 and 4100 km3, respectively). Based on mixing considerations alone, a 50 m average incision depth, and corresponding volume of regolith removal of 2050 km3, suggests a minimum volume of effused lava of 6970 km3 (depths of 10 m and 100 m instead suggest total effused lava volumes of ~1390 km3 and 13,950 km3). A more conservative scenario for formation of Kallistos Vallis involves an assumption that substantial incision by lavas only took place in the westernmost and

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central parts of the system, where somewhat steeper reaches characterized by relatively deep valleys or prominent erosional residuals are more abundant. The surface area of the part of this system that extends from the head depression southward and eastward to the termination of Longitudinal Profile 2 (Figure 3.7) is calculated to be ~8600 km2 (Appendix C), which is roughly 21% of the full system area as defined in Figures 3.9 and 3.10. A simplified scenario involving a uniform 50 m incision depth across this relatively small part of the channel system suggests removal of only ~430 km3 of substrate, and the basic thermal principles outlined above suggest a corresponding minimum effusion volume of ~1460 km3. Alternative eroded depths of 10 m and 100 m are instead associated with the removal of 86 km3 and 860 km3, respectively, and corresponding minimum total effused volumes of 292 km3 and 2924 km3. The eastern volcanic plains of the Kallistos Vallis system, located down- channel of Longitudinal Profile 2 (Figure 3.7) and west of the north-south oriented ridge, have a total surface area of about 32,400 km2. It’s not clear how thick the mantling lavas are in this plains region, but estimates of possible accumulated flow volumes in this terminal part of the channel system can be made by assuming particular depths of pooled lava. For example, uniform lava thicknesses of 10 m, 50 m, 100 m, and 200 m here respectively imply mantling lava volumes across these plains of ~324 km3, 1620 km3, 3240 km3, and 6480 km3. Still greater terminal volumes of lava are implied for the Kallistos Vallis system by the associated flows that apparently accumulated on the eastern side of the north-south oriented ridge. With the surface area of the flows on the eastern side being slightly greater than that of the flows on the western side, the lava volume on both sides of the ridge could certainly total about 15,000 km3. As noted above, lava temperatures do not strictly remain uniform over great distances and instead gradually decrease from eruptive centers, and thus the capacity for incision also decreases in this manner. Beyond the strictly invalid assumptions that are implicit in this type of estimation, the above estimations assume highly efficient

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thermal channel incision without e.g., periodic constructive emplacement of lava flows that must later be eroded. As a result of the limitations of the estimation method, only a lowermost bound is produced, and the actual range of possible lava volumes could realistically extend up to many times this amount.

5.2 Discharge-Related Determination of Minimum Lava Volume Effused at Kallistos Vallis A highly simplified rectangular-shaped channel system with a uniform width of 30 km, a length of 1200 km, and a depth of 57 m, would have a total volume of 2050 km3 (i.e., the same volume determined above for the uniform loss of 50 m of material over the entire system as defined in Figures 3.9 and 3.10). If lava properties are again simplistically assumed to remain constant along the full length of the channel system, and if a total thermomechanical incision rate of 3 m/day is conservatively assumed, a channel development time of 19 days is estimated (though system development by multiple shorter eruptive episodes separated by geological time is entirely possible), and a total erupted lava volume of 15,700 km3 is estimated if a temporally and spatially uniform discharge rate of 9.549 x 106 m3/s is assumed (derived from the 3.183 x 106 m3/s estimate previously made for 20-m-deep lavas flowing along channel reaches with widths of 10 km and a slope of 0.1°). If we consider the overall slope of the system today which is ~0.02°, then assuming a 1.5 m/day thermomechanical incision rate, gives us an estimated channel development time of 38 days. In this scenario the discharge decreases to 3.972 x 106 m3/s, which over the course of 38 days results in the total effusion of 13,042 km3 of effused magma. Thermal incision is proportionally higher in this lower slope regime. The above estimates are based on crude assumptions related to a small number of specific scenarios, and thus cannot be confidently assumed to quantify the full range of lava volumes potentially involved in the development of the Kallistos Vallis system. Nevertheless, the above estimates do suggest possible development of the system by eruption of up to roughly 7000 km3 of lava, and possibly in excess of double this volume. More generally, minimum eruption totals of thousands of cubic

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kilometers of lava, and possibly well in excess of 10,000 km3 of lava, are predicted. Such volumes, and the overall size of the Kallistos Vallis system, compare well with e.g. the Martian Athabasca Valles system, which has previously been hypothesized as a system possibly (e.g., Keszthelyi et al., 2017) or certainly (e.g., Leverington, 2009, 2011) formed entirely as a result of incision by low-viscosity lavas. The Athabasca Valles system is associated with lava flows with a total estimated volume of ~7500 km3 (Jaeger et al., 2014).

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CHAPTER VI

DISCUSSION Kallistos Vallis is a compound Venusian channel system located in the Ammavaru volcanic province. The system commences at a large topographic depression that marks the site of effusion of a low-viscosity fluid that first flowed southward and then eastward, terminating at a large ridgeline located in the southern part of Vaidilute Rupes in the systems eastern depositional plain. The elevation of the system drops from ~1300 m to ~925 m over a total distance of ~1235 km, with an average system slope of ~0.30 m/km. Based on cross-sectional profiles and overall channel appearances in radar datasets, the westernmost and central reaches of Kallistos Vallis may have been incised into local terrain as much as tens of meters. Substantial incision along the easternmost reaches is less apparent, with the topographic relief of associated channels and adjacent uplands relatively low. These eastern reaches are widely mantled by variously radar-dark and radar-bright lava flows. The overall surface area of the Kallistos Vallis system is ~41,920 km2, with the western and central reaches having a total area of ~8600 km2, and the wider eastern reaches having a total area of ~32,400 km2. Surface area calculations for Kallistos Vallis differ from the ~100,000 km2 surface area estimate from Baker et al., 1997. The larger area estimate is due to the inclusion of terminal deposits located to the east of Vaidilute Rupes. This area was omitted from this study as it was not considered a part of the primary channel system, and only served as a vast plain which collected deposits that overflowed or bypassed the north-south trending ridgeline. Cross-sectional profiles generated in this study differed from Baker et al., 1992 in that they were generated strictly from left-look radar, and not stereo, images. This is because the Baker group had access to a more robust elevation database. Since the resolution of the altimetry data is fairly low to begin with; therefore only making it possible to get a rough channel shape, this difference is not considered critical to the goals of this study. Where this study really

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departs from Baker et al., 1997 is in regards to estimates of flow conditions. The original Baker et al., study focused primarily on channel morphology, giving descriptive details of channel structures, as well as quantitative measurements of channel features such as system lengths, widths, depths, slopes, and area, based on the quantitative observations of SAR radar imaging. It did not attempt to determine actual flow parameters or estimates of channel incision. This study models the channel system using known method and equations used in the analysis of other analog systems found within the inner solar system. These calculations include, but are not limited to, the following: 1) rates of thermomechanical incision; 2) total volume of magma extruded; 3) total volume of substrate excavated; and 4) rates of discharge. Additionally, this study aimed to make both qualitative and quantitative comparisons to other analog systems in order to better understand the physical mechanisms of volcanic incision and channel formation as a whole. As the distance lava travels from the source increases, it is expected that its temperature will decrease and its viscosity will increase (Keszthelyi et al., 2006). The drop in temperature reduces the capacity of lava to thermally incise, and the increase in viscosity has a similar effect on mechanical erosion. It is therefore expected that if Kallistos Vallis formed via large effusions of magma onto the Venusian surface, then channel reaches located closer to the source would have been more likely to have formed erosively, whereas its more distal reaches would be more constructional in nature. Analyses of Magellan radar imagery agree with this hypothesis. The deepest areas of incision are within a structurally controlled trough, located within the northwestern half of Longitudinal Profile 2, where channel depths are as great as ~600 m (Baker et al., 1997). In addition to thermomechanical erosion, it should be noted that structural collapse appears to contribute to the ~600 m overall depth. This is evidenced by the appearance of mesa remnants (Baker et al., 1997). System depths then decrease with distance downstream. The most distal reaches of the system separate into three “finger-like” distributary channels (Longitudinal Profiles 3 - 5). These segments of the system spread out laterally on either side, overflowing their

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banks and forming lobate margins that are constructional in nature. The system finally empties out into a vast depositional plain whose contents (as with other volcanic analog systems) are at least in part comprised of materials originating in the northwestern source regions. The morphology and geological context of the Kallistos Vallis system are aligned with volcanic origins analogous to those expected of large ancient channel systems preserved at the surfaces of multiple bodies of the inner solar system. These bodies include the Earth, Moon, and Mercury (e.g., Leverington, 2014). Terrestrial and lunar analogs are up to hundreds of kilometers long and several kilometers wide (e.g., Williams et al., 2001, 2011; Hurwitz et al., 2012; Cataldo et al., 2019); whereas on Mercury, flows are no longer than ~160 km, but in places exceed 30 km in width (e.g., Byrne et al., 2013; Hurwitz et al., 2013a). The longitudinal slopes of lunar and Mercurian systems are typically no greater than 0.50° (Williams et al., 2001a; Hurwitz et al., 2012, 2013a; Byrne et al., 2013), although some original Mercurian slope calculations (such as for Angkor Vallis) are difficult to estimate due to the widespread mantling of channels by relatively thick sets of lava flows (Byrne et al., 2013). These estimations use slope values that are similar to those used in other studies that calculated lava flow rates (e.g., Williams et al., 1001a; Byrne et al., 2013; Hurwitz et al., 2013). The petrology of lavas involved in the development of analog volcanic systems is not uniform across the inner solar system. On Earth, involved lavas at systems such as those of northernmost Quebec and western Australia were high-Mg ultramafic flows erupted mainly in submarine environments (e.g., Williams et al., 1998, 2001, 2011, Le Vaillant et al., 2016), whereas lunar systems generally appear to have involved high-Fe and low-Mg flows of mafic to ultramafic compositions with a distinct anhydrous character (e.g., Head and Wilson, 1992; Hurwitz et al., 2010, 2012). The Mercurian systems formed in association with low-Fe and high-Mg flows and were similarly anhydrous in nature (Head et al., 2011; Stockstill-Cahill et al., 2012; Byrne et al., 2013; Hurwitz, 2013). Venusian channels have not yet been

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directly visited by landers, but the apparent anhydrous nature of the Venusian surface and the extraordinarily high surface temperatures that are very likely to have prevailed on Venus over extended geological time scales, strongly suggest that the fluids involved in the formation of the Venusian channels were lavas rather than water. The mafic flows sampled at the Venera 14 site, which are not associated with any known channels and instead are components of local volcanic plains, are estimated to have had viscosities of ~44 Pa s (Ashley and Ramsey, 2019). Some Venusian flows are separately estimated to have had minimum viscosities at least as low as ~4.5 to ~7.5 Pa s (Kargel et al., 1993). More generally, the minimum viscosities of lavas expected to have been involved in development of large analog channel systems of the inner solar system are as low as ~0.1 Pa s for the Earth (e.g., Williams et al., 1998, 2001, 2011), ~0.02 Pa s for Mercury (e.g., Byrne et al., 2013; Hurwitz et al., 2013), and ~0.5 Pa s for the Moon (e.g., Murase and McBirney, 1970, 1973; Hurwitz et al., 2012; Chevrel et al., 2014, Sehlke and Whittington, 2016). The lavas at the mouth of Martian channel Ma’adim Vallis are estimated to have had minimum viscosities of ~0.5 Pa s (Chevrel et al., 2014). The properties of lava flows erupted in association with the formation of Kallistos Vallis are likely to have varied in time and in space. Properties are likely to have changed from eruption to eruption, and for particular eruptive events. Lava temperatures are very likely to have been highest and viscosities lowest closer to the volcanic vents. In the simple eruptive scenarios considered in this study, if a lava viscosity of 1 Pa s is assumed, lavas with depths of 5 m and 20 m flowing on slopes of up to 1° are estimated to have been associated with velocities as great as ~55.28 m/s and discharges as great as ~1.11× 107 m3/s. Such flows will have been fully turbulent for essentially all slopes in excess of 0°. Assuming lava temperatures and substrate temperatures of 1350°C and 470°C, respectively, thermal incision rates of up to ~6.82 m/day are estimated for slopes of up to 1°. Kallistos Vallis could conceivably have formed in as little as 19 days; however, it should be noted this is only a minimum estimate and the system could theoretically have been formed as a result of numerous

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eruptions separated by considerable amounts of geological time. The above rates of incision are somewhat higher than those previously estimated to be typical of e.g. lunar, Mercurian, and Martian, systems (e.g., Williams et al., 2001, 2011; Byrne et al., 2013; Hurwitz et al., 2013a; Leverington, 2014), mainly due to the relatively high gravity and the very high substrate temperature of Venus, which will not have the same cooling effect as the colder substrates of other rocky bodies. Corresponding values for mechanical incision rates of up to ~41.40 m/day are estimated. Overall, the magnitudes of the values for both mechanical and thermal incision are in line with those previously estimated for various bodies of the inner solar system. Examples include: 1) the Martian Athabasca Vallis system (an analog system arguably most similar in morphology to Kallistos Vallis), which has estimated discharge rates as high as 20 × 106m3/s taking up to ~17 days to erupt 7500 km3 of lava (Jaeger et al., 2009); 2) Mercury’s wide valleys, which have estimated incision rates of up to ~17 m/day, discharge rates as high as 6.1 × 106m3/s, and a total erupted volume of 1.5 × 104 km3, despite their relatively short lengths of no more than ~160 km (Hurwitz et al., 2013); 3) Rima Prinz , a four-channel system of lunar sinuous rilles, whose second channel from the west has estimated incision rates up to 1.7 m/day, discharge rates as high as ~4400 m3/s and a total erupted volume as high as 250 km3 (Hurwitz et al., 2012); and 4) the largest known channel located within the Katinniq Member of the Raglan Formation, which is a terrestrial submarine sinuous rille that had thermal incision rates up to 1.5 m/day, discharge rates up to 106m3/s, and a total volume of effused lava in excess of 104 km3 for a system whose full length is unknown (Williams et al., 2011). Based on simplified thermal and other considerations, the minimum effused volume of lava required for the formation of Kallistos Vallis is estimated here to be of 292 km3 on the basis of assumptions of a surface area of ~8600 km2 (for the westernmost and central parts of the system), eroded depths of 10 m, and removal of 86 km3 of substrate. Even given the crude nature of such estimates, we can generalize that effused lava volumes are likely to have at least been on the order of thousands to

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tens of thousands of cubic kilometers. Overall thermomechanical incision rates cannot yet be calculated directly, but thermal and mechanical processes should complement each other and results should collectively exceed their separate effects. If a total thermomechanical incision rate of 3 m/day is assumed, a total effused lava volume of ~15,700 km3 is predicted for a particular simple model explored above. Estimates such as those given above are consistent with those made previously for other volcanic channel systems of the inner solar system. For example, the similarly-sized Athabasca Valles system of Mars is directly associated with an estimated ~7500 km3 of volcanic units that were clearly emplaced quickly and turbulently, and flowed with minimum viscosities at least as low as 10 Pa s (Jaeger et al., 2010; Keszthelyi et al., 2017). The relatively narrow Hrad Vallis system of Mars has a total length of ~1450 km and is estimated to have been formed by the eruption of as little as ~11,000 km3 of low- viscosity lava (Hopper and Leverington, 2014). The westernmost sinuous rille of the lunar system Rima Prinz, at an estimated length of only ~75 km, could have formed with as little as ~50 to ~250 km3 of erupted low-viscosity lava (Hurwitz et al., 2012). Finally, Mercury’s Angkor Vallis at a length of ~85 km, is estimated to have erupted a minimum of ~150,000 km3 of magnesium-rich, iron-poor lava; an amount required to fill the Kofi Basin located at the terminus of the channel (Byrne et al., 2013). The methods used to obtain modeling results for Kallistos Vallis can be expanded to other Venusian systems, as well as systems located on other rocky bodies of the inner solar system. Baltis Vallis, a Venusian canali, is the longest known volcanic channel of the inner solar system (and indeed is the longest known channel of any kind; Komatsu, 2007) and though this system arguably did not involve substantial incision and instead helped to constructively emplace associated lava flows, it is believed by at least some workers to have formed through mechanical erosional processes (Oshigami and Namiki, 2007).With an approximate length of ~6800 km, average width of ~2.2 km, and an average incision depth of ~46 m (Oshigami and Namiki, 2007), the system is calculated to have a total area of ~14,960 km2. Simplistically assuming a rectangular cross section and given the same thermal mixing

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and compositional considerations, the minimum effused volume of lava required for the formation of Baltis Vallis is ~2340 km3. This would have resulted in the excavation of ~688 km3 of substrate materials. These calculations are based on an assumption of the involvement of lavas of mafic or ultramafic composition, erupted at a temperature of ~1350°C. Oshigami and Namiki (2007) suggest that one of the most likely types of lava extruded in the formation of Baltis Vallis is carbonatite. This rather exotic, low-viscosity silicate magma would have been erupted at a much lower temperature (~500 to ~600°C), thereby requiring an adjustment in thermal mixing calculations to determine the total amount of extruded magma required for system development. Essentially all landforms observed on Venus were likely formed in the past 1 Ga, thereby, making it impossible with the current available datasets to determine what geological features and units may have formed or existed in earlier Venusian Epochs. Since the vast majority of large volcanic channels located on other rocky bodies of the inner solar system formed within the first ~1 to ~2 Ga of solar system history, it is reasonable to conclude that volcanic channels much greater in size than Kallistos Vallis may well have formed earlier in the planet’s history (e.g., Leverington, 2019). The development of Kallistos Vallis is consistent with that of other known analogous systems located within the inner solar system (e.g., Murase and McBirney, 1970, 1973; Williams et al., 1998, 2001, 2011; Leverington, 2004, 2009, 2011, 2014; Hurwitz et al., 2010, 2012, 2013; Head et al., 2011; Byrne et al., 2013; Hopper and Leverington, 2014;). These similarities include documented or presumed mafic to ultramafic lava compositions, lava viscosities ranging from 0.1 to 10 Pa s, high rates of lava discharge to the surface, extremely large total volumes of effused lavas (in numerous cases far exceeding 104 km3), occurrence of highly turbulent flow during channel development, and substantial involvement of incision via presumed thermomechanical processes.

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Based on the global cratering record, it is generally agreed that Venus was resurfaced over the last 1 Ga. Kallistos Vallis is one of the largest volcanic outflow systems in the solar system. Since Venus is much older than the geological features we are able to observe at the surface of the planet today, and given the planet-wide resurfacing that has taken place, it is entirely possible (and probable) that channel systems much larger than Kallistos Vallis existed earlier on in Venus’ geologic history. This has important implications to the study of other volcanic systems within the inner solar system, including the Earth. With regards to planetary size, mass, and gravitational acceleration, Venus is Earth’s twin. A better knowledge of Venusian igneous plumbing, both now and historically, can provide important contextual information regarding Earth’s volcanic and tectonic past. To better understand and answer these questions will require the collection of new data by future space missions. Among the most important types of data needed are in situ measurements of geological compositions, high resolution (meter scale) SAR images, optical and infrared remote sensing images of the Venusian surface, and new topographic data with sub-kilometer resolution. Currently VEXAG (Venera-D), a planned future joint US-Russian mission, consists of both an orbiting satellite to explore atmospheric dynamics, and a lander to study surface geology and chemistry. Among the proposed landing site types considered for VEXAG are lava flow fields, including volcanic channels where the substrate has been eroded (Senske and Zasova, 2017). Such sites have previously been suggested to have been formed by lavas whose compositions are analogous to carbonatites (Kargel et al., 1994), though the flow of silicate magmas at these systems would be more consistent with solar system analogs and expected magma compositions at Venus (e.g., Leverington, 2014). Direct in situ sampling and geochemical analysis of an eroded channel would help determine the type of lava involved in the formation of Kallistos Vallis and other Venusian channel systems. Beyond any future space mission, it is possible to model the flow of the channel itself (and its separate individual reaches) using Monte Carlo simulations. Monte Carlo simulations have been used to model Venusian planetary resurfacing

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(e.g., Romeo and Turcotte, 2010; Ashley and Ramsey, 2019). A more advanced method would be to model flow dynamics and channel incision as a function of 1) the changing lava chemistry due to gradual cooling; and 2) the incorporation of substrate materials. This type of modeling is not yet readily performed for Venus; however software packages such as MELTS are currently available for describing the changing chemistry of a flow as a function of temperature and distance (e.g., Chevrel et al., 2014; Ashley and Ramsey, 2019), and could potentially be adapted to the Venusian environment. Additionally, new modeling efforts are now being made with regard to the study of the three-dimensional formation of channels via thermal and mechanical incision on bodies such as the Moon (e.g., Cataldo et al., 2019;), and may in the near future provide new methodologies for the study of the development of large and complex volcanic systems including Kallistos Vallis.

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CHAPTER VII

CONCLUSIONS The morphology of the Kallistos Vallis outflow system is consistent with volcanic origins through thermal and mechanical incision by voluminous effusions of low viscosity lava. This channel system has morphological characteristics analogous to those of numerous other large volcanic channel systems found on rocky bodies within the inner solar system. Kallistos Vallis originates from a region of collapsed topography that marks the source of the channel, located east of Selu and Sarpantium Corona in the Ammavaru volcanic province. The head of the system is interpreted as the surface expression of a deeply rooted igneous plumbing system from which voluminous quantities of mafic or ultramafic lava were erupted. The main channel extends in a southeasterly direction before turning eastward and complexly anastomosing about multiple streamlined islands of varying sizes. Along its easternmost reaches, the system divides into three finger-like channels mantled by deposits that are both radar-bright and radar-dark, and characterized by lobate margins. Kallistos Vallis terminates in a large depositional plain that is separated into two parts by a large topographic ridge which comprises the southern portion of Vaidilute Rupes. Here extensive flows are estimated to have emplaced thousands of cubic kilometers of volcanic materials. In total, the longest continuous reaches of the channel system are ~1235 km, with an average slope of -0.3 m/km and channel sections up to 30 km wide. Cross- sectional and longitudinal profiles produced via the use of low-resolution Magellan altimetry data show topographic relief of at least tens of meters, and indicate kilometer-scale longitudinal slopes of much less than 1°, but otherwise fail to effectively constrain the form of the system. The total area encompassing the entirety of the outflow system, including the western half of the depositional plain (the area west of the Vaidilute Rupes ridgeline), is ~41,000 km2. Approximately 80% of this area encompasses the systems depositional plain; whereas, 20% encompasses the

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westernmost and central parts of the system where most channel incision is expected to have taken place. Flow conditions responsible for system development were estimated based on the nature of known volcanic analogs of the inner solar system, as well as known constraints of the Venusian environment such as the high surface temperatures and relatively high gravitational acceleration that characterize the surface. The incision rates estimated for 5 and 20-meter-deep flows are as great as ~41.40 m/day and ~6.82 m/day for mechanical and thermal regimes respectively, for slopes of up to 1, viscosities of 1 Pa s, Reynolds numbers up to ~3.10 × 106, and discharge rates as high as ~1.11 × 107m3/s. These flows could have attained velocities of tens of meters per second and would have been fully turbulent across essentially all channel slopes greater than 0. Development of Kallistos Vallis is estimated to have taken as little as tens of days, though system development by multiple discrete eruptive episodes separated by geological time is also possible. Though many uncertainties remain, the volumes of effused lava estimated to have been required for development of Kallistos Vallis range from thousands to tens of thousands of cubic kilometers. The eruptive and flow conditions estimated for Kallistos Vallis are consistent with those previously estimated for ancient large volcanic analog systems of the inner solar system, including those found on the Moon, Mercury, Mars, and early Earth. The nature of Kallistos Vallis highlights the notable differences in the character of modern terrestrial volcanism and that which dominated numerous rocky bodies during earlier epochs in the history of the solar system.

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APPENDIX A

SOURCE CODE FOR THE ITERATIVE CALCULATION OF MECHANICAL INCISION RATES

#include #include #include void clear_screen(); void intro();

/* This program makes flow and incision calculations on the basis of the */ /* equations outlined in Jaeger et al 2010 and Hurwitz et al 2010 + 2012. */ /* The incision processes modeled here are mechanical rather than thermal.*/ main() { double K_dimensional_ratio = 0.000000001; /* units are per Pa */ double rho_density = 2800.0; /* units are kg per m3 */ double g_gravitational_acceleration = 8.87; /* units are m per s2 */ double slope = 0.0; /* in degrees - set to zero initially */ double flow_width = 10000.0; /* flow width in m */ double flow_depth = 0.0; /* in meters - set to zero initially */ double sine_slope = 0.0; /* no units - is sine of slope */ double Q_total_discharge = 0.0; /* total Q - units are m3 per s */ double Q_partial = 0.0; /* Q per meter width - in m2 per s */ double flow_velocity = 0.0; /* flow velocity in m per s */ double incision_rate = 0.0; /* incision rate in m per s */ double Cf_friction_coefficient = 0.0; /* friction coefficient */ double Re_reynolds_number = 0.0; /* Reynolds number */ double mew_dynamic_viscosity = 1.0; /* dynamic viscosity of lava in Pa s */ /* NOT kinematic viscosity */

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double iteration = 0.0; /* calculations converge by iteration */ double number_of_iterations = 20.0;

double Cf_core = 0.0; /* is (2Re + 800)/41 */ double Cf_power92 = 0.0; /* is Cf_core to power 0.92 and then x 6.15 */ double Cf_log = 0.0; /* is log base 10 of Cf_power92 */ double Cf_power_neg2 = 0.0; /* is Cf_log raised to power -2 */ double Cf_1_32 = 0.0; /* is Cf_power_neg2 * 1/32 */

double velocity_core = 0.0; /* place holder used in velocity calculation */

FILE *fp_outputs; /* pointer for writing outputs to file */

clear_screen(); intro();

Re_reynolds_number = 100000.0; /* high initial Reynolds number seed value */

fp_outputs=fopen("outputs.txt","a"); fprintf(fp_outputs,"flow_depth in m, flow_width in m, slope in degrees, "); fprintf(fp_outputs,"Cf_friction_coefficient, flow_velocity in m/s, "); fprintf(fp_outputs,"incision_rate in m/s, incision_rate*86400 i.e. m/day, "); fprintf(fp_outputs,"Q_total_discharge in m3/s, Re_reynolds_number, "); fprintf(fp_outputs,"mew_dynamic_viscosity in Pa s"); fclose(fp_outputs);

/* ********* cycle through depths and slopes *********** */ for(flow_depth=5.0; flow_depth<51.0; flow_depth=flow_depth+5.0) {

for(slope=0.0; slope<1.01; slope=slope+0.01) { sine_slope = sin(slope*(3.14159/180.0));

/* ********* ITERATIONS BEGIN HERE *********** */ for(iteration=0.0;iteration

/* calculation of Cf friction coefficient */ Cf_core = (2.0*Re_reynolds_number + 800.0)/41.0; Cf_power92 = 6.15*(pow(Cf_core,0.92)); Cf_log = log10(Cf_power92);

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Cf_power_neg2 = pow(Cf_log,-2.0); Cf_1_32 = (1.0/32.0)*Cf_power_neg2; Cf_friction_coefficient = Cf_1_32;

/* calculation of lava flow velocity */ velocity_core = (g_gravitational_acceleration*flow_depth*sine_slope)/Cf_friction_c oefficient; flow_velocity = sqrt(velocity_core); /* calculation of new Re reynolds number */ Re_reynolds_number = (rho_density*flow_depth*flow_velocity)/mew_dynamic_viscosity;

/* calculation of incision rate */ Q_partial = flow_velocity*flow_depth; incision_rate = K_dimensional_ratio*rho_density*g_gravitational_acceleration*Q_par tial*sine_slope;

/* calculation of total discharge */ Q_total_discharge = Q_partial*flow_width;

printf("\n\niteration = %lf ",iteration); printf("\nK_dimensional_ratio = %lf",K_dimensional_ratio); printf("\nK * 1000000 = %lf",K_dimensional_ratio*1000000.0); printf("\nrho_density = %lf kg per cubic meter",rho_density); printf("\nmew_dynamic_viscosity = %lf Pa s",mew_dynamic_viscosity); printf("\ng_gravitational_acc = %lf m/s2",g_gravitational_acceleration); printf("\nflow_width = %lf meters",flow_width); printf("\nflow_depth = %lf meters",flow_depth); printf("\nslope = %lf degrees",slope); printf("\nsine_slope = %lf ",sine_slope); printf("\nCf_friction_coefficient = %lf", Cf_friction_coefficient); printf("\nflow_velocity = %lf meters per second", flow_velocity); printf("\nincision_rate = %lf meters per second", incision_rate); printf("\nincision rate per day = %lf meters", incision_rate*86400); printf("\nQ_total_discharge = %lf m3 per second", Q_total_discharge); printf("\nRe_reynolds_number = %lf", Re_reynolds_number); } fp_outputs=fopen("outputs.txt","a");

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fprintf(fp_outputs,"\n%lf, %lf, %lf, %lf, %lf, %lf, %lf, %lf, %lf, %lf", flow_depth, flow_width, slope, Cf_friction_coefficient, flow_velocity, incision_rate, incision_rate*86400, Q_total_discharge, Re_reynolds_number, mew_dynamic_viscosity); fclose(fp_outputs); } fp_outputs=fopen("outputs.txt","a"); fprintf(fp_outputs,"\n\n\n"); fclose(fp_outputs); } printf("\nDone: Program complete. Output file is 'outputs.txt'\n"); } void clear_screen() { int x; for(x=0;x<30;x++) { printf("\n"); } } void intro() { printf("\n\nLAVA FLOW MODELING PROGRAM Version 1.0\n"); printf("Compiled: "__DATE__" "__TIME__"\n"); printf("Output file is called outputs.txt\n\n\n"); }

110 Texas Tech University, Derek A. Berman, December 2020

APPENDIX B

SOURCE CODE FOR THE ITERATIVE CALCULATION OF THERMAL INCISION RATES

#include #include #include void clear_screen(); void intro(); /* This program makes flow and incision calculations on the basis of the */ /* equations outlined in Hurwitz et al 2012 and Williams et al 1998 + Hulme */ /* 1973. The incision processes modeled here are thermal.*/ main() { double lava_temperature = 1350.0; /* lava temperature in degrees C */ double k_lava_thermal_conductivity = 0.0; /* thermal conductivity in W/(m K); this is a calculated value */ double c_sub_g_specific_heat_substrate = 1500.0; /* in J/(kg C) */ double Pr_Prandtl_number = 0.0; /* dimensionless ratio of kinematic viscosity to thermal diffusivity */ double h_sub_T_heat_transfer_coefficient = 0.0; /* eqn4 hurwitz et al 2012 */ double L_sub_g_latent_heat_of_fusion_of_substrate = 587000.0; /* J per kg */ double f_sub_mg = 0.4; /* substrate fraction melted before movement */ double T_sub_mg = 1150.0; /* melting T of substrate in degrees C */ double T_sub_g = 470.0; /* initial temperature of ground in degrees C */ double rho_sub_g = 2900.0; /* density of solid substrate in kg per m3 */ double E_sub_mg = 0.0; /* energy reqd to melt substrate, in J / m3 */

double rho_density = 2800.0; /* lava density; units are kg per m3 */

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double g_gravitational_acceleration = 8.87; /* units are m per s2 */ double slope = 0.0; /* in degrees - set to zero initially */ double flow_width = 10000.0; /* flow width in m */ double flow_depth = 0.0; /* in meters - set to zero initially */ double sine_slope = 0.0; /* no units - is sine of slope */ double Q_total_discharge = 0.0; /* total Q - units are m3 per s */ double Q_partial = 0.0; /* Q per meter width - in m2 per s */ double flow_velocity = 0.0; /* flow velocity in m per s */ double incision_rate = 0.0; /* thermal incision rate in m per s */ double Cf_friction_coefficient = 0.0; /* friction coefficient */ double Re_reynolds_number = 0.0; /* Reynolds number */ double mew_dynamic_viscosity = 1.0; /* dynamic viscosity of lava in Pa s */ /* mew=mu; is NOT kinematic viscosity */

double iteration = 0.0; /* calculations converge by iteration */ double number_of_iterations = 20.0;

double Cf_core = 0.0; /* is (2Re + 800)/41 */ double Cf_power92 = 0.0; /* is Cf_core to power 0.92 and then x 6.15 */ double Cf_log = 0.0; /* is log base 10 of Cf_power92 */ double Cf_power_neg2 = 0.0; /* is Cf_log raised to power -2 */ double Cf_1_32 = 0.0; /* is Cf_power_neg2 * 1/32 */

double velocity_core = 0.0; /* place holder used in velocity calculation */

FILE *fp_outputs; /* pointer for writing outputs to file */

clear_screen(); intro();

Re_reynolds_number = 100000.0; /* high initial Reynolds number seed value */

fp_outputs=fopen("outputs_thermal.txt","a"); fprintf(fp_outputs,"flow_depth in m, flow_width in m, slope in degrees, ");

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fprintf(fp_outputs,"Cf_friction_coefficient, flow_velocity in m/s, "); fprintf(fp_outputs,"thermal incision_rate in m/s, "); fprintf(fp_outputs,"thermal incision_rate*86400 i.e. m/day, "); fprintf(fp_outputs,"Q_total_discharge in m3/s, Re_reynolds_number, "); fprintf(fp_outputs,"mew_dynamic_viscosity in Pa s, lava_temperature, "); fprintf(fp_outputs,"k_lava_thermal_conductivity, Pr_Prandtl_number, "); fprintf(fp_outputs,"h_sub_T_heat_transfer_coefficient, T_sub_mg"); fclose(fp_outputs);

/* ********* cycle through depths and slopes *********** */ for(flow_depth=5.0; flow_depth<51.0; flow_depth=flow_depth+5.0) {

for(slope=0.0; slope<1.0025; slope=slope+0.0025) { sine_slope = sin(slope*(3.14159/180.0));

Re_reynolds_number = 100000.0; /* high initial Reynolds number seed */

/* ********* ITERATIONS BEGIN HERE *********** */ for(iteration=0.0;iteration

/* calculation of k_lava_thermal_conductivity */ k_lava_thermal_conductivity = 2.16 - (0.0013*lava_temperature); /* see eqns 7abc in Williams et al 1998 */

/* calculation of Prandtl number */ Pr_Prandtl_number = (c_sub_g_specific_heat_substrate * mew_dynamic_viscosity) / k_lava_thermal_conductivity;

/* calculation of h_sub_T_heat_transfer_coefficient, from Hulme 1973 and as shown in Hurwitz et al 2012 eqn 4 */ h_sub_T_heat_transfer_coefficient = (0.017 * k_lava_thermal_conductivity * (pow(Re_reynolds_number,0.8)) * (pow(Pr_Prandtl_number,0.4))) / flow_depth;

/* calculation of E_sub_mg; energy reqd to melt substrate in J / m3 */ E_sub_mg = rho_sub_g * ((c_sub_g_specific_heat_substrate * (T_sub_mg -

113 Texas Tech University, Derek A. Berman, December 2020

T_sub_g)) + (f_sub_mg * L_sub_g_latent_heat_of_fusion_of_substrate));

/* calculation of thermal incision rate */ incision_rate = (h_sub_T_heat_transfer_coefficient * (lava_temperature - T_sub_mg)) / E_sub_mg;

/* calculation of Cf friction coefficient */ Cf_core = (2.0*Re_reynolds_number + 800.0)/41.0; Cf_power92 = 6.15*(pow(Cf_core,0.92)); Cf_log = log10(Cf_power92); Cf_power_neg2 = pow(Cf_log,-2.0); Cf_1_32 = (1.0/32.0)*Cf_power_neg2; Cf_friction_coefficient = Cf_1_32;

/* calculation of lava flow velocity */ velocity_core = (g_gravitational_acceleration * flow_depth * sine_slope) / Cf_friction_coefficient; flow_velocity = sqrt(velocity_core);

/* calculation of new Re reynolds number */ Re_reynolds_number = (rho_density * flow_depth * flow_velocity) / mew_dynamic_viscosity;

/* calculation of total discharge */ Q_partial = flow_velocity*flow_depth; Q_total_discharge = Q_partial*flow_width;

printf("\n\niteration = %lf ",iteration); printf("\nrho_density = %lf kg per cubic meter",rho_density); printf("\nmew_dynamic_viscosity = %lf Pa s",mew_dynamic_viscosity); printf("\ng_gravitational_acc = %lf m/s2",g_gravitational_acceleration); printf("\nflow_width = %lf meters",flow_width); printf("\nflow_depth = %lf meters",flow_depth); printf("\nslope = %lf degrees",slope); printf("\nsine_slope = %lf ",sine_slope); printf("\nCf_friction_coefficient = %lf", Cf_friction_coefficient); printf("\nflow_velocity = %lf meters per second", flow_velocity); printf("\nthermal incision_rate = %lf meters / second", incision_rate); printf("\nthermal incision rate/day = %lf meters", incision_rate*86400);

114 Texas Tech University, Derek A. Berman, December 2020

printf("\nQ_total_discharge = %lf m3 per second", Q_total_discharge); printf("\nRe_reynolds_number = %lf", Re_reynolds_number); } fp_outputs=fopen("outputs_thermal.txt","a"); fprintf(fp_outputs,"\n%lf, %lf, %lf, %lf, %lf, %lf, %lf, %l f, %lf, ", flow_depth, flow_width, slope, Cf_friction_coefficient, flow_velocity, incision_rate, incision_rate*86400, Q_total_discharge, Re_reynolds_number); fprintf(fp_outputs," %lf, %lf, %lf, %lf, %lf, %lf", mew_dynamic_viscosity, lava_temperature, k_lava_thermal_conductivity, Pr_Prandtl_number, h_sub_T_heat_transfer_coefficient, T_sub_mg); fclose(fp_outputs); } fp_outputs=fopen("outputs_thermal.txt","a"); fprintf(fp_outputs,"\n\n\n"); fclose(fp_outputs); } printf("\nDone: Program complete. Output file is 'outputs_thermal.txt'\n"); } void clear_screen() { int x; for(x=0;x<30;x++) { printf("\n"); } } void intro() { printf("\n\nLAVA FLOW MODELING PROGRAM - THERMAL INCISION Version 1.0\n"); printf("Compiled: "__DATE__" "__TIME__"\n"); printf("Output file is called outputs_thermal.txt\n\n\n"); }

115 Texas Tech University, Derek A. Berman, December 2020

APPENDIX C

SOURCE CODE FOR AREA CALCULATIONS

#include #include #include main() { FILE *fp; /* file pointer for reading mask data */ float pixel_count=0.0; /* variable for counting #pixels with depth>0 */ float latitude=0.0; /* latitude of row being read from file */ int pixel=0; /* corresponds to pixel # in longitude direction */ int value=0; /* ie number, read from file */ int dummy=0; /* dummy variable for end of program */ float pixel_area=0.0; /* ie area of pixel, based on latitude */ float rate=0.000709823; /* lat change from row to row, in decimal degs */ float total_area=0.0; /* ie total area of whole region (whole feature) */ float problem_count=0.0; /* variable for counting problematic values of255 */

printf("\n\nArea calculation started...\n");

fp=fopen("dem.txt","r"); if(fp==NULL) { printf("File dem.txt cannot be opened or does not exist.\n"); exit(1); }

for(latitude=-47.0;latitude>(-51.85);latitude=latitude-rate) { for(pixel=0;pixel<14085;pixel++) { fscanf(fp,"%d",&value); if(value==1) { pixel_count=pixel_count+1.0; pixel_area=(0.0750177)*(cos(latitude*0.017453277)*0.0750177); total_area=total_area+pixel_area; } if(value==255) {

116 Texas Tech University, Derek A. Berman, December 2020

problem_count=problem_count+1.0; } } } printf("\n\nArea calculation complete\n"); printf("\ntotal area of feature is %f km2\n\n", total_area); printf("\n\nTotal number of pixels with value of 1 = %f",pixel_count); printf("\n\nTotal number of pixels with value of 255 = %f",problem_count); scanf("%d",&dummy); }

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