Variability of Subglacial Drainage Across the Greenland Ice Sheet: a Joint Model/Radar Study

Home , Bailey Ice Stream, Scambos Glacier, Slessor Glacier

Variability of Subglacial Drainage Across the Greenland Ice Sheet: A Joint Model/Radar Study

Wing Yin Chu

Submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2017 c 2017

Variability of Subglacial Drainage Across the Greenland Ice Sheet: A Joint Model/Radar Study

Wing Yin Chu

Over the last several decades, the majority of the Greenland outlet glaciers have accelerated due to the increased warming in both the atmosphere and the oceans around the polar latitudes. While there is a clear overall acceleration trend over this period, there is significant variability in the glacier responses to climate on seasonal and year-to-year timescales. This variability observed around Greenland is very likely tied to the differences in internal dynamics of individual glaciers and the complex interaction with its local environment. Here I investigate the interaction between ice and water along the ice base as an important mechanism contributing to the observed variability among glaciers in Greenland. I use a range of modeling and radar sounding approaches to study the subglacial hydrology for three types of outlet glaciers, including slow moving, marine terminating glaciers in the west, a land-terminating system in the southwest, and a fast moving, marine-terminating glacier in northern Greenland. These case studies allow me to characterize the basal water distribution, its variability throughout the year and how this drainage behavior varies across different regions of Greenland. To start, I use a hydrological routing model to characterize the subglacial hydrology for three neighboring slow moving (< 100myr−1), marine terminating glaciers in western Greenland. The hydrologic model allows me to examine the sensitivity of basal water routing to subtle changes in basal water pressures. My results reveal that Greenland subglacial drainage can be rerouted across 100’s of km in response to changes in basal water pressures as small as 10%. I conclude that water piracy and subsequent dramatic changes in ice velocity, similar to that observed around the Siple Coast in West Antarctica, can occur in Greenland. Next, I move to a more data-orientated approach and use airborne radar sounding to examine the seasonal variability of basal water distribution. To robustly characterize basal water from radar bed power, I use a novel radar analysis approach that integrates a thermomechanical ice-sheet model to predict the spatial variations of radar attenuation. I improve this approach by including a least-squares minimization to correct for power offsets due to the different radar systems deployed in multiple field seasons. This improved method is first applied to two land-terminating glaciers in the southwest, Russell Glacier, and Isunnguata Sermia. Using two seasons of radar sounding data, I find that the basal water distribution can change between the wintertime and the summertime. My results reveal that during the winter, water resides primarily in small pockets on top of bedrock ridges. In the summer, these pockets of water on the ridges connect and drain into the nearby basal troughs. This seasonal shift in the basal water distribution is actively controlled by the material properties of the bed. Therefore, in addition to the bed topography, the permeability of the bed and the presence of basal sediments could also exert a critical influence on the seasonal development of subglacial drainage. Finally, I apply the radar analysis approach to a fast-flowing marine terminating glacier for Petermann Glacier in Northern Greenland. Here I incorporate an additional step to address the spatial variation in ice chemistry and its effect on radar attenuation. I use this approach to examine the relationship between basal water, ice deformation and the onset of glacier flow. In addition to finding basal water in the fastest flowing region near the ice margin, I identify substantial basal water in the ice sheet interior where meltwater must either be related to the advection of water from upstream or be generated by internal heating due to ice deformation. My results show there are three basal water networks beneath Petermann that connect the ice sheet interior to the margin. Together, the interaction between these basal water networks and the ice deformation enhances and sustains fast flow in the interior of the Petermann catchment. Overall, the research presented in this dissertation suggests that subglacial hydrology is high variable in both space and time. This variation in the hydrologic system can influence the fundamental structure of the ice sheet through changing the transport and storage of basal water and through interacting with ice deformation and the thermal properties of the bed. Table of Contents

List of Figures iv

List of Tables vi

Acknowledgements vii

Dedication ix

1 Introduction 1 1.1 MotivationandGoals ...... 1 1.2 Subglacialhydrologyandicedynamics ...... 4 1.3 Techniques to study subglacial hydrology ...... 8 1.3.1 Hydrologicalmodels ...... 8 1.3.2 Airborneradarsounding...... 9 1.4 Scopeofchapters...... 11

2 ReroutingandPiracyofWaterinWestGreenland 14 2.1 Abstract...... 14 2.2 Introduction...... 15 2.2.1 WestGreenlandstudysite...... 17 2.3 Data...... 18 2.3.1 Lamont-Dohertysurvey ...... 19 2.3.2 CReSISSurvey ...... 20

i 2.4 Methods...... 22 2.4.1 Interpolationoftopography ...... 22 2.4.2 Erroranalysis...... 22 2.4.3 Subglacial flow paths and catchment delineation ...... 23 2.5 Results...... 26 2.5.1 Flow paths change with water pressure conditions ...... 26 2.5.2 Flowdependenceontopography ...... 28 2.5.3 InfluenceoferrorinDEMsonflowpaths ...... 31 2.6 Discussion...... 31 2.6.1 Potential impact on seasonal ice velocity ...... 31 2.6.2 Potential impact on water budget assessments...... 34 2.7 Conclusion ...... 35 2.8 Supportinginformation ...... 36 2.8.1 Comparison of water routing with BedMachine ...... 36 2.8.2 Influence of uncertainties in DEMs on water routing ...... 37 2.8.3 Influence of localized changes in water pressure on routing...... 39

3 Variations in Water Storage in Southwest Greenland 41 3.1 Abstract...... 41 3.2 Introduction...... 42 3.3 DataandMethods ...... 43 3.4 Results...... 44 3.5 Discussion...... 48 3.5.1 Control of bed properties on subglacial hydrology ...... 48 3.5.2 Volume of water storage and its impact on water budget ...... 49 3.5.3 Impact of storage on early season velocity ...... 50 3.6 Conclusion ...... 51 3.7 Supportinginformation ...... 52 3.7.1 IceBridgeradarsoundingdata ...... 52

ii 3.7.2 Radarbedechoanalysis ...... 52 3.7.3 Icesheetmodel...... 55 3.7.4 Radarattenuationmodel ...... 56 3.7.5 Comparison with empirical based methods...... 58 3.7.6 Uncertaintyinicetemperatures...... 61 3.7.7 Hydraulicpotentialanalysis ...... 63

4 Variations in Water Production Beneath Northern Greenland 66 4.1 Abstract...... 66 4.2 Introduction...... 67 4.3 IceBridgeradarsoundingdata...... 68 4.4 Overviewofradaranalysisapproach ...... 69 4.5 Results...... 75 4.6 Discussion...... 79 4.6.1 Distribution and sources of basal water in Petermann ...... 79 4.6.2 Relation between water and deformation at the onset region . . . . . 81 4.7 Conclusion ...... 83

5 Conclusion 86

Bibliography 90

iii List of Figures

1.1 Recent changes in Greenland mass loss and sea level contributions . . . . . 2 1.2 Key variables in determining Greenland mass balance ...... 3 1.3 Surface and subglacial drainage components in Greenland...... 4 1.4 Diﬀerent forms of subglacial drainage underneath Greenland...... 6 1.5 Observed ice velocity changes produced by variations in subglacial hydrology 7 1.6 A radar echogram showing distinctive subglacial water bodies ...... 10 1.7 Potential caveats for identifying water from radar ...... 11 1.8 Inﬂuence of deformed ice bodies on radar returned power ...... 12

2.1 Sarqardliup Sermia, Alángordliup Sermia and Nordenskiöld Gletscher in WesternGreenland...... 19 2.2 Gridded maps of ice thickness and bed elevation ...... 20 2.3 Crossovererrorsinicethickness...... 21 2.4 Rerouting of subglacial water flow paths beneath West Greenland...... 27 2.5 Drainage flow paths and water catchments for different water pressure scenarios...... 28 2.6 Evolving dependence of water flow directions on ice surface slope and bed slope...... 30 2.7 Changes in ice velocity pattern related to subglacial waterpiracy ...... 32 2.8 Estimated water flow paths using a previously published bed elevation map 37 2.9 Localized changes in water pressure resulted in subglacial water rerouting . 40

iv 3.1 Russell Glacier and Issunguata Sermia in Southwest Greenland ...... 45 3.2 Seasonal changes in subglacial water storage shown alongaprofile . . . . . 46 3.3 Seasonal changes in subglacial water storage across the Russell-Isunnguata Catchment ...... 47 3.4 Comparison between observed and modeled water storage locations. . . . . 49 3.5 Effect of leveling to correct for radar power offsets across multiple seasons . 54 3.6 Estimated ice velocity and temperature from a thermomechanical model . . 56 3.7 Estimated radar attenuation losses across Russell-Isunnguata ...... 57 3.8 Probability distribution of relative reflectivity ...... 60 3.9 Comparison of reflectivity values calculated using my model-integrated techniquewithotherpreviousapproaches ...... 61 3.10 Bivariate histogram of relative reflectivity and ice thickness ...... 62 3.11 Comparison between modeled and observed ice temperature at Russell catchment...... 62 3.12 Impact of ice temperature uncertainties on radar reflectivitypattern . . . . 63 3.13 Impact of ice temperature uncertainties on radar reflectivity distribution . . 64 3.14 Subglacial storage occurs on higher bed elevations ...... 65

4.1 Petermann Glacier in Northern Greenland ...... 69 4.2 Different components in my combined model-radar analysis techniques . . . 70 4.3 Effect of leveling to correct for radar power variations across multiple seasons 72 4.4 Effect of ice chemistry on radar attenuation ...... 74 4.5 Radar attenuation and its uncertainty across the Petermann catchment . . 76 4.6 Estimated relative reflectivity and subglacial water distribution across the Petermanncatchment ...... 77 4.7 Modeled basal melt rates along three profiles ...... 84 4.8 Relationship between water distribution, ice velocity, and basal melting . . 85 4.9 Development of subglacial water network and uplift of basal ice close to the onsetoffastflowinthePetermanncatchment...... 85

v List of Tables

3.1 Values of dielectric properties of Holocene ice and constants used in the radar attenuation model to calculate reﬂectivity...... 59

4.1 Characteristics of airborne ice penetrating radar system in 2010 and 2011 . 71 4.2 Values of dielectric properties of ice and constants used in the radar attenuation model to calculate reﬂectivity...... 73

vi Acknowledgments

Like any other five to six year-long program, the road to my graduate degree has been long and winding, yet there has never been a moment when I regreted the decision to come and study at Columbia University. Over the last six years, I have met many exceptional individuals who have motivated me to move forward and have made me grow as a scientist, and more importantly, as a person. Here I would like to express my gratitude to all of you who have made a positive difference in shaping the start of my academic career. First and foremost I want to thank my adviser Robin Bell. It was an honor to work with her as a student. Robin always sees the good in the work other people have produced. The joy and enthusiasm that she has in science have motivated me throughout the years. Robin has always inspired me to dream big and not to be afraid to share ideas with other people, no matter how stupid these ideas sounded in my head. I am thankful for the excellent example she has provided as a successful female scientist and as a mentor. I would also like to thank my committee members, Meredith Nettles, Timothy Creyts and Roger Buck. I appreciate all of their contributions, time and ideas that have made my academic experience more productive and stimulating. Meredith provided clarity and direction for my Ph.D. and beyond, and reminded me that I am a strong and smart person in times when I thought I was neither. Tim encouraged me to persist and keep trying different ways to solve a problem until I found a solution. His infectious laughs and silly jokes kept me smiling when I lost my sense of humor. Roger broadened my perspective and demonstrated to me that we share many ideas between geodynamics and glaciology. Many thanks to the members of the Polar Geophysics group, especially to Kirsty, Indrani, Dave, and Nick, who have given me a source of friendship, scientific advice, and

vii collaboration. I am also thankful for my classmates with special thanks to Mike who was here when I started and now has moved on; to Sophia and Asmi who have been here throughout my degree; to Alex and Julian who have joined recently. I appreciate all of your friendship and mental support. In addition to the Lamont community, I am also very grateful for the generous advice I have received outside Columbia. I owe a very important debt to Dusty Schroeder, who paved a path forward for me when I was lost. He always goes out his way to help me, and his belief in me was sometimes all that kept me going. I also would like to express my gratitude to Helene Seroussi, who has always made time for me since I ﬁrst met her at a summer school. She always willing to assist me with my work even if the topics were outside her research interest. Finally, I would like to extend my deepest gratitude to those who are closest to me. To my best friends, Cherry, Leona, and Petra, who have always be there for me since we were kids. To Kenneth, my little brother, who has always been a joy in my life. To my dad, who has taught me that failures do not deﬁne who we are. To my mom, who has always encouraged me to pursue my dreams no matter how rocky things get. All of you have been a constant positive force in my life. I hope I have made you proud.

viii I dedicated this thesis to Professor Seymour Laxon, my master adviser who encouraged me to pursue a career in science. He passed away shortly after I met him at my ﬁrst AGU, where I promised that we would catch up and drink beers together every year. A wonderful human being, professor, and a lifelong mentor.

ix CHAPTER 1. INTRODUCTION 1

Chapter 1

Introduction

1.1 Motivation and Goals

The Greenland Ice Sheet is one of the world’s two largest reservoirs of freshwater. About 80% of the surface of Greenland is covered by ice. This ice mass has the potential to raise global sea level by approximately 7 m if it melts entirely (Bamber et al., 2007; Fretwell et al., 2013). Over the past two decades, the rate of mass loss from Greenland has accelerated from 34 6 Gtyr−1 between 1992 – 2001, to 215 157 Gtyr−1 between ± ± 2002 – 2011 (Sasgen et al., 2012; Shepherd et al., 2012). Greenland has become the largest contributor to current sea level rise, accounting for approximately 0.7 1.1 mmyr−1 over − the period of 1992 to 2011, roughly doubled the contribution from Antarctica (Shepherd et al., 2012). Greenland loses mass primarily through ablation on the ice surface, together with acceleration and retreat of fast-flowing outlet glaciers (Cuffey and Paterson, 2010). These mass losses are balanced by the mass gain through snow accumulation in the ice-sheet interior. Traditionally, it was thought that the increased accumulation at higher elevations due to climate warming would offset the marginal ice loss, leading to a gradual retreat over a millennial timescale (Huybrechts et al., 1991; Oerlemans, 1991; van de Wal and Oerlemans, 1994). Recent observations of ice flow, however, suggest that Greenland ice- CHAPTER 1. INTRODUCTION 2

Figure 1.1: Recent changes in Greenland mass loss and sea level contributions between the period 1992 - 2011. (a) Rate of mass loss. (b) Cumulative sea level contribution from Greenland. Figures from Shepherd et al. 2012. dynamic changes could respond to climate over a much faster timescale than changes in surface mass balance, leading to rapid mass losses on a yearly to decadal period (Howat et al., 2007; Joughin et al., 2010; Pritchard et al., 2009). At present, annual rates of dynamic mass loss are roughly equal to the contribution from surface ablation (Howat et al., 2007; Rignot and Kanagaratnam, 2006; van den Broeke et al., 2009). With no indications in the observations that the rate of mass loss from Greenland will slow down in the coming century, rapid dynamic changes are projected to exert an increasingly larger role in determining Greenland’s stability in the future (Howat et al., 2007; Parizek and Alley, 2004; Vieli and Nick, 2011). Despite the importance of glacier acceleration, processes that allow for rapid coupling between ice ﬂow and climate forcing are not well understood (Alley et al., 2005; Vieli and Nick, 2011). Currently, large-scale ice sheet models used to predict future sea level rise cannot realistically reproduce the complex velocity changes observed in outlet glaciers around Greenland (Aschwanden et al., 2016; Bindschadler et al., 2013; Vieli and Nick, 2011). One the greatest challenges in representing ice ﬂow in models is the variability in individual glaciers response to climate forcing (Csatho et al., 2014; Moon et al., 2014; Nowicki et al., 2013). CHAPTER 1. INTRODUCTION 3

Figure 1.2: Key variables in determining Greenland mass balance. (a) Satellite measurements of ice velocity between 2007 – 2009 (Rignot and Mouginot, 2012). (b) Changes in surface elevation between 2003 – 2008 that provides an indication to the rates of dynamic mass loss from the acceleration of outlet glaciers (Pritchard et al., 2009). (c) Mean surface mass balance between 1989 – 2004 from a regional climate model (Ettema et al., 2009).

This variability observed around Greenland is very likely tied to the local-scale processes and their variations among individual glaciers (Moon et al., 2014). Subglacial hydrology is one of the critical processes that can induce rapid changes in ice ﬂow (e.g. Bartholomaus et al., 2008; Zwally et al., 2002). The presence of basal water can modulate ice ﬂow, but how is the basal water distributed in an ice catchment, does it change throughout the year, and how does this drainage behavior vary across the Greenland Ice Sheet? These are the important questions that we must investigate in order to fully understand why ice sheets behave as they do now, and from there, to predict how they might behave in the future. The purpose of this dissertation is to investigate the variability of subglacial hydrology as a critical mechanism in contributing the observed rapid dynamic changes across the Greenland Ice Sheet. CHAPTER 1. INTRODUCTION 4

1.2 Subglacial hydrology and ice dynamics

Water drainage along the ice sheet base can cause variations in ice ﬂow. The presence of subglacial water increases basal velocity through facilitating sliding and deformation of saturated till (Alley et al., 1989; Bindschadler, 1983; Tulaczyk et al., 2000; Weertman, 1972). Along the ablation zone of Greenland, summer melt delivered by moulins and supraglacial lakes provides an abundant water source to the ice sheet bed (Figure 1.3)(e.g. Zwally et al., 2002). This surface input acts to raise basal water pressures, resulting in a transient increase in ice velocity (Bartholomaus et al., 2008; Das et al., 2008; Meierbachtol et al., 2013). When this water reaches the bedrock, higher basal water pressures encourage the growth of subglacial cavities on the lee side of bed protrusions (Fowler, 1986; Iken, 1981; Lliboutry, 1968). The growth of subglacial cavities locally separates the ice from the bed, causing a reduction in basal resistance and thereby enhances sliding (Hooke et al., 1989; Raymond et al., 1995). Where the water input reaches a bed composed of till, higher water pressure also weakens and deforms the sediment layers in additional to promoting sliding (Alley et al., 1989; Clarke, 1987; Fischer and Clarke, 2001; Iverson et al., 1995).

Figure 1.3: Various drainage components in the accumulation and ablation zones of Greenland (Zwally et al., 2002). In the ablation zone, supraglacial lakes, moulins, and crevasses deliver surface melt to the base of the ice sheet. Fluctuations in this melt input can cause signiﬁcant changes in ice ﬂow.

The distribution of basal water pressures is strongly dependent on the structure of CHAPTER 1. INTRODUCTION 5 the subglacial hydrologic system (Nienow et al., 1998; Schoof, 2010). In Greenland, water is thought to flow along the ice base in two forms of the hydrologic system, broadly characterized as ‘distributed’ or ‘channelized’ (Figure 1.4). The hydrologic system is thought to switch between these two forms over time with meltwater input (e.g. Flowers, 2015; Hewitt, 2013). For the majority of the year, when the meltwater input is low, the system is highly inefficient and spatially distributed. In this distributed state, drainage either occurs through interconnected cavities or thin water film or Darcian porewater flow in till (Clarke, 1987; Kamb, 1987; Walder, 1986; Weertman, 1972). As surface melt production increases during the early summer, the large water influx into a distributed system quickly exceeds its drainage capacity, leading to high basal water pressures over an extended area. The associated glacier speedup, termed a ‘spring event’, can be as great as 300% increase from the annual velocity and may last up to a few days (Bartholomew et al., 2011; Cowton et al., 2013; Hoffman et al., 2011; Palmer et al., 2011). As the season progresses towards late summer, the subglacial drainage develops from spatially distributed to a well-connected network of discrete channels (Röthlisberger, 1972; Shreve, 1972). The development of channels causes ice motion to become less sensitive to the additional surface melt input as channels can efficiently transport large discharge at low basal water pressures (Bartholomew et al., 2012; Nienow et al., 1998; Schoof, 2010). By autumn, the cessation of surface melt limits any further growth of the channels, and the conduits begin to shrink in size by creep closure (Fountain and Walder, 1998; Walder, 1986). During the winter, drainage eventually switches back to a distributed form and high background water pressures are once again established. The interaction among these different forms of the subglacial system produces a complex velocity pattern that varies spatially and temporally within a glacier catchment (Figure 1.5) (Andrews et al., 2014; Fitzpatrick et al., 2013; Joughin et al., 2013; Palmer et al., 2011; Sole et al., 2013). At any given time during the melt season, subglacial channels and a distributed system can coexist and exchange water with each other (Fountain and Walder, 1998; Gordon et al., 1998; Hubbard and Nienow, 1997). Water can drain laterally in either direction between these two systems depending on the pressure differences (Flowers, 2015; Hewitt et al., 2012). When large channels dominate, CHAPTER 1. INTRODUCTION 6

Figure 1.4: Idealized components of subglacial hydrologic systems that are broadly characterized into ‘channelized’ and ‘distributed’ forms (adapted from Flowers 2015). water will leak transversely out of the highly pressurized distributed system to coalesce into the channels that operate at lower mean pressures. Conversely, when the water level and the pressures rise inside these channels, reversed pressure gradients can force water back to the surrounding distributed system. Over till dominated beds, water flow can also move vertically between the channels and the distributed groundwater systems that exist in the sediment layers (Bougamont et al., 2014; Flowers, 2015). These local exchanges of subglacial water between different hydraulically active regions of the bed have the potential to produce widespread changes in the basal stress distribution and ice motion (Andrews et al., 2014; Gordon et al., 1998; Hubbard and Nienow, 1997; Mair et al., 2002; Murray and Clarke, 1995). Therefore, better characterization on how the storage, distribution, and exchange of subglacial water evolve over time is critical to understanding the individual catchment responses to climate around Greenland. Direct observations of the subglacial hydrologic system at the temporal and spatial scales where ice flow is influenced, however, have been limited. Furthermore, point-based CHAPTER 1. INTRODUCTION 7

Figure 1.5: Satellite measured ice surface velocity speedup relative to the winter mean during the summer of 2010 along a land-terminating margin in Southern Greenland. Velocities show (a) spring speedup in 6 May, (b) early summer speedup in 19 June, and subsequent slowdown in (c) 20 June and (d) 22 July (adapted from Fitzpatrick et al. 2013). measurements of ice motion often reveal contrasting results about the influence of varying water drainage on glacier velocity, even when these results are from the same catchment. Observations taken near the ice sheet margin show that the net annual ice flow is relatively insensitive to the short-term variations in subglacial water storage during the summer (Sole et al., 2013; Sundal et al., 2011; Tedstone et al., 2015). In contrast, results taken from the ice sheet interior have suggested that this insensitivity of the annual ice motion does not hold across broad spatial scales (Doyle et al., 2014; Meierbachtol et al., 2013). The discrepancy between these point-based studies and the complex patterns of ice flow observed across Greenland highlight the need to examine the spatial variation in the subglacial hydrology over a regional scale, in order to fully CHAPTER 1. INTRODUCTION 8 understand the coupling between ice and water flow.

1.3 Techniques to study subglacial hydrology

A better understanding of the coupling between ice and water ﬂow requires examining the glacier bed at a sub-kilometer resolution over a catchment-scale. Hydrological models and airborne radar sounding are the only two practical techniques that can provide this necessary spatial resolution and coverage to characterize the subglacial environment.

1.3.1 Hydrological models

Hydrological models are commonly used to study groundwater flow and storage. These models use flow algorithms to determine drainage directions based on the gradients in hydraulic head and route water either down a single, steepest gradient (Budd and Warner, 1996; Tarboton, 1997) or partition it into multiple neighboring cells (Quinn et al., 1998; Tarboton, 1997). Accurate knowledge of the hydraulic gradient is, therefore, essential to determine the correct drainage flow paths. For ice sheet applications, hydraulic gradients depend on both the gradients of water pressures, Pw, and bed geometry, zb, given by, ∇ ∇

φ = ρwg zb + Pw, (1.1) ∇ ∇ ∇ where ρw is the density of water, and g is the gravitational acceleration (Shreve, 1972). Since the gradients of water pressure are not well known, they are often approximated as fractions of the ice overburden pressure, Pi, that are easier to measure, as,

Pw = f Pi, (1.2) ∇ ∇ where f is the flotation fraction, in which f = 1 indicates that water pressure equals the ice overburden pressure and f<1 means the water pressure is below the overburden pressure. Hydrological models have been applied to estimate subglacial water flow paths on both mountain glaciers (Flowers and Clarke, 1999; Sharp et al., 1993) and ice sheets in Greenland (Banwell et al., 2013; Lewis and Smith, 2009; Livingstone et al., 2013) and Antarctica (Wolovick et al., 2013; Wright et al., 2008). While the accuracy of subglacial flow paths is limited by the resolution of the Digital Elevation Models (DEM) of ice CHAPTER 1. INTRODUCTION 9 surface and bed elevation, hydrological model has proven to be an useful tool to examine the sensitivity of subglacial routing in response to subtle changes in surface elevation (Karlsson and Dahl-Jensen, 2015; Wright et al., 2008) and basal water pressures (Chu et al., 2016a; Flowers and Clarke, 1999; Lindbäck et al., 2015).

1.3.2 Airborne radar sounding

Airborne radar sounding is another powerful tool that can characterize subglacial conditions at a high resolution. This dissertation focuses on the deep ice-penetrating radar data collected as part of the NASA Operation IceBridge (OIB) campaign. This campaign is designed to fill the data collection gap between the loss of ICESat-I in 2010 and the launch of the ICESat-II satellite in 2018. The deep ice-penetrating radar system on board the NASA aircraft, the Multi-Channel Coherent Radar Depth Sounder (MCoRDS), is designed by the Center for Remote Sensing of Ice Sheets (CReSIS) at the University of Kansas. This system transmits long chirped pulses at 500 to 1500 W to measure ice thickness and resolves the structures of internal layers and the ice sheet bottom (Gogineni et al., 2001; Li et al., 2013). Contrasts in the dielectric properties and conductivities between these internal layers and along the ice-bed interface allow the radar to collect high-resolution images of the ice sheet. These internal and basal features can be further resolved through a combination of coherent averaging and focused synthetic aperture radar processing. The presence of subglacial water can be interpreted from the radar echograms. One way this is done is through interpreting flat and bright features along the ice sheet base as subglacial water (Bell et al., 2002; Carter et al., 2009; Siegert et al., 2005). Water produces a brighter radar reflector because of its increased dielectric contrast with the overlying ice (Figure 1.6). Drawdown of radar internal layers may also indicate higher rates of basal melting, especially when these deformed layers are found close to the flat and bright features (Bamber et al., 2013b; Wolovick et al., 2013). However, there are severe limitations to interpreting water based on the flatness and brightness of the radar reflectors. Any water bodies that are below the along-flow resolution of the radar system would not be detected as ‘flat’. Differential dielectric attenuation within the ice that CHAPTER 1. INTRODUCTION 10

Figure 1.6: An example of a clear, bright bed reﬂector in a radar echogram that is indicative of subglacial water beneath the East Antarctica Ice Sheet (adapted from Wolovick et al. 2013). depends on the ice temperature and chemistry can also impact the brightness of the bed (Figure 1.7)(MacGregor et al., 2007; Matsuoka, 2011; Matsuoka et al., 2012b). For example, a region with anomalously colder ice or ice that contains less chemical impurities than the surrounding ice can produce a brighter bed reﬂector that is unrelated to the basal condition or subglacial water. Conversely, in a region with warmer and more attenuating ice, for example where there are large, deformed ice bodies (Bell et al., 2014; Wolovick et al., 2014), the bed could appear dimmer than it should otherwise (Figure 1.8). Correcting for these variations in englacial attenuation rates is necessary to accurately determine the spatial distribution of subglacial water. Early attempts to constrain the englacial attenuation rates have mostly been focused in Antarctica (Dowdeswell and Siegert, 2003; Jacobel et al., 2009; Macgregor et al., 2011; Rippin et al., 2004; Schroeder et al., 2016). Far fewer attenuation estimates have been done for Greenland (Jordan et al., 2016; Oswald and Gogineni, 2008). Further, most of these early studies in Antarctica are empirically based and assume a uniform depth- averaged attenuation rate (Jacobel et al., 2009; Macgregor et al., 2011; Rippin et al., 2004). Although this assumption may hold for small regions where the ice temperature, chemistry, and basal condition do not vary greatly, at a regional or continental scale an empirical approach is unsatisfactory for constraining subglacial water distribution. Across the ice sheet, depth-averaged attenuation rates can vary by more than two orders of magnitude CHAPTER 1. INTRODUCTION 11

Figure 1.7: In order to use high radar reflectivity anomaly as an indication for basal water, we need to correct for variations in the radar attenuation. For example, in the case above notice that the wet bed (blue patches) have a lower bed reflectivity than the region with no melt to the left. The reduced bed reflectivity is due to the increased englacial attenuation in the ice over the wet region. Figure adapted from Matsuoka et al. 2012a. from < 10 to 30 dBkm−1 (MacGregor et al., 2015b; Matsuoka et al., 2012a). More recent work has improved on constraining these large-scale attenuation variations by utilizing the radar internal layers (MacGregor et al., 2015a). While applicable at the ice-sheet scale, this layer-based approach is limited by the existence and persistence of layers in the radar echograms. Therefore, another approach is necessary for the fast-flowing outlet glaciers where the layers are absent, as well as in some regions in the ice sheet interior where the layers are disturbed by large, deformed ice bodies. The second part of this dissertation addresses this issue, and use a novel joint modeling and radar technique to more robustly constrain the attenuation rates in these challenging regions.

1.4 Scope of chapters

The primary focus of this dissertation is to examine variability in subglacial hydrology as a potential mechanism that could contribute to observed velocity changes across the Greenland Ice Sheet. This work is structured as a series of studies examining spatial and temporal variations in subglacial drainage across diﬀerent sectors in Greenland. CHAPTER 1. INTRODUCTION 12

Figure 1.8: Low basal reﬂectivity is indicative of high attenuation due to temperature or chemistry of the deformed basal ice body. These components need to be considered before basal water distribution can be eﬀectively mapped.

Chapter 2 focuses on the variations in drainage flow paths beneath three slow-moving outlet glaciers in West Greenland. I use a hydrological modeling approach described in Section 1.3.1 to investigate the potential for water piracy between adjacent catchments. I demonstrate that subtle changes in basal water pressures, for example after a supraglacial lake drainage event, could lead to a major rerouting of water across 100’s of km in Greenland, similar to those observed beneath West Antarctica. A version of this chapter was published in the Journal of Geophysical Research-Earth Surface under the title “Rerouting of subglacial water flow between neighboring glaciers in West Greenland” with co-authors T.T. Creyts and R.E. Bell. Chapter 3 focuses on the seasonal variations in subglacial storage beneath a land- terminating glacier in Southwest Greenland. I employ a more data oriented approach and use ice-penetrating radar in conjunction with ice sheet modeling to characterize the basal water distribution for two seasons on a catchment-scale for the first time. This study reveals extensive subglacial water storage primarily on basal ridges in the wintertime, while the drainage pattern switches in the summertime with the deep troughs conducting CHAPTER 1. INTRODUCTION 13 water as the ridges drain. Together, my results suggest that both the spatial variation in bed properties and the subglacial water storage at the start of melt season lead to differing glacier velocity responses to surface melting across Greenland. A version of this chapter was published in the Geophysical Research Letters under the title “Extensive winter subglacial water storage beneath the Greenland Ice Sheet” with co-authors D. M. Schroeder, H. Seroussi, T.T. Creyts, S. J. Palmer and R.E. Bell. Chapter 4 extends this radar technique to examine the spatial variations of subglacial water production and drainage beneath a fast-moving marine-terming glacier, Petermann Glacier, in Northern Greenland. Together with the results from earlier chapters, this study allows me to examine the how subglacial drainage behavior vary geographically, between a surface water-fed system in western Greenland and a basal water-fed system here in the Petermann catchment. In this chapter, I find that internal deformation process within the ice sheet exerts a critical role in generating basal melting in the ice sheet interior where both surface and viscous melting are limited. Together, the interaction between deformation and basal water enhances and sustains fast ice flow in the interior of the Greenland Ice Sheet. In this work I have collaborated with co-authors D. M. Schroeder, H. Seroussi, T.T. Creyts and R.E. Bell. Chapter 5 is a short conclusion that summarizes the findings of Chapter 2 to 4 to provide new insights into the variations of the subglacial hydrology and its role in modulating ice flow across the Greenland Ice Sheet. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 14

Chapter 2

Rerouting and Piracy of Water in West Greenland

Published as Chu, W., T. T. Creyts, and R. E. Bell (2016), Rerouting of subglacial water ﬂow between neighboring glaciers in West Greenland, J. Geophys. Res. Earth Surf., 121(5), 925938, doi:10.1002/2015JF003705

2.1 Abstract

Investigations of the Greenland Ice Sheets subglacial hydrological system show that the connectivity of different regions of the system influences how the glacier velocity responds to variations in surface melting. Here I examine whether subglacial water flow paths can be rerouted beneath three outlet glaciers in the ablation zone of western Greenland. I use Lamont-Doherty and CReSIS ice-penetrating radar data to create a new ice thickness map. I then use a simple subglacial water flow model to examine whether flow paths can be rerouted and identify the topographic conditions that are sensitive to subglacial rerouting. By varying water pressures within an observationally constrained range, I demonstrate that moderate changes in pressure can cause flow paths to re-route and exchange water from one subglacial catchment to another. Flow across subglacial overdeepenings is particularly sensitive to rerouting. These areas have low hydraulic gradients driving flow, so subtle water pressure variations have a strong CHAPTER 2. WATER REROUTING IN WEST GREENLAND 15 influence on water flow direction. Based on correlations between water flow paths and ice velocity changes, I infer that water piracy between neighboring catchments can result in a different spatial pattern of hydrologically induced ice velocity speedup depending on the amount and timing of surface melt. The potential for subglacial water to reroute across different catchments suggests that multiple hydrographs from neighboring glaciers are likely necessary to accurately ascertain melt budgets from proglacial point measurements. The relationship between surface runoff, ice dynamics and proglacial discharge can be altered by rerouting of subglacial water flow within and across outlet glaciers.

2.2 Introduction

The Greenland Ice Sheet has been losing mass at an increasing rate over the last several decades and currently contributes 0.7 – 1.1 mmyr1 to global sea level rise (IPCC, 2013; Khan et al., 2014; Shepherd et al., 2012). The mass loss is due to a combination of negative surface mass balance (Box and Colgan, 2013; Fettweis et al., 2011; Hanna et al., 2013) and the increased ice discharge across grounding lines associated with faster ice flow velocities (Joughin et al., 2008; Rignot and Kanagaratnam, 2006; van den Broeke et al., 2009). One of the mechanisms that can cause variability in ice flow velocity is through lubrication at the base of the ice sheet as melt water penetrates to the bed from the surface (Bartholomaus et al., 2008; Das et al., 2008; Pimentel and Flowers, 2010; Schoof, 2010; Zwally et al., 2002). Changes in basal lubrication cause daily and seasonal variations in flow velocity (Bartholomew et al., 2012; Hewitt, 2013; Hoffman et al., 2011; Joughin et al., 2008; Sole et al., 2011; Sundal et al., 2011). However, it is uncertain how significant the seasonal speedup events are to the overall mass loss of the glaciers, and what controls the response of different glaciers to a similar increase in surface melting. Theoretical and observational studies have suggested that the response of glaciers to surface melting is largely determined by the evolution of the subglacial hydrological system (Bartholomaus et al., 2008; Bartholomew et al., 2010; Iken and Bindschadler, 1986; Schoof, 2010; Sundal et al., 2011; van de Wal et al., 2008). The transition between CHAPTER 2. WATER REROUTING IN WEST GREENLAND 16 a slow, inefficient subglacial system and a fast, efficient system can result in a different velocity response to the same supply of meltwater from the ice surface. Following the examples of mountain glaciers, the structure of the Greenland subglacial hydrological system is thought to evolve between the slow and fast forms in response to seasonal and daily variations in meltwater input (Bartholomaus et al., 2008; Bingham et al., 2005; Mair et al., 2002). During winter, with little input of surface meltwater, the drainage flow paths are restricted and poorly connected, yielding inefficient water transport. In spring, when surface meltwater reaches the bed, the inefficient system is unable to cope with the input leading to higher water pressures. The elevated pressures reduce the contact area between the ice and bedrock causing increased sliding and elevated ice flow velocities (Iken, 1981; Iken and Bindschadler, 1986). Sliding allows the subglacial flow paths to connect. The subglacial flow paths eventually channelize as increased water flow melts the overlying ice along the pathways (Bartholomew et al., 2010; Röthlisberger, 1972; Schoof, 2010; Sundal et al., 2011; van de Wal et al., 2008). If meltwater discharge is steady, water pressure drops in the channels and water flows to the adjacent inefficient drainage system, increasing ice bed contact and resulting in the slowing of ice flow. For locations that have daily variations in meltwater discharge, the drainage system tunes to average conditions. During the increase of melt in the daytime, flooding causes high pressures in channels that leak water to an adjacent subglacial system. During nighttime, meltwater sources diminish and the water system drains. The net effect of the daily variations in pressure is similar to the steady case because regions of distributed high pressure are not persistent and coupling between ice and bed increases. Variations in the flow paths are governed by the hydraulic potential with the ice surface driving flow with a much smaller component dependent on bed topography (Shreve, 1972). Hydraulic potential analyses have shown that subglacial pathways have the potential to reroute in response to modest changes in surface elevation (Karlsson and Dahl-Jensen, 2015; Wright et al., 2008). In Antarctica, competition of subglacial water between glacier catchments or water piracy has been thought to trigger the onset or shutdown of ice stream flow (Alley et al., 1994; Anandakrishnan and Alley, 1997; Carter et al., 2013; Vaughan et al., 2008). Detailed studies of bed topography in Antarctica show that topography CHAPTER 2. WATER REROUTING IN WEST GREENLAND 17 tends to aid in determining the direction of subglacial flow paths by adding structure to a relatively smooth ice surface (Wolovick et al., 2013). Together, rerouting and water piracy can occur beneath Greenland because the catchments are not topographically constrained. This is in contrast to mountain glaciers where drainage is tightly constrained along valleys. Water piracy can impact ice flow by redistributing surface meltwater and regional water pressure (Lindbäck et al., 2015). Water flow beneath Greenland may reroute in response to the variations in water pressure (Cuffey and Paterson, 2010). Here I examine whether subglacial flow paths could be rerouted among three west Greenland outlet glaciers under different subglacial water pressure scenarios. Using radar-constrained topography and an analytical, steady state water flow model, I examine the sensitivity of rerouting of subglacial flow to changes in water pressures and identify critical topographic areas that control the sensitivity.

2.2.1 West Greenland study site

This study region along the west coast of Greenland has a subglacial hydrological system that changes rapidly with highly variable and episodic surface meltwater input (Das et al., 2008; Joughin et al., 2013, 2008) (Figure 2.1). This region, located to the south of the fast flowing Jakobshavn Isbræ(> 1000 m yr−1), drains three slower moving marine terminating glaciers with average velocities of 100 to 200 m yr−1: Alángordliup Sermia, Sarqardliup Sermia and Nordenskiöld Gletscher (hereinafter referred as Alángordliup, Sarqardliup, and Nordenskiöld). Previous studies by Joughin et al. (2008) and Das et al. (2008) examined the influence of supraglacial lake drainage on ice flow velocities. GPS instruments installed around two supraglacial lakes (white triangles in Figure 2.1) showed fast (< 2 hrs) drainages of lakes to the base of the ice sheet caused accelerated ice flow 100 times the background velocity Das et al. (2008). Using 24-day repeated synthetic aperture radar (SAR) data, Joughin et al. (2008) found that the localized accelerated ice motion was short-lived, and the net annual speedup was spatially uniform across the region. The spatial uniform speedup is interpreted as the presence of a well-connected subglacial hydrological system dispersed the localized changes in water pressure uniformly across the region (Tedstone et al., 2015). However, using the more CHAPTER 2. WATER REROUTING IN WEST GREENLAND 18 frequently sampled ( 11 days) TerraSAR-X (TSX) observation, Joughin et al. (2013) ∼ find a greater spatial heterogeneity in the peak summer velocity speedup from two melt seasons. In June 2009, the greatest speedup is concentrated in the upstream region of Sarqardliup and Alángordliup above 30 km from the ice sheet margin (Figure 2.1b). The downstream 30 km region experienced < 40% summer velocity speedup from the winter velocity. In contrast, the greatest summer speedup occurred in July 2010 was more spatially extensive (Figure 2.1b). The downstream 30 km regions of Alángordliup and Sarqardliup experienced greater speedup (> 80% of the winter velocity). The spatially heterogeneous ice flow speedup pattern suggests a more spatially and temporally variable hydraulic interaction between the different regions of the subglacial hydrological system. In this paper, I examine the relationship between the potential routing of subglacial water and the inter-annual variations in the spatial pattern of ice flow velocity between 2009 and 2010.

2.3 Data

The configuration of surface and bed topography largely controls the direction of subglacial water flow (Shreve, 1972). For the study region, Joughin et al. (2013) noted that bed topography needs to be better constrained to understand the interaction between subglacial hydrology and ice flow. Using the high-resolution ice thickness data collected by Lamont-Doherty and data from the Center for Remote Sensing of Ice Sheets of University of Kansas (CReSIS), I reconstruct a new bed elevation map to examine the influence of topography on subglacial water routing. Bed elevations are calculated by subtracting the ice thickness data from a digital elevation model (DEM) of ice surface. Surface elevation is from the 30 m resolution DEM of Greenland Ice Mapping Project (GIMP) that combines ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer), SPOT-5 (Système Pour I’Observation de la Terre) and AVHRR (Advanced Very High Resolution Radiometer) photoclinometry (Howat et al., 2014). CHAPTER 2. WATER REROUTING IN WEST GREENLAND 19

Figure 2.1: (a) Sarqardliup Sermia, Alángordliup Sermia and Nordenskiöld Gletscher in Western Greenland with ice flow velocity from RADARSAT collected in the winters of 2007 – 2008 (Joughin et al., 2010). The black arrows indicate directions of ice flow, and the color map shows speed. White triangles locate the supraglacial lakes studied by Das et al. (2008) and Joughin et al. (2013, 2008). White rectangle shows the area displayed in Figure 2.1b and c. (b) Increase in summer 2009 flow velocity relative to winter velocity (expressed as percentage of winter speed) from TerraSAR-X data on 16 July 2009. (c) Increase in summer 2010 flow velocity relative to winter velocity on 11 June 2010 (Joughin et al., 2013). These dates are chosen to show the maximum spatial extent of the summer speedup for each year.

2.3.1 Lamont-Doherty survey

Ice penetrating radar data for Sarqardliup and Alángordliup were collected using a Twin Otter aircraft in June 2008. The survey ( 533 line km) comprises ten northeast-southwest ∼ trending lines spaced 2.5 km apart, intersected by two along flow lines spaced 10 km apart (black lines in Figure 2.2). The radar system, developed collaboratively with CReSIS, CHAPTER 2. WATER REROUTING IN WEST GREENLAND 20 has a 150 MHz center pulse, a bandwidth of 10 MHz, and a transmit power of 2 kW. The system uses both a 3 µs low-gain and a 10 µs high-gain signal (Gogineni et al., 2001; Jezek et al., 2006). The pulse repetition interval is 100 µs, and depending on the flight velocity typically samples the ice at less than 2 m intervals in the along-track direction. The radar footprint is approximately 1 km in the cross-track direction. The low and high- gain channels are combined and migrated using a 1D Synthetic Aperture Radar (SAR) algorithm to produce radar echograms (Hélière et al., 2007). The ice thickness is picked using a hybrid manual-automatic system along the sharpest vertical gradient of the radar signal (Wolovick et al., 2013). A crossover analysis of the Lamont-Doherty thickness data gives a mean instrumental error of 14 m(N = 20) (Figure 2.3a). ±

Figure 2.2: (a) Ice thickness map from kriging the Lamont-Doherty (black lines) and CReSIS data (grey lines). (b) Bed topography calculated from subtracting the interpolated ice thickness from the GIMP surface elevation DEM. A in Figure 2.2 b highlights the subglacial overdeepening where major water rerouting occurs.

2.3.2 CReSIS Survey

The majority the ice thickness data in this study were acquired by CReSIS (https: //data.cresis.ku.edu/data/rds/) (Gogineni et al., 2001). I use the radar-sounding data collected by a series of instruments from 1999 to 2013 to compile the new ice thickness dataset (grey lines in Figure 2.2). Most of the data (62%) were collected between 2010 and CHAPTER 2. WATER REROUTING IN WEST GREENLAND 21

2013 by the Multi-Channel Coherent Radar Depth Sounder (MCoRDS). Approximately 34% of the data are from 2003 – 2005 acquired by the Advanced Coherent Radar Depth Sounder (ACORDS). The remaining 4% are from 2006 – 2009 collected by the Multi- Channel Radar Depth Sounder (MCRDs) and from 1999 – 2002 by the Improved Coherent Radar Depth Sounder (ICORDS). These data have an average track spacing of 10 – 20 ∼ km, spanning a region about 290 km north-south by 65 km east-west. The ice thickness measurements have a nominal precision of 10 m (Gogineni et al., 2001). The actual ± accuracy of the data varies with location and the quality of the radar picks. The primary error sources are system electronic noise, multiple reflections, and off-nadir scattering from the presence of crevasses, water and rock outcrops. Other error sources include the uncertainties in the correction for firn depth and in the dielectric properties of ice. A crossover analysis of the CReSIS data yields a mean instrument error in thickness of 42 ± m (N = 10945) for the study region (Figure 2.3 b).

Figure 2.3: Crossover errors in ice thickness from (a) the Lamont-Doherty data and from (b) the CReSIS data. (c) Interpolation errors in ice thickness across the catchment expressed in term of percentages of ice thickness. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 22

2.4 Methods

2.4.1 Interpolation of topography

The Lamont-Doherty and CReSIS ice thickness data are interpolated to a regular grid using ordinary kriging. Ordinary kriging estimates thickness H(x,y) at a given location using nearby measurements, Hi, with a discrete spatial weighting function, λi(x,y) assigned according to the elevation covariance, so that

n H(x,y)= λi(x,y)Hi, (2.1) i=1 X with n representing the nearest 100 measurements within a radius of 50 km. Ordinary kriging assumes that the mean of the data points is unknown but constant and requires the weights to sum to 1, n λi(x,y) = 1. (2.2) i=1 X The weights are calculated to minimize the variance of the estimation error. The spatial covariance of the measurements is derived from an exponential semivariogram model. I ﬁnd a best ﬁt between the model and measurements with a variogram of a sill of 24 km, a range of 1.5 km, and a nugget of 35 m. The sill represents the variance of the ice thickness measurements. The range represents the distance limit beyond which the ice thickness data are no longer correlated. The nugget was given by the mean measurement errors of the Lamont and CReSIS data. The thickness data are interpolated to a regular Cartesian grid with 500 m spacing. Bed elevation is derived by subtracting the ice thickness grid from the GIMP ice surface DEM (Howat et al., 2014).

2.4.2 Error analysis

A reliable estimate of the error in the DEMs is crucial to assess the uncertainty in the subglacial hydrological potential. The two primary sources of error are from the ice thickness observations and the interpolation error. Observation errors are constrained by a crossover analysis of the ice thickness dataset that includes both the Lamont-Doherty and CReSIS thickness described previously. A total of 10,965 crossover differences are CHAPTER 2. WATER REROUTING IN WEST GREENLAND 23 calculated and the mean observation error in thickness is 31 m. The histograms of thickness crossover differences from the two campaigns are shown in Figure 2.3a and b. The GIMP ice surface DEM contributes 10 m of uncertainty. ± The interpolation error in the ice thickness DEM depends on point density of the observations and variability of the measured ice thickness. I estimate this uncertainty using a standard statistical error analysis, bootstrapping (Bamber et al., 2013b; Cressie, 1994; den Hertog et al., 2006). I calculate the interpolation error by removing an observation from the dataset and using the remaining data to interpolate the value at the observation location. Using the known observation value at this location, the interpolation error is represented by the difference between the interpolated and observed values. The observation is then returned into the dataset, and the process is repeated for all of the 5,427,487 observations to obtain a mean interpolation error at individual locations shown in map view in Figure 2.3c. Interpolation errors at points far from the data lines dominate the uncertainty in the bed. Figure 2.3c shows that the largest errors are in the southern region where the flight lines spacing are about 40 km apart. Because of the sparsity of data, the ice thickness of Nordenskiöld is poorly constrained with an averaged error in thickness of 80 m. In contrast, in regions near Sarqardliup and Alángordliup the errors are significantly smaller with an averaged error of 20 m because of the dense data coverage provided by the 2.5 km spaced Lamont tracks and the 10 km spaced CReSIS tracks. Thus, the influence of the ∼ error in DEMs on the subglacial water flow paths should be smaller in the regions near Sarqardliup and Alángordliup relative to Nordenskiöld. The impact of error in DEMs on water flow is examined in section 4.3.

2.4.3 Subglacial ﬂow paths and catchment delineation

To examine how the predicted routing of subglacial water flow responds to a change in the regional water pressure, I use the gridded topography product with a subglacial water flow model to calculate flow paths and catchment areas for a range of pressure values. The water flow model follows a Darcian-type formulation where water flux, Q, flows down the hydraulic potential gradient, φ, according to ∇ CHAPTER 2. WATER REROUTING IN WEST GREENLAND 24

Q = k φ, (2.3) − ∇ where k is the hydraulic conductivity of the subglacial hydrological system. Similar hydraulic potential analysis has been applied in Greenland (Banwell et al., 2013; Karlsson and Dahl-Jensen, 2015; Lewis and Smith, 2009; Livingstone et al., 2013) and Antarctica (Creyts et al., 2014; Wolovick et al., 2013; Wright et al., 2008) to estimate subglacial drainage ﬂow paths. Following the Shreve [1972] formulation, φ is calculated ∇ from

φ = ρwg zb + Pw = ρwg zb + Pi N, (2.4) ∇ ∇ ∇ ∇ ∇ −∇ where ρw is the density of water, g is gravitational acceleration, zb is the elevation of the bed, Pw is water pressure, Pi is ice overburden pressure, and N is effective pressure defined as the difference between ice overburden pressure and water pressure N = Pi Pw. The − effective pressure gives a measure of how the water system is pressurized relative to ice overburden. I continue to simplify equation 2.4 by introducing the ice thickness as the difference in ice surface elevation and bed elevations: H = zs zb, so that −

φ = ρwg zb + ρig H N. (2.5) ∇ ∇ ∇ −∇ Following earlier studies (e.g. Banwell et al., 2013; Willis et al., 2012), I use the simplification of Shreve (1972) to group effective pressure into the ice overburden pressure using a prefactor f, called the flotation fraction on the water pressure Pw = fPi,

f(ρig H)= ρig H N, (2.6) ∇ ∇ −∇ so that

N = (1 f)ρig H. (2.7) ∇ − ∇ Formally deﬁned, f is the ratio of water pressure to ice overburden pressure, f =

Pw/Pi. In this case, f < 1 indicates that the water pressure is below the ice overburden pressure, f = 1 indicates that the water pressure is at the ice overburden pressure, and f > 1 means that water pressure is above the ice overburden pressure. A natural lower CHAPTER 2. WATER REROUTING IN WEST GREENLAND 25 boundary for the pressures is limited by atmospheric pressure (f = 0). The other natural condition is slightly overpressured (f = 1.11) based on the difference of the densities of water and ice where a crevasse or moulins could be filled to the ice sheet surface and effective pressures would be modestly negative. The final form of the hydraulic gradient is

φ = ρwg zb + fρig( zs zb) (2.8) ∇ ∇ ∇ −∇ 3 3 2 with ρw = 1000kg m , ρi = 917kg m , and g = 9.8m s . I calculate the hydraulic potential surfaces for a range of flotation fraction values defined by these natural boundaries. Similar to a previous study by Flowers and Clarke (1999), I run a D routing algorithm Tarboton (1997) on the hydraulic potential ∞ surfaces to calculate water flow paths and delineate catchment area. I estimate subglacial flow paths assuming that the flotation fraction value varies between the limits of 0.6 to 1.11 to examine the sensitivity of flow paths to changes in water pressure. The flotation limit is selected based on the observations of the evolution of subglacial water pressures in southwest Greenland (Andrews et al., 2014; Meierbachtol et al., 2013) and in alpine glacier environments (Fudge et al., 2009; Harper et al., 2005; Iken and Bindschadler, 1986; Sugiyama and Gudmundsson, 2004). While alpine glaciers may not be a perfect analog to Greenland (Hoffman et al., 2011), they provide annual records of subglacial water pressure that are currently absent for Greenland. The range of flotation fraction values represents a modest spectrum from relatively low water pressure where the subglacial system likely channelizes to an overpressured state where water would distribute across the bed. Exact morphological transitions are absent from my study because they would require the use of more sophisticated models (Creyts and Schoof, 2009; Hewitt, 2013; Pimentel and Flowers, 2010; Schoof, 2010; Werder et al., 2013). Because the purpose of this paper is to examine the interaction of subglacial flow paths with topography, I choose to use a simpler, analytical model that can include realistic topography to calculate water flow paths. Similar analytical water models have been applied elsewhere in Greenland, and the calculated flow paths are considered to represent the long-term steady state configuration (Ahlstrøm et al., 2005; Banwell et al., 2013; Hagen et al., 2000; Willis et al., 2012). CHAPTER 2. WATER REROUTING IN WEST GREENLAND 26

2.5 Results

2.5.1 Flow paths change with water pressure conditions

My results show how subglacial flow paths are rerouted when a moderate change in the flotation fraction is applied uniformly across the study region. The response of individual pathways varies from minor adjustments to the flow tributaries within the ice catchment to a major rerouting that causes piracy between neighboring glaciers. For my study region, I find that when the flotation fraction varies from 0.6 to 1.0, a minor adjustment occurs in the small hydrologic tributaries (Figure 2.4). However, when the catchment is ovepressured to a flotation fraction of 1.11, major rerouting of water pathways occur and piracy between neighboring catchments ensures (Figure 2.5). For f = 0.6to1.0, Nordenskiöld receives the majority of the subglacial water draining from the upstream catchment further than 60 km from the ice sheet margin (Figure 2.4a to c). In contrast, Sarqardliup and Alángordliup have confined subglacial catchment areas that receive water mainly from the downstream regions within 30 km from their termini. Subglacial water that drains from the upstream regions is diverted away by the adverse slope along the bed that aligns parallel to the coast to roughly 30 km from the glacier termini (Figure 2.5a). Instead of draining through the downstream regions of Sarqardliup and Alángordliup, this upstream water is transported toward Nordenskiöld along the subglacial overdeepening (A in Figure 2.2b). This configuration of subglacial flow paths contrasts sharply when water is overpressured and the flotation fraction is set to 1.11 (Figure 2.4d). At 111% of the overburden pressure, drainage pathways that previously flow along the overdeepening are rerouted to flow across the adverse-sloped bed (Figure 2.5b). Water is pirated from Nordenskiöld to the downstream catchment of Alángordliup. If no water is stored at the bed, this rerouting could lead to a 30% increase in drainage discharge into the fjord of ∼ Alángordliup. While I do not expect flotation conditions to exist everywhere across the catchment, my results indicate that localized pressure in excess overburden at critical locations can cause rerouting of subglacial water (see Supporting information 2.8.3). In particular, if moulins or fractures drain surface water at or upstream of these locations, I CHAPTER 2. WATER REROUTING IN WEST GREENLAND 27

Figure 2.4: Subglacial water flow paths (blue lines) for the three glaciers assuming a flotation fraction of (a) f = 0.6, (b) f = 0.8, (c) f = 1.0, and (d) f = 1.11. The f = 1.0 case (black box) is the typical assumption that people made in hydrological modeling. anticipate that subglacial flow paths could be rerouted up and out of the overdeepening. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 28

Figure 2.5: Flow paths from Figure 2.4 with the spatial extent of subglacial water catchment (red polygons) overlaid on the bed topography. The black diamonds highlight the regions where water reroutes with a 10% increase of flotation fraction. The white line shows the location of the along-flow profile in Figure 2.6. (a) For the flotation example where the system is at the ice overburden pressure (f = 1.0), Nordenskiöld receives most of the water in the region. (b) This contrasts sharply with the flotation example at f = 1.11 where Alángordliup drainage catchment captures majority of the water.

2.5.2 Flow dependence on topography

The configurations of subglacial water flow paths are strongly dependent on topography (Shreve, 1972). Rerouting of water flow occurs when the relative dependence on surface and bed topography is modified with changes in water pressure. When water pressure reaches flotation, equation 2.8 shows that the ice surface slopes are 11 times more important than bed slopes in steering flow. If the system reaches overpressure at f = 1.11, surface slopes dominate the water flow direction. However, the dependence of subglacial flow on surface slope reduces with lower water pressures, and bed slopes show a greater influence on the water flow direction. At f = 0.8, for example, bed slopes that are 2.7 times the surface slopes have equal influence on flow paths direction. At f = 0.6, bed slopes that exceed 1.2 times the surface slopes dominate flow direction, and the hydraulic potential surface closely mimics the variations in bed topography (Figure 2.6). As the water pressure drops below these thresholds, I expect subglacial flow paths to CHAPTER 2. WATER REROUTING IN WEST GREENLAND 29 reroute as surface or bed topography becomes more important to flow direction. In the case of my study region, the water system is predicted to overcome the bed topography as the subglacial system reaches overpressure. The pressure threshold where surface slope dominates water routing varies across the catchment and depends on the local ratio of surface and bed slopes. Because the dependence of water flow on topography changes with the flotation fraction, I find that the regions where major rerouting occurs are near subglacial overdeepenings, locations of local closed depressions with bed slopes reversed with respect to the surface slopes. An example is the overdeepening beneath Nordenskiöld and Sarqardliup at 30 – 50 km from the ice sheet terminus (A in Figure 2.2b). A similar, but less significant rerouting occurs in the adverse-sloped bed at 10 km from the ∼ terminus where subglacial flow paths are predicted to reroute between Sarqardliup and Alángordliup (black diamonds in Figure 2.5b). Another reason that subglacial rerouting is more likely to occur in overdeepened areas is that the adverse-sloped bed flattens the gradient of hydraulic potential across the region (Creyts et al., 2013, 2014). A flatter potential gradient surface is more prone to changes for a smaller perturbation in the water pressure (Cook and Swift, 2012; Creyts et al., 2013). Overdeepenings also tend to be regions that have water pressures close to or slightly above flotation (Hooke and Pohjola, 1994; Lawson et al., 1998). An addition of surface water such as from a supraglacial lake drainage event could elevate pressures further. In the melt season when lake drainage events occur, overdeepenings may frequently reach superflotation pressures that could potentially cause water piracy between Nordenskiöld and Alángordliup. This piracy between the two catchments would depend on the timing of lake drainages as well as the seasonal development of the subglacial hydrological system. Because overdeepenings tend to have flatter ice surface slopes (Cook and Swift, 2012; Gudmundsson, 2003), supraglacial lakes form preferentially near these regions where the subglacial system is sensitive to rerouting (Echelmeyer et al., 1991; Sergienko and Hindmarsh, 2013). The supraglacial lake studied by Das et al. (2008) (North lake) is located at 5 km upstream from the subglacial ∼ overdeepening where rerouting between Nordenskiöld and Alángordliup is predicted to CHAPTER 2. WATER REROUTING IN WEST GREENLAND 30

Figure 2.6: Along-flow profile for Alángordliup across the regions of rerouting of subglacial water flow paths (black diamond). The rerouting locations are shown in relation with the surface and bed topography (shaded patch), and the supraglacial lake (North Lake) studied by Das et al. (2008) and Joughin et al. (2013, 2008)(white triangle). Hydraulic head surfaces for different assumptions of flotation fractions are also shown to illustrate the increasing dependence of water flow on bed topography at lower flotation fraction (colored lines). occur at pressures in excess of flotation (Figure 2.6). If the drainage of this lake causes the subglacial water pressure to exceed flotation then my findings predict that the melt water would be transported to Alángordliup. In contrast, if the drainage occurs when pressure is below flotation then the water would instead be delivered to Nordenskiöld (Figure 2.7). I suggest that therefore the rapid supply of surface melt water to an underdeveloped subglacial drainage system may trigger the catchment-scale rerouting of subglacial water pathways. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 31

2.5.3 Inﬂuence of error in DEMs on ﬂow paths

Because relatively small changes in water pressure may result in the rerouting of subglacial flow, small errors in the DEMs may also have the same effect on the modeled flow paths. I expand the hydraulic potential equation 2.8 to examine the perturbation in hydraulic head due to the errors in the surface and bed DEMs, as well as the possible effects of density variation in the ice column following Creyts et al. (2014) (Suporting Information 2.8.2). The perturbation analysis shows that the error in the DEMs contributes to 24 m of uncertainty in the hydraulic head averaged over the entire study region. This 24 m is equivalent to a 2.5% change in flotation fraction and represents the minimum resolution of the DEMs. Because of the high data density in the regions of subglacial rerouting, the uncertainty in these locations is smaller (13 m) than the average value over the study area. An increase of flotation fraction from f = 1.0 to f = 1.1 would result in a 98 m change in hydraulic head averaged across the study region. Therefore, the predicted rerouting of water flow between Nordenskiöld and Alángordliup is not a byproduct of the errors in the DEMs.

2.6 Discussion

2.6.1 Potential impact on seasonal ice velocity

While the pattern of surface meltwater delivery has thought to change ice flow velocity (Bartholomew et al., 2010; Colgan et al., 2011; Hoffman et al., 2011; Palmer et al., 2011), here our results indicate that if water is delivered to critical areas of the bed, rerouting of drainage pathways can cause glaciers to respond differently to the same meltwater input. I investigate the impact of water rerouting on the glaciers transient response to melt by examining two snapshots of the summer ice motion from 16 July in 2009 and 19 June 2010 (Figure 2.1b and c). These two snapshots represent the periods of greatest summer speedup measured that year. The velocity snapshots illustrate that the spatial pattern of the transient speedup varies substantially from year to year (Joughin et al., 2013) (Figure 2.1b and c). When the subglacial water flow paths are overlain on these CHAPTER 2. WATER REROUTING IN WEST GREENLAND 32 velocities, a qualitative spatial correlation between the velocity and drainage pathways emerges. This correlation suggests the intra-annual difference in the speedups pattern may be related to water piracy between Nordenskiöld and Alángordliup. The 2009 summer velocity snapshot shows that the regions of greatest speedup (> 100% of winter velocity) occur principally in the subglacial overdeepening in the upper catchment (Figure 2.6a). In contrast, the downstream region experiences a lower flow speedup of < 40% of the winter velocity. The sharp transition of the flow speedup roughly aligns with an area near the adverse-sloped bed near the subglacial overdeepening. This general spatial pattern of the 2009 summer speedup shows strong similarity to the configuration of the subglacial drainage pathways at or near the ice overburden pressure (f = 0.8 and 1.0). The transition of the flow speedup coincides with the divergence of the Alángordliup subglacial water flow paths toward Nordenskiöld.

Figure 2.7: Subglacial water flow paths (dark blue lines) for two flotation examples, at flotation and overpressure, overlain with the observed ice velocity speedup for 2009 and 2010 summer and the two supraglacial lakes studied by Das et al. (2008) and Joughin et al. (2013) (white triangles). (a) Flow paths for f = 1.0 with the 16 July 2009 summer speedup. (b) Flow paths for f = 1.11 with the 11 June 2010 summer speedup. The additional water along the base of Alángordliup due to rerouting may have contributed to the higher velocities in the lower catchment in 2010.

In contrast to the 2009 observations, the 2010 summer velocity snapshot shows that CHAPTER 2. WATER REROUTING IN WEST GREENLAND 33 the regions of greatest summer speedup expand across the adverse-sloped bed farther downglacier (Figure 2.6b). The similarity between the spatial speedup pattern and the inferred drainage pathways when water pressure is excess of overburden (f = 1.11) suggests that the subglacial system is likely highly pressurized at this time. The 2010 melt season was anomalously warm and had higher surface melting in the ablation zone than in the melt season of 2009 (Mernild et al., 2011; Tedesco et al., 2011), so that an overpressured subglacial system could be responsible for this early and extensive transient speedup. Landsat imagery from around the time of greatest speed up reveals that many supraglacial lakes developed in late June of 2010, approximately 2 weeks earlier than in 2009. The rapid supply of meltwater from supraglacial lake drainage events to the subglacial hydrologic system could have resulted in localized pressures above flotation. If such overpressurization occurs near the overdeepening, my results predict it would lead to water piracy from Nordenskiöld to Alángordliup. The increase of subglacial water to Alángordliup may reduce the basal resistance in the downstream region and contribute to the transient summer speedup in the downstream region of Alángordliup observed in the 2010 velocity snapshot. Because the three outlet glaciers are marine terminating, ocean related forcing such as retreat of the grounding lines could potentially impact the glaciers surface velocity. When icebergs calve, the loss of resisting force may potentially trigger a surface velocity speedup of the inland ice (Joughin et al., 2012; Podrasky et al., 2012; Vieli and Nick, 2011). The force perturbation from the grounding lines should be greatest at the ice sheet margin and decays with distance up-glacier (Cuffey and Paterson, 2010). However, the velocity in 2010 shows the opposite speedup variation at Alángordliup and Sarqardliup with lower speedup closer to the calving front than the upstream ice. Also much of the differences in the transient summer speedups between 2009 and 2010 occurred in the interior of the ablation zone (> 30 km from the ice termini) where the force perturbation related to grounding line changes may have decayed significantly. It is therefore more likely the transient summer speedup in 2010 is associated with the reduction of basal resistance from hydrological changes at the bed coincident with a greater surface melt year. The net effect of these transient speedups on the annual ice motion is likely small (e.g. Joughin CHAPTER 2. WATER REROUTING IN WEST GREENLAND 34 et al., 2008; Tedstone et al., 2015). Nonetheless, my study indicate that the sensitivity for the Greenland Ice Sheet to subglacial water piracy means that the spatial distribution of the transient summer speedups can vary substantially from year-to-year depending on the subglacial hydrologic configuration.

2.6.2 Potential impact on water budget assessments

Water piracy between neighboring subglacial catchments also changes the hydrographic assessments of water budget for individual glaciers. Point measurements of hydrographs at proglacial rivers as well as salt and temperature budgets at fjord outlets have been used to infer the configurations of subglacial hydrologic system and their relationship with changes in ice velocity (Chandler et al., 2013; Cowton et al., 2013; Hasholt et al., 2013; Mernild et al., 2011). Changes in hydrograph shape and amplitude are often interpreted as a transition in the subglacial hydrologic system (e.g. Jobard and Dzikowski, 2006; Swift et al., 2005). Most discharge budget analyses assume that the meltwater is confined within the ice catchment directly upstream of the sampling sites. While this assumption is realistic for small topographically constrained alpine catchments, my study suggests that the same assumption is not always valid for Greenland catchments where glaciers are less topographically constrained and have lower hydraulic gradients. Greenland-type glaciers are more likely to undergo water piracy between catchments than alpine-type glaciers (Lindbäck et al., 2015). The tendency for Greenland glaciers to experience subglacial water rerouting means that the imbalance in the discharge budget analyses could imply changes in water transport in addition to changes in water storage (Lindbäck et al., 2015; Rennermalm et al., 2012; Smith et al., 2015). My findings suggest that both extent of the supraglacial catchments and the subglacial catchment are necessary to understand how discharge budgets reflect the water sources. In addition, detail measurements of subglacial topography and estimates of water pressure are necessary to determine the subglacial pathways for a catchment. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 35

2.7 Conclusion

My results show that changes in water pressure may result in rerouting of subglacial flow between adjacent glaciers. By incrementing water pressure from 60 to 111% of the ice overburden pressure, I show that small changes in flotation fraction from 1.0 to 1.11 occur at critical locations at the bed can result in major subglacial flow rerouting. An increase of water pressure above flotation from f = 1.0to1.11 can potentially divert subglacial water flow between Nordenskiöld and Alángordliup. The diversion of subglacial water appears to correlate with the transient summer speedup in the high melt year of 2010 where water would create additional lubrication at the ice bed interface. Subglacial flow paths are sensitive to the water pressure condition because it modifies the dependence of flow on topography. Water pressures in excess of the overburden pressure tend to drive flow in the direction of surface slope. In contrast, low pressures tend to steer water flow along bed slopes. The sensitivity of subglacial flow to variations in water pressure is not uniform across the ice catchment. Flow paths are more likely to reroute in regions where subtle changes in pressure impact a near-flat hydraulic potential surface. This difference is particularly important where bed slope is significant and adverse to the surface slopes, such as in areas of subglacial overdeepening where surface slopes tend to be subdued. In these adverse-sloped bed regions, water flow can periodically be rerouted between predominately bed slope and surface slope- dependent pathways when water pressure fluctuates. I predict that in my study region, subglacial flow reroutes from bed slope-directed flow toward Nordenskiöld to surface slope-directed flow toward Alángordliup when water pressure increases above the local flotation pressure. Localized supply of meltwater from the ice surface, for example, through episodic and rapid supraglacial lakes drainage could lead to the rerouting of subglacial flow in critical areas by increasing the water pressure locally. I suggest that catchment-scale rerouting of subglacial water may modify the spatial pattern of basal resistance. This change in resistance could lead to a more spatially extensive or restricted summer velocity speedup depending on the local effects on drainage. The surface velocity observation from 2010 summer provides potential support that the more CHAPTER 2. WATER REROUTING IN WEST GREENLAND 36 extensive velocity speedup in the lower 30km region of Alángordliup is a result of the rerouting of subglacial water from Nordenskiöld to Alángordliup Additionally, the rerouting of subglacial water flow has implications on the assessment of glacier water budgets. Piracy of water between neighboring subglacial water catchments can result in an imbalance between the local measurements of input surface runoff and output discharge at the ice sheet margin. In sum, my study demonstrates that the configuration of subglacial water flow paths beneath Greenland can evolve over time and is particularly sensitive to water pressure and its interaction with topography. Because my calculations assume steady state and uniform water input, I suggest that further investigations using dynamic models are needed to better assess the effects of topography and the critical locations for water rerouting relative to surface drainage in the Greenland Ice Sheet.

2.8 Supporting information

2.8.1 Comparison of water routing with BedMachine

Bed topography influences the hydraulic potential gradient that governs flow paths of subglacial water. The type of gridding methods used to produce the bed topography DEM can exaggerate or subdue certain topographic features that may lead to unphysical rerouting of subglacial flow. Here, I examine the influence of gridding method on the water routing calculation by replacing my bed topography DEM derived from kriging with the DEM derived from Mass Conservation (MC) (Morlighem et al., 2014). The MC bed topography DEM is produced using similar CReSIS bed elevation data from those included in my kriging product. The bed topography derived from MC has a more pronounced trough beneath Nordenskiöld Gletscher that is approximately 42 m deeper than the trough in my bed DEM. However, the water routing results calculated using the MC bed topography show that this elevation difference is insignificant to the routing analysis. The major rerouting between Nordenskiöld and Alángordliup at f = 1.0 to f = 1.11 can be reproduced using the MC bed in the hydraulic potential calculation (Figure 2.8). On a local scale, the predicted routing of the secondary water flow tributaries CHAPTER 2. WATER REROUTING IN WEST GREENLAND 37 is different from the the results produced using my bed topography DEM. The rerouting of subglacial water between two ice catchments is therefore not a byproduct of the gridding method of the bed topography DEM.

Figure 2.8: Estimated subglacial water flow paths (blue lines) for the study region using the bed topography DEM from Mass Conservation (Morlighem et al., 2014). The calculated flow paths for (a) f = 1.0 and (b) f = 1.11 shows a similar rerouting between Nordenskiöld and Alángordliup to the one calculated using my kriging bed topography DEM.

2.8.2 Inﬂuence of uncertainties in DEMs on water routing

Because relative small changes in water pressure (11%) modifies subglacial water flow paths, errors in the bed and surface DEMs also can have the same effect. Errors in the surface and bed topography as well as density variation in ice column can affect the calculation of the hydraulic potential and thus the water flow paths. Here I expand the hydraulic potential equation using a perturbation formulation. The results show that the uncertainties in the DEMs and ice column density are insignificant to the thresholds necessary to cause catchment-scale subglacial rerouting. I add a perturbation to the hydraulic potential following Creyts et al. (2014) to calculate the influence of errors in the surface and bed DEMs,

′ ′ ′ ′ ′ φ + φ = ρwg(zb + z )+(ρi + ρ )g(zs + z zb z ), (2.9) b i s − − b ′ where primed values are the perturbations of the bed elevation (zb) , surface elevation ′ ′ ′ (zs) and ice density (ρi ). φ is the perturbation to the hydraulic potential. Removing the CHAPTER 2. WATER REROUTING IN WEST GREENLAND 38 steady part of the equation gives the perturbation as,

′ ′ ′ ′ φ =(ρw ρi)gz + ρigz + ρ (zs zb). (2.10) − b s i −

Rewriting equation 2.10 for the perturbation in hydraulic head h = φ/ρwg, gives

′ ′ (ρw ρi) ′ ρi ′ ρi h = − zb + zs + (zs zb). (2.11) ρw ρw ρw − At this point, I replace the perturbation terms with discrete diﬀerences in hydraulic head to give,

(ρw ρi) ρi ∆ρi ∆h = − ∆zb + ∆zs + (zs zb). (2.12) ρw ρw ρw − In the equation 2.12, the three right-hand side terms are the errors in the hydraulic potential due resulting from perturbations in the bed DEM, the surface DEM and the variation in the column ice density respectively. The uncertainty in the bed DEM, ∆zb, is given by the largest error value derived from the crossover and bootrapping analyses as

180 m. The uncertainty in the surface DEM, ∆zs, is 10 m (Howat et al., 2014). I take −3 the uncertainty from ice column density to be ∆ρi = 917 910 = 17 kgm . I assign − −3 −3 ρw = 1000 kgm and ρi = 917 kgm . Using these values in 2.12, I estimate the error in hydraulic potential as ∆h = 15 m + 9 m + 18 m = 42 m from the uncertainties in the DEMs and column ice density. If the column ice is relatively uniform spatially across the study region, this gives an error in hydraulic head of 24 m from the uncertainty in the DEMs. Any rerouting of subglacial water flow paths resulted from a change in hydraulic head that is smaller than this error value is potentially a byproduct of the uncertainty in the DEMs. The hydraulic head required to produce the major catchment-scale rerouting I have predicted is around 98 m and is substantially larger than the error. The rerouting of water flow paths between f = 1.0 and f = 1.11 is likely not a result of the uncertainties in the DEMs. Additionally, the 24 m error in hydraulic head is calculated using the maximum uncertainty in the bed DEM. The actual error in hydraulic head in the rerouting region between Nordenskiöld and Alángordliup is smaller than this maximum value, because CHAPTER 2. WATER REROUTING IN WEST GREENLAND 39 the region where the flow paths switch has densest data coverage from the Lamont and CReSIS surveys.

2.8.3 Inﬂuence of localized changes in water pressure on routing

Localized changes in pressure modify the regional hydraulic potential gradients and thus may result in water piracy between neighboring ice catchments. Here I examine the potential for subglacial water to reroute in response to a localized overpressure condition (f = 1.11) around a supraglacial lake (North Lake, top white triangle in Figure 2.9). The model is setup to have a flotation fraction of f = 1.0 across the three glacier catchments, but f = 1.11 in the region surrounding the North Lake (Figure 2.9a). I modify the flotation fraction to f = 1.11 in three scenarios: a circle with a 5 km radius, a circle within a 10 km radius and a circle with a 15 km radius around the North Lake (Figure 2.9a, red circles). The calculated routing of subglacial water flow for these three scenarios is shown in Figure 2.9. Figure 2.9 shows that localized elevation in water pressure above overburden can potentially lead to water piracy between glaciers. The area of influence matters, however. When the overpressurization is confined within 5 km radius around the North Lake, the subglacial water routing is similar to the f = 1.0 scenario and no water piracy occur. In contrast, when the overpressurization occurs over a larger area (within 10 km and 15 km radius from the lake), some of the subglacial water flow is rerouted from Nordenskiöld to Alángordliup in the vicinity of the North Lake. While the potential rerouting is not as significant as the basin-scale water piracy when overpressure exists everywhere, the results demonstrate that localized overpressures at critical locations are sufficient to cause subglacial rerouting. CHAPTER 2. WATER REROUTING IN WEST GREENLAND 40

Figure 2.9: Influence of localized overpressurization on the routing of subglacial water. (a) Model setup with the red circles indicate the regions within which the flotation fraction is modified to f = 1.11. Flotation fraction is modified around 5 km, 10 km and 15 km radius around the North Lake (top white triangle). (b) to (d) calculated flow paths when f = 1.11 is within (b) 5 km, (c) 10 km and (d) 15 km radius around North Lake. Potential water piracy is predicted when overpressures occur locally within 10 km or more around the lake. CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 41

Chapter 3

Variations in Water Storage in Southwest Greenland

A slightly modiﬁed version was published as Chu, W., D. M. Schroeder, H. Seroussi, T. T. Creyts, S. J. Palmer, and R. E. Bell (2016), Extensive winter subglacial water storage beneath the Greenland Ice Sheet, Geophys. Res. Lett., 484492, doi:10.1002/2016GL071538.

3.1 Abstract

Surface meltwater that reaches the base of the Greenland Ice Sheet exerts a fundamental impact on ice flow but observations of catchment-wide movement and distribution of subglacial water remain limited. Using radar-sounding data from two seasons, I identify the seasonal distribution of subglacial water in western Greenland. My analysis provides evidence of widespread subglacial water storage beneath Greenland in the wintertime. The winter storage is located primarily on bedrock ridges with higher bed elevations in excess of 200 m. During the melt season water moves to the subglacial troughs. This inverse relationship with topography indicates the material properties of the glacier bed strongly influence subglacial drainage development. Both the spatial variations in bed properties and the initial state of the subglacial hydrology system at the start of the melt season lead to differing glacier dynamical responses to surface melting across the Greenland Ice CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 42

Sheet.

3.2 Introduction

The contribution of the Greenland Ice Sheet to sea level rise has doubled in the last decade, with a significant contribution from increased melting on the ice sheet surface (Rignot and Kanagaratnam, 2006; van den Broeke et al., 2009). When this surface melt water reaches the bed, it lubricates the interfaces and can cause a transient increase in glacier speed (Alley et al., 2005; Das et al., 2008; McMillan et al., 2007; Smith et al., 2015). The seasonal transition in subglacial drainage controls the coupling between surface melting and ice motion (Andrews et al., 2014; Bartholomew et al., 2011; Schoof, 2010; Sundal et al., 2011; Zwally et al., 2002). In winter, when the supply of melt water is low, drainage pathways close and the system is poorly connected (e.g. Bartholomew et al., 2012; Hewitt, 2013). During the melt season, the supply of surface water to the bed increases the connectivity of the drainage system. This addition of water at the bed increases water pressures until the capacity of the drainage system increases to accommodate the additional water input (e.g. Schoof, 2010; Sundal et al., 2011; Tedstone et al., 2013). Competing effects of sliding, variations in meltwater input and evolution of the subglacial drainage system cause variations in speed through the melt season. The exact effects of surface melt are not well understood, but the system is widely viewed as hysteretic with spring and summer water input yielding increased sliding to a threshold (Iken and Bindschadler, 1986; Schoof, 2005). Once that input threshold is reached, an increase in water input leads to a decrease in sliding during late summer and the transition into fall and winter (Sole et al., 2013; Tedstone et al., 2013). In Greenland, this seasonal melt supply produces complex velocity changes with strong variability at scales of tens of kilometers. Within individual catchments, seasonal glacier speed-ups range from 10% to over 300% above the winter speeds (Andrews et al., 2014; Joughin et al., 2013; Palmer et al., 2011; Zwally et al., 2002). Across Greenland, individual glaciers also show substantially different responses for similar surface melt production and climate forcing (Fitzpatrick et al., 2013; Joughin et al., 2010; Moon et al., 2014). Part CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 43 of this complexity is governed by the spatial distribution of moulins and supraglacial lakes (Joughin et al., 2013; Smith et al., 2015). However, when this meltwater reaches the bed, seasonal changes in basal water pressures can reroute its flow paths subglacially across neighboring catchments (Chu et al., 2016a; Lindbäck et al., 2015). Catchment-scale observations of subglacial drainage are necessary to establish the spatial linkage between surface melt, subglacial drainage and ice velocity. Ice-penetrating radar is a powerful technique for catchment-scale detection of subglacial water bodies. Higher radar bed reflectivity can indicate subglacial water as water produces a stronger dielectric contrast with the overlying ice compared to the surrounding bedrock (Jacobel et al., 2009; Matsuoka et al., 2012b; Schroeder et al., 2016). Previous studies have suggested thresholds ranging from 10 to 25 dB can be used to identify subglacial water bodies beneath ice sheets (Dowdeswell and Siegert, 2003; MacGregor et al., 2012; Matsuoka, 2011; Peters, 2005; Wolovick et al., 2013). However, variations in englacial attenuation due to changes in ice temperature and chemical impurities can influence the basal echo intensity and interfere with the delineation of subglacial water bodies. Imaging subglacial water using radar reflectivities thus requires correcting for these variable attenuation losses.

3.3 Data and Methods

Here, I apply a model-integrated method to correct for this variable attenuation loss and estimate basal reflectivity for Russell Glacier and Isunnguata Sermia (Russell-Isunnguata) in western Greenland. I apply this method to IceBridge MCoRDS radar sounding data from two seasons to examine changes in subglacial water distribution (Gogineni et al., 2001)(Chapter 3.7.1). These data include nine profiles collected during the melt season of May 2010 when there was significant surface runoff (4 – 7 cmday−1) and melt season ice flow speed-up ( 110% above the winter velocity) (Figure 3.1). Additionally, I examine a ∼ high-resolution survey of the catchment acquired 11 months later in April 2011 at the end of winter before the onset of surface melting (Figure 3.1b). I calculate basal reflectivity after correcting for the englacial attenuation, geometric CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 44 spreading losses and radar system variations between flights (Jacobel et al., 2009; Matsuoka et al., 2012a; Schroeder et al., 2016; Wolovick et al., 2013) (Chapter 3.7.2). To estimate the temperature dependent attenuation rates, I use the temperature fields calculated using a three-dimensional steady state thermomechanical ice sheet model (Larour et al., 2012; Morlighem et al., 2010; Seroussi et al., 2013) (Chapter 3.7.3). The ice temperature field is then used in a radar attenuation model (MacGregor et al., 2007) to estimate radar attenuation losses from temperature variations (Chapter 3.7.4). I also estimate the attenuation losses due to the chemical impurities in the ice. The Russell/Isunnguata ice is primarily composed of Holocene chemistry (MacGregor et al., 2015b). Therefore, I apply an uniform chemistry correction in the radar attenuation model and calculate basal reflectivities based on the Holocene impurities content (Table 3.1). Following previous studies, I interpret high reflectivity anomalies as subglacial water and lower values as relatively drier regions (e.g. Jacobel et al., 2009; Schroeder et al., 2016; Wolovick et al., 2013).

3.4 Results

Differences in the reflectivity values for the melt season profiles and the winter survey show the seasonal changes of subglacial water distribution beneath Russell-Isunnguata (Figure 3.2). The 2010 melt season profile reveals two regions of high relative reflectivities separated by a more homogeneous region of low relative reflectivity values (Figure 3.2b). The melt season reflectivity map shows that these higher relative reflectivity regions are generally found in the sediment-filled troughs (Dow et al., 2013; Lindbäck and Pettersson, 2015; Mikkelsen et al., 2013) indicating widespread water, whereas the lower and more homogeneous reflectivities on the intervening bedrock ridges indicating a comparatively drained bed (Figure 3.3c). Eleven months later, at the end of winter in April 2011, the reflectivity data capture a contrasting distribution of subglacial water. The range of the reflectivity is reduced, and the reflectivity attributes of the ridges and troughs are reversed. In the wintertime, the troughs are characterized by lower bed reflectivities, whereas the ridges have CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 45

Figure 3.1: (a) Russell Glacier and Issunguata Sermia in Southwest Greenland with ice flow velocity from Advanced Land Observation Satellite (ALOS) and TerraSAR-X in winters of 2008 and 2009 (Joughin et al., 2010). IceBridge radar-sounding flight lines are shown as purple lines. The blue line indicates the location of the selected profile shown in Figure 3.2. (b) Velocity and surface runoff record from January 2010 to December 2011 at Site S5 along the K transect (Van De Wal et al., 2015). The gray bar represents the time period when the radar data were collected. discontinuous patches of higher reflectivities (Figure 3.2c). These reflectivity characteristics are consistent throughout the 1500 km2 area covered by the radar observations (Figure 3.3a). The high reflectivities regions generally occur in areas with higher average bed elevation (200 to 470 m a.s.l) (Figure 3.14). Both the single profile and the catchment map indicate that in the wintertime there is a substantial amount of subglacial water storage on the bedrock ridges compared to the troughs. Notably, these winter storage regions are localized in areas with nearby flat hydraulic potential gradients (> 9 Pam−1) that favor slow water flow and subglacial ponding CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 46

Figure 3.2: Seasonal changes in subglacial water storage shown along a profile (a) Ice surface and bed elevation along a selected profile where there is an overlapping 2010 and 2011 lines. Location of this profile is indicated by the blue line in Figure 3.1. The orange patches indicate the regions of winter subglacial water storage. The blue patches indicate the regions of melt season water distribution. (b) Melt season relative reflectivity profile collected on 15 May 2010. Relative reflectivities that exceed +9 dB from the zero line (i.e., 1 standard deviation from the mean) are interpreted as melt season water. (c) Winter relative reflectivity profile collected on 13 April 2011. Relative reflectivities that exceed +8 dB (i.e., 1 standard deviation from the mean) are interpreted as winter water.

(Figure 3.4). The storage also aligns with the smaller tributaries of my modeled hydrologic pathways, indicating that drainage was likely restricted along these smaller flow paths during the wintertime (Figure 3.3b). I identified more subglacial storage regions than the potential ponds calculated from a lower resolution hydraulic potential surface (150 m). Many small subglacial lakes, below the resolution of the hydraulic potential surface, may likely exist in this region. This seasonal change in regional subglacial water distribution is captured where the CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 47 two datasets overlap (Figure 3.3d). Two surveys, one in May 2010 and one in April 2011, have coincident geophysical survey lines. Positive differences show where the 2010 relative reflectivities exceed the 2011 values. The differences of +5 to 10 dB found along the basal troughs show increased meltwater drainage, whereas the negative differences (-5 to -10 dB) on the basal ridges indicate a relatively drained bed during the melt season.

Figure 3.3: Seasonal changes in subglacial water storage across the Russell-Isunnguata Catchment. (a) Winter relative reflectivity map with 150 m bed contours. Higher reflectivity values are interpreted as the locations of subglacial water. (b) Bed topography with the same 150 m contours (Morlighem et al., 2014) and the calculated subglacial water flow accumulation from a routing analysis (Chu et al., 2016a). (c) Melt season relative reflectivity map with 150 m bed contours. (d) Difference of relative reflectivity between the melt season and winter maps. Positive differences indicate where the reflectivity is higher (wetter bed) in the melt season compared with the winter condition. The blue line in Figure 3.3a indicates the location of the selected profiles from 2010 and 2011, same line shown in Figure 3.2. CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 48

3.5 Discussion

3.5.1 Control of bed properties on subglacial hydrology

The difference in reflectivity values across Isunnguata-Russell reveals the presence of wintertime subglacial water storage and provides a spatial context for subglacial water movement. The presence of water storage primarily on the basal ridges where the ice is thin (< 500 m), in contrast to the troughs with thicker ice (> 800 m) and potentially higher basal melting, is surprising but arises from the low surface slope. The storage of water on topographic highs covered with relatively thin ice suggests that the material properties of glaciers bed, in addition to bed geometry, strongly influence subglacial water distribution. The basal ridges are bedrock as shown by the high spectral roughness (Lindbäck and Pettersson, 2015). The presence of wintertime water storage indicates these bedrock ridges have relatively low hydraulic conductivity. The discontinuous wintertime reflectivity characteristics suggest the water bodies are isolated, likely in some form of linked cavities system (Figure 3.2c) (Bartholomaus et al., 2011; Lliboutry, 1968; Walder, 1986). This cavity system isolates in the fall when the summer drainage conduits collapse viscously as effective pressures drop in response to lessening surface melt. My interpretation is that these isolated, sealed water pockets are what the radar sampled on bedrock ridges as measured in the winter. During the melt season, the shift to a homogeneously lower reflectivity (Figure 3.2b) indicates increased in connectivity within these isolated systems as drainage pathways open or enlarge, allowing water to flow to the nearby active regions along the subglacial troughs (Andrews et al., 2014). In contrast, the subglacial troughs contain porous sediments as indicated by seismic data(Booth et al., 2012; Dow et al., 2013) and the low spectral roughness (Lindbäck and Pettersson, 2015). As the summertime drainage system contracts during the fall and winter, water drains out of the ice-contact system while it closes (Clarke, 1987; Flowers, 2015; Iverson et al., 1995). Any remaining subglacial water then continues to seep through groundwater drainage, leaving little wintertime storage at the ice-bed interface. During the melt season, higher reflectivities localized in the troughs indicate that drainage is CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 49 focused in the low topography once the upstream drainage system on the ridges connects to the troughs. An upstream supply of meltwater keeps the bed flooded, resulting in the specular, higher reflectivities during the melt season.

Figure 3.4: Comparison between observed and modeled water storage locations (a) Modeled hydraulic sinks with flat hydraulic potential gradients (black polygons) with contours of hydraulic potential of 2.5 MPa spacing. (b) Locations of observed winter water storage, defined by a high-reflectivity threshold of 1 standard deviation (+8 dB) (light blue dots) and 2 standard deviation (+15 dB) (dark blue dots). The black polygons are the modeled sinks shown in Figure 3.4a.

3.5.2 Volume of water storage and its impact on water budget

Subglacial water storage is an integral part of the water budget in Greenland (Lindbäck et al., 2015; Rennermalm et al., 2012; Smith et al., 2015; Van As et al., 2012). Previous studies at Isunnguata Sermia revealed a large disagreement between the modeled runoff and the measured bulk proglacial discharge at Isortoq River (Lindbäck et al., 2015; Smith et al., 2015). The missing volume of 1.8 to 2.7 km3 has been attributed to either storage of subglacial water (Smith et al., 2015) or water piracy by Russell Glacier (Lindbäck CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 50 et al., 2015). I examine whether the observed storage could explain this missing volume. I use a high reflectivity threshold of one standard deviation from the mean reflectivity to determine the maximum horizontal extent of the wintertime storage (Figure 3.4b). If all the missing water were stored in the observed winter storage area, water depths of 28 – 50 m (4 – 6% of the mean ice thickness) would be required. While subglacial water bodies deeper than 50 m are found in Antarctica (Siegert et al., 2005; Smith et al., 2009), it is unlikely that this volume of water is stored in my studied region. I did not observed a pronounced surface elevation change that would otherwise produced by the drainage of a 50 m subglacial lake. Therefore, the large, 50 m water depth required suggests that storage cannot solely explain the discrepancy in the water budget. A combination of storage and other processes, such as water piracy, groundwater losses, and supraglacial and englacial meltwater storage, are likely responsible for the missing water at Isunnguata Sermia (Lindbäck et al., 2015).

3.5.3 Impact of storage on early season velocity

I also examined the impact of subglacial water storage on the summer ice flow pattern at Russell-Isunnguata. Despite the similar surface melt forcing and topography configurations, previous studies show that the summer ice flow patterns vary considerably between Isunnguata Sermia and Russell Glacier (Fitzpatrick et al., 2013; Joughin et al., 2010; Lindbäck et al., 2015; Palmer et al., 2011). Compared to Isunnguata Sermia, Russell Glacier has a more pronounced speed up in early summer and a stronger deceleration at the end of summer to below the wintertime values (Lindbäck et al., 2015; Tedstone et al., 2015). The more pronounced speed up at Russell Glacier suggest that basal water pressure rises more rapidly in early summer than at Isunnguata Sermia (Chandler et al., 2013; Cowton et al., 2013; Meierbachtol et al., 2013). This higher pressure increase could be attributed to the greater variability in the rates of summertime supraglacial water drainage at Russell compared with Isunnguata (e.g. Palmer et al., 2011; Schoof, 2010). In addition, any spatial variations in the state of the wintertime basal hydrologic system would also affect the rates of pressurization during the start of surface melting. The less pronounced early summer acceleration at CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 51

Isunnguata Sermia could be associated with the widespread subglacial water storage that maintains elevated basal water pressures over the winter (Bartholomaus et al., 2011; Clarke, 2005; Flowers, 2015; Harper et al., 2005). In contrast, the lack of substantial wintertime storage at Russell Glacier would result in a greater increase in basal water pressure at the start of the melt season and thus a more pronounced early summer speed up. Hence, I suggest that the individual catchment response to surface melting is determined by a combination of the subglacial hydrologic state at the start of the melt season as well as the variations in spring- and summertime water input. The stronger late summer deceleration at Russell relative to Isunnguata indicates the formation of a focused, channelized subglacial drainage there (Tedstone et al., 2014), leading to efficient evacuation of basal meltwater at the end of summer. This is consistent with my radar results that indicate well-drained bed at the northern catchment of Russell in the wintertime. Together, my findings suggest that the spatial variations in subglacial topography, rates of surface meltwater input, as well as the subglacial water storage at the start of the melt-season, lead to differing glacier dynamic responses to surface melting across the Greenland Ice Sheet.

3.6 Conclusion

I present radar reflectivity analyses from two different seasons to understand the seasonal subglacial drainage development in Isunnguata Sermia and Russell Glacier. My observations provide evidence of wintertime subglacial water storage in Isunnguata Sermia. This wintertime storage is primarily observed on bedrock ridges but not in subglacial troughs. In contrast, my reflectivity results in the melt season reveal large amounts of water focused in the deep troughs but little observed on the ridges. This distinct seasonal drainage evolution suggests the material properties and the permeability of the glacier bed strongly influence the distribution of basal water. While the subglacial water storage I observed is widespread, this storage likely represents the tail end of the summer meltwater volume delivered to the bed from the ice surface. Furthermore, my findings suggest the state of the subglacial hydrology at the onset of CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 52 the melt season impacts the glaciers dynamic response to surface melting in the early summer. My study highlights the need for more detailed observations of how water moves subglacially throughout the year. Regional observations of meltwater distribution both on top of and beneath the ice sheet would help to improve assessment of changes in Greenland water budget in response to climate change.

3.7 Supporting information

3.7.1 IceBridge radar sounding data

The L1B IceBridge radar sounding data were collected with a 195 MHz system, Multi-Coherent Radar Sounding (MCoRDS2) built and operated by the Center for Remote Sensing of Ice Sheets (CReSIS) at University of Kansas. The data product were downloaded from CReSIS data website (http://data.cresis.ku.edu) (Gogineni et al., 2001). For my analysis, I use the radar data with the high receiver gain setting instead of the combined low and high gains data to avoid artifacts in the return power where the ice-bed interface intercepts with the depth where the two channels are combined. Pulse compression is performed on the high-gain channel data with application of a 20% Tukey window in the time domain and either a boxcar or hanning window is applied in the frequency domain. The data are stacked coherently before focused synthetic aperture radar processing. The range resolution for radar data is approximately 0.4 m. The along track resolution is about 25 m with a sample spacing of about 14 m. The cross track resolution varies depending on surface roughness. For a smooth surface, the cross track resolution is approximately 168 m in resolution for an ice thickness of 2000 m and an aircraft elevation of 8000 m. Bed depths where the returned bed echo strengths are deﬁned are picked by CReSIS with automatic detectors and manual pickers.

3.7.2 Radar bed echo analysis

Bed reﬂectivity calculated from radar bed echo strengths can be used to characterize the distribution of subglacial water at the base of the ice sheet (Jacobel et al., 2009; MacGregor et al., 2007; Matsuoka et al., 2012b; Schroeder et al., 2016; Wolovick et al., 2013). The CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 53 bed echo power in dB, [P ], is related to bed reﬂectivity, [R], given by,

[P ]dB =[R]dB [B]dB [G]dB [L]dB +[S]dB (3.1) − − − where square brackets represent quantities in decibel scale, B is the power losses due to birefringence, G is the geometric spreading losses, L is englacial attenuation, and S is the power variation related to radar system parameters. I assume losses from birefringence is constant across the surveys (Matsuoka et al., 2012a; Schroeder et al., 2016). The geometric spreading loss, G, is given by,

[G]dB = 2(h + H/√ε) (3.2) where h is the aircraft height, H is the ice depth, and ε is the real permittivity of ice. The englacial attenuation, L, is related to the one-way englacial attenuation rates, Na, and ice thickness, H, as follows,

[L]dB = 2NaH (3.3)

Producing relative reflectivity values thus requires an accurate estimation of Na. The englacial attenuation rates are dependent on ice temperature and chemistry impurities content (MacGregor et al., 2015b; Matsuoka et al., 2012a). I constrain the ice sheet thermal structure using a thermomechanical ice sheet model detailed in Chapter 3.7.3. The thermal solution is then used to inform a radar attenuation model detailed in Chapter 3.7.4 to calculate L. The final correction for calculating relative reflectivity requires accounting for S. The common approach is to assume S is constant along the radar profiles so that it can be corrected by removing the mean of the bed power (Jacobel et al., 2009; Schroeder et al., 2016). Since I compiled radar data collected in five separate surveys, the radar system settings may not be constant between these surveys. The common mean removal approach is therefore insufficient to correct for S in my case. To correct for S, I apply a leveling method that is conventionally used in aeromagnetic surveys to account for observation offsets (Gadallah and Fisher, 2009; Mandea and Korte, 2011). In leveling, the correction for S is calculated for each radar profile by minimizing the least square CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 54 difference in the geometrically corrected relative power of the profiles that crossed at each intersection points. Figure 3.5 shows the mean relative bed power before and after leveling. Prior to leveling (Figure 3.5a), there are large offsets in geometrically corrected relative power between different radar profiles, notably near the coast and in the ice catchment interior where the along-flow profiles crossed with the turning profiles. After leveling (Figure 3.5b), the power offsets are reduced and the bed power is more consistent where the along-flow and turning profiles crossed. I found that leveling has reduced the mean crossover error of relative bed reflectivity from 11.3 dB prior to leveling to 5.8 dB after leveling. Leveling does not impact the spatial pattern of relative reflectivity across the basal ridges and troughs.

Figure 3.5: Maps of geometrically corrected relative bed power calculated (a) prior to and (b) after leveling. Also shown are the crossover errors in the relative reﬂectivity calculated c. prior and d. after leveling. Leveling produces more consistent pattern of relative bed power across the survey tracks, resulting in relative reﬂectivity values with an improved crossover error. CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 55

3.7.3 Ice sheet model

The thermal structure of Russell Glacier and Isunnguata Sermia is modeled using a finite element model, Ice Sheet System Model (ISSM), developed at the Jet Propulsion Laboratory (Larour et al., 2012). The model is setup on a 3D adaptive mesh with 62,814 elements divided into 30 vertical layers (Figure 3.6a). The mesh has a horizontal resolution ranging from 250 m in the fast flow regions to 1 km in the slow-moving regions. The mesh resolution is selected to minimize the interpolation error in the surface velocities (Joughin et al., 2010). Ice is modeled as a viscous incompressible material. The ice sheet geometry is provided by a surface digital elevation model (Bamber et al., 2013a), and the mass conservation bedrock topography (Morlighem et al., 2014). A full-Stokes stress balance model is used to calculate the horizontal and vertical velocity components that are used to inform the thermal model (Morlighem et al., 2010; Seroussi et al., 2013). The velocity components are calculated by optimizing the basal friction coefficients to match the modeled surface velocity to the observed velocity (Joughin et al., 2010) (Figure 3.6a and b). A stress-free surface is applied at the ice-air interface and a linear viscous friction law is applied at the ice-bed interface (Cuffey and Paterson, 2010). Velocity at the other boundaries is set equal to the observed surface velocity. Since I are only using a static model, the basal friction solution would converge to the same value regardless of the choice of the friction law (Morlighem et al., 2010). The thermal model uses the calculated velocities to compute the advective heat fluxes. The model uses an enthalpy formulation that allows both temperate ice and cold ice to be included without the complication of tracking the cold/temperate transition boundary (Aschwanden et al., 2012; Kleiner et al., 2015). The ice-air interface of the thermal model is defined by the 2011 annual mean surface temperature from the regional atmospheric climate model RACMO (Noël et al., 2015). At the ice-bed interface, I impose a heat flux coming from geothermal flux (Shapiro and Ritzwoller, 2004) and frictional heat flux given by the full-Stokes model. The inflow boundary at the ice sheet interior, temperatures are fixed by the steady-state temperature profiles calculated from a continental scale study (Seroussi et al., 2013). The continental temperatures are used at the inflow boundary to CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 56

Figure 3.6: Horizontal ice surface velocity from (a) TerraSAR-X observation (Joughin et al., 2010) with 2D anisotropic mesh of a horizontal resolution of 250 m to 1 km. The mesh is vertically extruded to form a 3D mesh. (b) Modeled velocity using a full-Stokes stress balance model. (c) Difference between the observed and modeled horizontal velocity. (d) Depth-averaged modeled ice temperature. account for the advection of cold ice from the ice sheet interior to the ablation zone. The calculated temperature structure is shown as depth-averaged values in Figure 3.6d. It is worth noting that the enthalpy model does not include the influence of englacial water storage of percolation of surface melt water into the ice sheet (Forster et al., 2013). Englacial water storage could potentially modify the ice sheet thermal structure through cryohydrological warming (Phillips et al., 2010) Without accounting for the englacial water influence, my estimated temperature structure may be colder than reality, which would lead to an underestimation of the englacial attenuation and lower relative reflectivity values.

3.7.4 Radar attenuation model

Producing relative reﬂectivity from the radar bed echo strengths requires correction of the englacial attenuation. The englacial attenuation rate, Na, is proportional to ice CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 57

conductivity, σ∞, which depends on the ice temperature and the content of soluble ions in the ice given by 10 log10 e Na = σ∞ (3.4) 1000ε0√εic where ε0 and εi are the permittivity of free space and ice respectively, and c is the speed of light (MacGregor et al., 2015a, 2007).

Figure 3.7: Map of two-way englacial attenuation in dB estimated using the thermal model integrated method. The englacial attenuation is spatially variable across the Russell Glacier catchment, with higher values in the basal valleys where ice is thickest.

To estimate Na, I use a radar attenuation model that has been previously been applied to Greenland (MacGregor et al., 2012). The attenuation model assumes σ∞ is an Arrhenius-form dependence on ice temperature and a linear dependence on the concentration of lattice-soluble impurities of acids (H+), sea salt chloride (Cl−) and + ammonium (NH4 ). The contributions of pure ice and each of these impurities to σ∞ have diﬀerent temperature dependencies, CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 58

Epure 1 1 σ∞ = σpure k T − T r + EH+ 1 1 + µH+ [H ]exp k Tr − T (3.5) − ECl− 1 1 + µ 1− [Cl ]exp C k T − T r E + + NH4 1 1 + µ + [NH4 ]exp NH4 k T − T " r # (3.6) where σpure is the conductivity of pure ice, E is activation energy, k is the Boltzmann + − + constant, [H ], [Cl ] and [NH4 ] are the molarities for the respective impurities T is ◦ temperature and Tr is the reference temperature (-21 C). Temperature is given by the thermal model solution sampled along each of the radar survey tracks. The molarities for impurities content have values that are approximated for the Holocene epoch (0 – 11.7 ka) (Table 3.1). The Holocene values are appropriate for my study region, because Russell Glacier and Isunnguata Sermia are primarily composed of Holocene ice (MacGregor et al., 2015a).

3.7.5 Comparison with empirical based methods

Similar relative reflectivity studies have been performed in Antarctica primarily using two empirical-based approaches (Jacobel et al., 2009; Schroeder et al., 2016). Here I apply these previously developed empirical methods to the Russell/Isunnguata catchment. I compare the relative reflectivity calculated from these methods to those estimated using my model-based method to examine its relative performance. The first empirical method (hereinafter referred as the constant rate correction) applies a single englacial attenuation correction for the entire ice catchment (Jacobel et al., 2009). The constant correction assumes that the reflectivity varies around the mean value so that c a line can be fit to the bed power, Pr , plotted against ice thickness, H,

c P = 2Na(H H); (3.7) r − − CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 59

Table 3.1: Values of dielectric properties of Holocene ice and constants used in the radar attenuation model to calculate reﬂectivity.

Symbol Description Values(M07modela) Units

◦ Tr Referencetemperature -21 C −1 σpure Conductivityofpureice 9.2 0.2 µSm ± + −1 −1 µ + Molar conductivity of H 3.2 0.5 Sm M H ± − −1 −1 µ − Molar conductivity of Cl 0.43 0.07 Sm M Cl ± + −1 −1 µ + Molar conductivity of NH4 0.8 Sm M NH4 [H+] Mean impurity concentrations for H+ 1.6 1.2 µM ± [Cl−] Mean impurity concentrations for Cl− 0.4 0.4 µM ± NH+ Mean impurity concentrations for NH+ 0.5 0.6 µM 4 4 ± Epure Activationenergyofpureice 0.51 0.01 eV ± + E + Activation energy of H 0.20 0.04 eV H ± − E − Activation energy of Cl 0.19 0.02 eV Cl ± + E + Activation energy of NH4 0.23 eV NH4 k Boltzman constant 0.23 m2kgs−2K−1 −12 3 −1 4 2 ε0 Permittivityofvacuum 8.85 10 m kg s A × εi Permittivityofpureice 3.17 nounit a M07 model following (MacGregor et al., 2007). CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 60

Figure 3.8: The range of relative reflectivity calculated using the thermal-model integrated methods in this study. The range is slightly larger than the typical range of wet-dry bed condition in Antarctica, but is within reasonable range given the temperate ice condition in Greenland. Following similar studies in Antarctica (Carter et al., 2009; MacGregor et al., 2012; Matsuoka, 2011; Wolovick et al., 2013), I choose to use a range of reflectivity threshold to delineate subglacial water: 1 standard deviation from the mean reflectivity value (7.7 dB) and 2 standard deviation (15.1 dB). Note that 10 dB was considered as the nominal threshold for distinguishing wet and dry bed in MacGregor et al. (2012) and Matsuoka (2011), while other studies have used 15 dB as the threshold for wet bed (e.g. Peters, 2005). where H is the mean ice thickness. The second empirical method (hereinafter referred as the linearly variable rate correction) applies a linearly variable attenuation rate correction to each individual radar tracks (Schroeder et al., 2016). The linearly variable rate correction allows the attenuation rate to vary linearly with distance, x , so that,

δNa Na = Na + (x x) (3.8) δx − δNa where x is the mean along-track position and δx is the along-track derivative of the englacial attenuation rate. Figure 3.9 shows the relative reflectivity distributions resulting from these two empirical based methods and my model based approach. The standard deviation of the reflectivity values produced by the empirical methods exceeds the potential range of CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 61 values for subglacial materials (MacGregor et al., 2007). These reflectivity values are also unrealistically skewed toward the negatives. In comparison, my model-based approach produces more physical reflectivity values with smaller standard deviation and more normally distributed. This demonstrates the importance of properly accounting for the spatially varying attenuation rates in Greenland.

Figure 3.9: Comparison of the relative reﬂectivity calculated using my model-integrated methods with other two existing methods: constant englacial attenuation rate methods from Jacobel et al. (2009) (grey), linear attenuation rate method from Schroeder et al. (2016) (blue). My thermal model integrated method from this study is shown in red. Out of three methods, my method produces the most physically realistic reﬂectivity values for the Russell-Isunnguata catchment region.

3.7.6 Uncertainty in ice temperatures

Uncertainties in the modeled thermal structure affect englacial attenuation and thus my estimation of the relative reflectivity. I estimate the uncertainty in the thermal model by comparing the modeled temperature with the observed temperature profile from a borehole drill site 35 km upstream from the ice margin of Isunnguata (Figure 3.11a). ∼ The modeled temperature in general is 0.3 to 2 ◦C warmer than the observed temperature (Van As et al., 2012). I define the temperature difference as the uncertainty of the thermal model. I use the largest temperature difference of 2 ◦C to recalculate a new thermal steady state. The CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 62

Figure 3.10: Bivariate histogram of relative reflectivity and ice thickness in (a) three- dimensional and (b) two-dimensional views that there is no significant correlation (r2 = 0.08) between reflectivity and ice thickness on a local-scale. new model is initialized with a 2 ◦C colder ice surface temperature to account for the temperature difference between the observations and the original model. The difference between the new and original modeled temperatures would be a conservative estimate of the thermal model uncertainty.

Figure 3.11: (a) Comparison between ice temperatures measured at a drill site (black line) (Harrington et al., 2015) (Site S5) and modeled temperature calculated using the RACMO surface temperature (blue dots) and a 2 ◦C colder surface temperature (red dots). (b) The englacial attenuation at the drill site calculated using the two modeled temperature proﬁles.

I propagate the new thermal solution to the radar attenuation model and calculate new englacial attenuation rates. At the drill site, a 2 ◦C cooling of the surface temperature results in a 4.1 to 7.8 dB decrease in englacial attenuation rates. I propagate the new englacial attenuation to relative reﬂectivity in 3.4 to examine the CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 63 impact of a 2 ◦C adjustment of surface temperature on the reﬂectivity values.

Figure 3.12: Relative reﬂectivity calculated using the thermal model with a 2 ◦C colder surface temperatures. The spatial pattern of the reﬂectivity values is similar to those calculated with the original thermal model used in the text.

Figure 3.13 shows that a 2 ◦C uncertainty in the thermal model does not alter the spatial pattern of the relative reflectivity. Similar to the results produced from the original thermal model, the basal ridges have higher relative reflectivity while the troughs have lower values (Figure 3.12). The difference in the estimated relative reflectivity from the two thermal models is small ( 6 dB) in comparison to the 20 dB contrasts between ± ± the ridges and troughs. The reflectivity difference in general is typically less than 2 dB. The basal troughs have the largest difference in reflectivity, but the difference is positive meaning that I have overestimated the reflectivity in the troughs by 4 to 6 dB.

3.7.7 Hydraulic potential analysis

I calculate the hydraulic potential gradient, φ , to estimate the subglacial water routing ∇ for my study catchment (Banwell et al., 2013; Chu et al., 2016a; Lindb¨ack and Pettersson, 2015). Hydraulic potential gradient is a steady-state proxy of water ﬂow (Shreve, 1972) and is the sum of overburden ice pressure gradient, Pi, and the elevation potential ∇ gradient, Pe, ∇ φ = Pi + Pe = kρigH + ρwgzb (3.9) ∇ ∇ ∇ where ρi is the density of ice, ρw is the density of water, g is the gravitational CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 64

Figure 3.13: Difference in relative relativity values calculated using thermal models with the RACMO surface temperature (results in the text) and a 2 ◦C colder surface temperatures. (a) A histogram of the reflectivity difference showing that the magnitude of difference is small compares to the 20 dB range of reflectivity values on basal ridges ± and troughs. (b) A map of the relative difference showing that the 2 ◦C uncertainty in the thermal model could result in a lower reflectivity values than calculated in the basal troughs.

acceleration, H is the ice thickness, zb is the bed elevation, f is the flotation fraction coefficient. Formally defined, f is the ratio between ice overburden pressure and the water pressure. In this case, I assume f = 1 for the whole catchment, meaning the subglacial drainage is completely filled with water. The assumption of a spatially uniform f is unrealistic as f fluctuates over time and space throughout the year. However, this assumption is sufficient for the purpose of this paper where I are interested in comparing the first order approximation of subglacial water flow with my radar observations. I use the 150 m mass conversation ice thickness and bed elevation models for the hydraulic potential analysis (Morlighem et al., 2014). To determine subglacial water routes, I apply a D routing algorithm to the gridded hydraulic potential ∞ gradient (Tarboton, 1997). I compared the calculated subglacial drainage pathways and hydraulic flatness (or sinks) with the observed locations of subglacial water from the radar analysis (Figure 3.8). The high level of agreement between the modeled pathways CHAPTER 3. WATER STORAGE IN SOUTHWEST GREENLAND 65 and the locations of the observed water bodies provides confidence to my radar analysis, supporting my interpretations of potential water storage beneath the Russell and Isunnguata catchment region.

Figure 3.14: Histograms of bed elevations over the entire study region (in grey scale) and over the winter storage regions only (blue). The winter storage regions generally are found in the areas with higher bed elevations around 200 to 450 m a.s.l. CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 66

Chapter 4

Variations in Water Production Beneath Northern Greenland

4.1 Abstract

In the Greenland Ice Sheet, variations of subglacial water influence basal lubrication and modulate glacier motion (Bartholomew et al., 2010; Zwally et al., 2002). Along the ice sheet margin, distribution of meltwater along the ice surface is reasonably well characterized. In the interior, however, relatively little is known about production and distribution of basal water at the ice sheet base. Here I present evidence from ice-penetrating radar for widespread meltwater generated by both basal and englacial processes in Petermann Glacier. By combining an ice sheet model and radar bed reflectivity, I identify basal water underneath the fast ice near the ice margin and three other distinct water networks located in the ice sheet interior. Near the ice sheet margin, basal water is generated locally by viscous heating associated with ice velocity above 200 myr−1. In the interior, water exists along the paleofluvial canyon and underneath the western and center sections of the ice catchment. These interior water networks are produced either by advection of water from upstream or by strain heating related to the massive deformed basal ice bodies. Further upstream, the onset of Petermann ice flow is coincident with the headwater of the subglacial water network along with localized uplift of warm basal ice. Together, ice deformation and basal water flow enhance and sustain CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 67

Petermann’s motion in the ice sheet interior where both surface and viscous melting are limited.

4.2 Introduction

The basal thermal regime and subglacial hydrology exert critical controls on ice sheet dynamics. Melting or freezing at the base of the ice sheet can increase or reduce the amount of basal water in the subglacial hydrologic system, thereby altering the rate of sliding and ice velocity. In Greenland, ice-penetrating radar and modeling studies have shown that large portions of the northern ice catchments are melting at the bed (MacGregor et al., 2016; Rogozhina et al., 2016; Seroussi et al., 2013). This widespread basal ice melt is likely due to the elevated geothermal heat fluxes that range from 70 to 106 mWm−2 in the southeast and northwest sections of Greenland (Rogozhina et al., 2016). Within the Petermann Glacier catchment in northern Greenland, basal melting in the interior produces a dynamic subglacial hydrology. This subglacial hydrologic system exerts a critical role in connecting the interior basal meltwater to the coast, where the discharge of freshwater across the ice front drives active submarine melting that carves elongate basal channels in the base of the Petermann ice shelf (Dutrieux et al., 2014; Johnson et al., 2011; Rignot and Steffen, 2008). While pre-existing paleofluvial channels may provide a conduit for water to travel from Greenlands interior to the coast (Bamber et al., 2013b), recent radar observations reveal that some portion of the basal melt generated in the ice sheet interior likely refreezes along its flow path before reaching the coast (Bell et al., 2014). These localized areas of basal freeze-on can elevate resistance along the ice bed and may cause the ice sheet stratigraphy to buckle and fold over regions of higher basal resistance (Wolovick et al., 2014). The refreezing of meltwater also acts to warm and soften the overlying ice column that can aid the formation of large-scale, deformed ice bodies observed in the Petermann catchment interior. Constraining the spatial distribution of basal water is, therefore, critical to the understanding of basal sliding, ice deformation, and ice shelf processes that drive changes along the periphery of Petermann. In this paper, I present high-resolution observations of the production and transport of CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 68 basal meltwater beneath Petermann Glacier in northern Greenland using ice-penetrating radar data from NASA’s Operation IceBridge (OIB). I use the radar reflectivity as a proxy to distinguish basal water after correcting for the variations in the radar system and the influence of overlying ice attenuation. My analysis reveals the presence of basal water along the fast flowing regions near the ice sheet margin. I also observe three other basal water networks in the ice sheet interior along the paleofluvial canyon and underneath the western and center sections of the ice catchment. I examine the relationship between these water networks and the deformed ice bodies to understand the origins of this water and how it may be related to the onset of Petermann ice flow.

4.3 IceBridge radar sounding data

In the Petermann region, NASA IceBridge has collected a dense 8 km spaced grid across a two-year span between March in 2010 and April to May in 2011. The two years of radar data cover a survey area that extends from the grounding line up to 250 km into the ice sheet interior. The radar images reveal that Petermann Glacier is characterized by a 800 – 1100 m deep canyon that extends 750 km from the ice sheet interior to the margin. The interior portion of the catchment also contains large-scale folding and deformed basal ice on the order of 5 to 10 km wide and 200 to 1100 m thick (Figure 4.1b). The 2010 survey primarily covers the marginal region below 60 km from the coast, while 2011 survey mostly covers the interior portion of the catchment. For my analysis, I use the L1B synthetic aperture radar (SAR) products that are processed and provided by the Center for Remote Sensing of Ice Sheets (CReSIS) at University of Kansas (http://data.cresis.ku.edu). The basic CReSIS processing steps involve pulse compression with time, and frequency windowing followed by motion compensation, coherent stacking and focused synthetic radar processing. Further details about the CReSIS processing is described in Gogineni et al. (2014). The depth range resolution in ice after the final processing is approximately 4.3 m. The along-track resolution is about 25 m with a sample spacing of about 14 m. Although both surveys in 2010 and 2011 use the same radar system, the Multi-Channel Coherent Radar Depth Sounder (MCoRDS), the instrument is operated at 189–198 MHz CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 69 frequency on the DC-8 aircraft in 2010, while in 2011 the instrument is at 180 – 210 MHz on the P-3 aircraft with different antenna configurations (Table 4.1). Therefore, before using the radar reflectivity as a proxy for the basal condition, I need to account for the differences in the radar systems.

Figure 4.1: (a) Petermann Glacier with ice flow velocity from Advanced Land Observation Satellite (ALOS) and TerraSAR-X in winters of 2008 and 2009 (Joughin et al., 2010). IceBridge radar-sounding flight lines are shown in grey. The red lines indicate locations of deformed ice bodies mapped by Bell et al. (2014). (b) Example radar echogram showing a deformed basal ice body. The location of this profile is shown in blue in (a). (c) Geometrically corrected relative radar bed-echo strengths measured along the example radar line.

4.4 Overview of radar analysis approach

Variations of radar reﬂectivity across the ice catchment provide one of the most direct methods to characterize the basal conditions. I estimate reﬂectivity, [R], from the radar returned bed power, [P ], after correcting for variations in power from radar system setting, [S], attenuation loss, [L], geometric spreading loss, [G] and birefringence loss, [B], as follows, CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 70

[P ]=[S] [L] [G] [B]+[R] (4.1) − − − where I use the decibel notation [X] = 10log10X following Matsuoka et al. (2012b). In this study, I assume [B] is constant across the Petermann catchment following other similar studies (e.g. Jordan et al., 2016; Matsuoka et al., 2012b; Schroeder et al., 2016; Wolovick et al., 2013) and correct for all the other remaining terms in equation 4.1. My approach expands on the methods developed by MacGregor et al. (2015b, 2007) and Jordan et al. (2016) and is particularly suited to examine the radar bed power across multiple seasons and over regions where the ice stratigraphy is deformed. An overview of my approach is shown in the ﬂow diagram in Figure 4.2. The basic procedure includes the standard correction for geometric spreading loss, followed by three additional corrections that are introduced in this study that account for 1) the diﬀerence in the radar system between the 2010 and 2011 survey, and for the radar attenuation based on 2) variations in the ice temperature and 3) changes in the ice chemistry composition.

Figure 4.2: Flow diagram for the components of the modeling-radar integrated technique used in this study to calculate basal reﬂectivity.

I ﬁrst correct for the system variations across multiple seasons, [S], by applying a CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 71

Table 4.1: Characteristics of airborne ice penetrating radar system in 2010 and 2011

Campaign Radar system Bandwidth (MHz) Transmit power (W) Acquisition channels

2010 DC8 MCoRDS 189.15 – 198.65 550 8 2011 P3 MCoRDS2 180 – 210 1050 16 least-squares crossover analysis to minimize the power offsets on intersecting radar profiles (Chu et al., 2016b). This approach examines the mean differences in bed power between intersecting profiles within a radius of 5 radar echoes at each crossover points and adjusts the radar profiles individually to minimize that difference. Figure 4.3 shows the minimization primarily raised the level of the 2010 bed power to match the 2011 data. Overall, this leveling procedure reduces the averaged power offsets between 2010 and 2011 from 12.2 dB to 4.8 dB, producing a more spatially consistent bed power pattern in Petermann. While some of the power offsets between the two years are real inter-annual signals, it is likely that the seasonal variations are relatively small, given that majority of the Petermann catchment lies above the mean snow line with basal melting constitutes the primary water source. After minimizing the crossover error of geometrically corrected bed power, I estimate the radar attenuation losses [L]. Radar attenuation varies spatially due to the influence of both the ice temperature and the concentrations of acid and sea-salt chloride on ice conductivity (Figure 4.4b). I estimate the attenuation rates using an Arrhenius model, M07, based on MacGregor et al. (2015b, 2007). This model assumes the depth-averaged attenuation rates are exponentially dependent on the inverse ice temperature and linearly dependent on the chemical impurities within the ice sheet (Corr et al., 1993; MacGregor et al., 2015b, 2007; Wolff et al., 1997). I first estimate the temperature influence on radar attenuation by calculating the temperature field using a three-dimensional ice sheet thermo-mechanical model that solves the coupled mass, momentum and energy conservation equations (Larour et al., 2012; Morlighem et al., 2010; Seroussi et al., 2013). This temperature field is then applied to the Arrhenius model to estimate the depth-averaged attenuation rates, Na, based on the CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 72 temperature variations. This approach has been previously applied by Chu et al. (2016b) to identify the water distribution in the Russell Glacier catchment in southern Greenland (Chapter 3).

Figure 4.3: Diﬀerences in radar bed power prior to and after correcting for variations in the radar systems between 2010 and 2011.

The folding and deformation in the Petermann catchment produces a tremendous variation in the thickness of Holocene ice (Figure 4.4c). Thus in addition to the temperature inﬂuence, I evaluate the contribution of the Holocene and Last Glacial Maximum (LGM) ice to the radar attenuation losses. Holocene ice is more conductive and thus more attenuating than the LGM-aged ice because the Holocene ice contains greater concentrations of acid and sea salt chloride (Table 4.2, Figure 4.4b). To account for these chemistry eﬀects, I trace the bottom of the Holocene layer at 11.7 kyr across the Petermann catchment derived from the chronology data from the NEEM ice core (Rasmussen et al., 2013) (Figure 4.4c). Using this constraint on the Holocene ice thickness throughout the study region, I CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 73

Table 4.2: Values of dielectric properties of ice and constants used in the radar attenuation model to calculate reﬂectivity.

Symbol Description Values(M07modela) Units

◦ Tr Referencetemperature -21 C −1 σpure Conductivityofpureice 9.2 0.2 µSm ± + −1 −1 µ + Molar conductivity of H 3.2 0.5 Sm M H ± − −1 −1 µ − Molar conductivity of Cl 0.43 0.07 Sm M Cl ± + −1 −1 µ + Molar conductivity of NH4 0.8 Sm M NH4 1.6 1.2 (Holocene) [H+] Mean impurity concentrations for H+ ± µM 0.2 0.5 (LGM) ± 0.4 0.4 (Holocene) [Cl−] Mean impurity concentrations for Cl− ± µM 1.8 1.0 (LGM) ± + + 0.5 0.6 (Holocene) NH4 Mean impurity concentrations for NH4 ± µM 0.4 0.4 (LGM) ± Epure Activationenergyofpureice 0.51 0.01 eV ± + E + Activation energy of H 0.20 0.04 eV H ± − E − Activation energy of Cl 0.19 0.02 eV Cl ± + E + Activation energy of NH4 0.23 eV NH4 k Boltzman constant 0.23 m2kgs−2K−1 −12 3 −1 4 2 ε0 Permittivityofvacuum 8.85 10 m kg s A × εi Permittivityofpureice 3.17 nounit a M07 model following (MacGregor et al., 2007). CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 74

Figure 4.4: Effect of ice chemistry on radar attenuation (a) Radargram showing the location of the Holocene-LGM transition (base of Holocene ice) in red. (b) Dependence of radar attenuation rates on ice temperature and chemical concentrations at GRIP core, assuming an Arrhenius model, M07, in MacGregor et al. (2007).(c) Elevation of the base of Holocene ice across the Petermann catchment. Black box shows the location for Figure 4.9. Black arrow highlights the onset of Petermann concentrated flow identified based on the velocity contour spacing. estimate the additional radar attenuation using a mixture of Holocene and LGM ice chemistry in the Arrhenius model. While I can consistently trace the base of the Holocene within 100 km of the ice sheet margin, upstream in the interior deformed ice bodies often significantly disrupt the ice stratigraphy. Around these deformed bodies, the transition can be drawn down by 500 m or more on either side. I was able to resolve these sharp changes using a manual digitization. Together, these corrections provide a spatially variable depth-averaged radar attenuation rates (Na) across the Petermann catchment (Figure 4.5a). Values range between less than 14 dBkm−1 along the eastern shear margin to more than 25 dBkm−1 within 50 km of the ice sheet margin. Across most of the Petermann catchment, the attenuation rates are within 15 to 17 dBkm−1. CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 75

This range of attenuation rates exceeds the uncertainty associated with the thermal and chemical corrections (Na)(Figure 4.5b). I estimated this uncertainty by summing up the errors from the thermomechanical model and the chemistry correction as follows, f

Na = Na +(NaHOL NaLGM ), (4.2) T − where Na is the error from thef thermomechanicalf model and NaHOL NaLGM represents T − the uncertainty from the chemistry correction, defined as the difference in attenuation f rate calculated with a 100% Holocene chemistry and with a 100% LGM chemistry (i.e. differences between the red and blue curves in Figure 4.4). NaT is calculated by comparing my modeled ice temperatures with the observed temperatures at the closest ice core site, f NGRIP (Figure 4.5b, inset)(Andersen et al., 2004). This gives a -3.23 ◦C difference in depth-averaged temperatures between my model and NGRIP, which translates to a NaT = −1 −1 1.93dBkm . Across the most of the Petermann catchment, Na is less than 5 dBkm . − f Although there is a slightly larger uncertainty exceeding 8 dBkm−1 within 50 km of the f ice sheet margin, overall the uncertainty range is significantly lower than the actual range of attenuation rates. Also, note that this uncertainty is an upper-bound estimate as the actual error for the chemistry correction should falls within the difference in attenuation rates using a 100% Holocene and 100% LGM ice chemistry. After accounting for the variations in radar attenuation from both the ice temperature and chemistry, I estimate radar reflectivity and infer the bed condition using the high reflectivity anomalies, or relative reflectivity, as a proxy for basal wetness.

4.5 Results

The radar bed reflectivity values range from -41 to -79 dB and reveal several regions of high reflectivity anomaly both near the ice sheet margin and in the ice sheet interior. High reflectivity anomalies are defined by where the bed reflectivity is at least above two standard deviations from the regional mean (-48 dB or more). These high reflectivity anomalies are shown as the dark blue dots in Figure 4.6b and c. Within 50 km of the ice sheet margin, there is a concentrated region of elevated CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 76

Figure 4.5: Radar attenuation and its uncertainty across the Petermann catchment. (a) Depth-averaged englacial attenuation rates (b) Uncertainty in the attenuation rates associated with the temperature and chemistry corrections. Inset shows the comparison between my modeled temperature (blue line) and the observed borehole temperature from NGRIP ice core (dotted black line). reflectivity beneath the fastest portion of Petermann, where the ice velocity ranges from 200 – 1000 myr−1. This high reflectivity region is continuous from 30 km above the grounding line up to about 110 km inland. The lower 50 km of this reflectivity anomaly extends below the mean snow line. The upper limit of this marginal feature is confined by the 200 – 400 m deep basal trough (Figure 4.6a, black dotted line). Above 50 km from the margin in the ice sheet interior, I also identify three other distinctive regions of high reflectivity along the canyon and beneath the western and central sections of the main ice trunk (Figure 4.6). Along the 800 – 1100 m deep canyon, I observe intermittent high bed reflectivities that occupy 3% of the lines crossing the canyon (Figure 4.6b, feature I). Underneath the western section of Petermann ice trunk, the radar shows another discontinuous reflectivity anomaly located above 100 km from the glacier terminus CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 77

(Figure 4.6b, feature II). In contrast to the canyon, here the reflectivity anomaly is more widespread and spans 30 – 50 km across the catchment. This western anomaly extends from 100 km up to 150 km into the ice sheet interior, consisting of a lower and upper high reflectivity distribution. These two features are connected by a sinuous high reflectivity line that appears to align with an ice surface depression feature (Figure 4.6c). Finally, there is third reflectivity anomaly along the center section of the Petermann ice trunk. This central anomaly is about 80 km long, beginning at 110 km from the grounding line and extending all the way up to 190 km inland (Figure 4.6b, feature III). Similar to the western high reflectivity anomaly, the high reflectivities here are not confined by any distinctive bed troughs. The width of this central anomaly appears to be aligned with the rugged ice surface features that bound the Petermann Glacier up to 220 km into ice sheet interior.

Figure 4.6: (a) Estimated relative reflectivity (b) Basal water delineated using a high reflectivity anomaly threshold that exceeds 2 standard deviation from the mean. Separate thresholds were used for 2010 and 2011. Also shown are the locations where the profiles in Figure 6 were extracted. (c) Calculated subglacial hydrologic pathways. The black dotted area outlines the upstream catchment that potentially feeds the basal water network around the onset of Petermann Glacier.

I interpret these high reflectivity anomalies as basal water networks underneath the Petermann catchment. The radar indicates substantial basal water near the ice sheet margin below 50 km that generally aligned with the fastest ice (> 200myr−1) or with the CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 78 shear margin of Petermann. Above 50 km, the water distribution is less concentrated and is widespread across the ice sheet interior. In this interior region, three other distributions of subglacial water exist along the bed canyon and underneath the western and central sections of Petermann’s main ice trunk. In the canyon, this subglacial network is topographically confined along the 800 – 1100 m deep valley. The intermittent characteristic of the high reflectivities indicate that this canyon system consists of isolated subglacial ponds. These ponds are primarily found in local bed depressions along the canyon. Beneath the main trunk, I also find basal water along the western and center sections. In contrast with the canyon network, here basal water is widespread and not confined by topography. The central water network extends up to 180 km inland from the ice sheet margin, with some indication that melting may reach as far as 200 km inland. Similarly, the western water network extends at least 200 km inland perhaps reaching up to 250 km into the ice sheet interior. Both the western and central water networks occur in a region where the ice stratigraphy is heavily deformed and is characterized by large-scale folding that reaches 200 – 1100 m into the ice column (Figure 4.4c) (Bell et al., 2014; Dahl-Jensen et al., 2013). In addition, I estimate the hydrological pathways using a routing model (Chu et al., 2016a) and Digital Elevation Models of bed topography (Morlighem et al., 2014) and ice surface (Howat et al., 2014). The radar observed water distribution generally agrees with the modeled pathways (Figure 4.6c). In particular, there is an excellent agreement between the model and observation along the bed canyon. Beneath the main trunk, the observed water distribution is more widespread than predicted, but generally clusters around the modeled drainage tributaries. The hydrological model also suggests that some of the high radar reflectivity anomalies along the shear margins of Humboldt and Petermann may be related to water draining toward Humboldt. However, since this shear margin is also characterized by specular radar reflections (Jordan et al., 2017), it is possible that some of the high reflectivities anomalies are related to the smoother bed roughness in this region. In contrast, beneath the main ice trunk, the bed is uniformly rough characterized with diffuse radar reflections CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 79

(Jordan et al., 2017). The higher radar reﬂectivities I observed in these areas are thus most likely related to the presence of subglacial water.

4.6 Discussion

4.6.1 Distribution and sources of basal water in Petermann

Radar reflectivity reveals that beneath Petermann Glacier substantial basal water exists in both the ice sheet margin and above the ablation zone. To examine these marginal and interior water networks more closely, I extract a profile along the canyon following the calculated hydrologic network and two more that align with ice flow beneath the western and center sections of the Petermann ice trunk. Along these profiles, I interpolate ice sheet topography, satellite measured ice velocity, the 11.7 kyr transition as well as basal melt rates estimated from my thermomechanical model. These profiles allow me to investigate the potential sources for the water systems and their relationship with the deformed basal ice bodies. All three profiles show that near the ice sheet margin below 20 – 40 km along the profiles, water networks occur in the regions of substantial basal melting with 0.1 myr−1 or more (Figure 4.7). The high basal melt rates indicate that these marginal water networks are generated by viscous heating associated with the fast (200 – 800 myr−1) ice velocity near the ice sheet margin. Some of water in the western margin also appears to be aligned with the steep slopes in the northwest of Petermann (Figure 4.6b, feature II). Shear heating along this ice/rock boundary may have also contributed to the formation of the basal water networks near the ice sheet margin. Further, as these water bodies are found below the mean snow line (Figure 4.6a, black dotted line), there could also be some contribution from surface meltwater draining though moulins and crevasses to the ice base. In addition to the ice sheet margin, I also identify three other basal water networks above the ablation zone of Petermann in the bed canyon and along the western and center sections of the ice catchment. Along the canyon, subglacial ponds exist above 120 km along the profiles are located in a region where the ice velocity is below 50 myr−1 (Figure 4.7a). CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 80

Basal melt rates, estimated from the thermomechanical model, are also below < 0.05 myr−1. Both the low ice velocity and basal melt rates indicate that the interior water networks are advected from an upstream source and collected in the canyon. A potential source could be from the high geothermal heat fluxes of 70 to 130 mWm−1 that extends from the NEEM ice core down to about 79 ◦N (Rogozhina et al., 2016). In contrast to the topographic confined canyon network, I observe a more widespread water distribution along the western and central sectors of the ice catchment. Beneath the western sector, basal water exists between 40 to 110 km along the profile above the fast flowing regions (Figure 4.7b). Here ice velocity is less than 100 myr−1 and rapidly decreases down to 10 myr−1 at 110 km inland. Basal melt rates within this interior region are below 0.05 myr−1. The reduced ice velocity upstream indicates that viscous heat dissipation along the ice sheet bed is likely too low to generate the basal water networks in the ice sheet interior. Notably, this interior water network along the western sector does not connect all the way to the ice sheet margin. The discontinuity of the interior drainage could be related to the local consumption of meltwater, for example by refreezing. Alternatively, the water draining from the interior may be diverted downstream at 79.5 ◦N and 79.7 ◦N driven by the strong convergence of ice flow near the ice sheet interior (Joughin et al., 1999, 2010). It is possible that this water is captured by the neighboring drainage system located beneath the center sector of the ice catchment. Similar to the western water network, the basal water along the center profile extends above the fast flowing downstream region and into the low velocity, low basal melt zones between 60 to 80 km along the profile (Figure 4.7c). Without significant contributions from either surface melting and localized viscous heating related to fast ice flow, these interior water bodies along both the center and western profiles must be generated by advection of basal water from an upstream water catchment (Figure 4.6c, the dotted polygon) or by internal heating within the ice sheet. A likely candidate for this internal heat source could be related to the large-scale deformed ice structure previously identified by Bell et al. (2014) and Dahl-Jensen et al. (2013). Basal water networks along the western and central Petermann catchment are CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 81 located within the regions where deformed basal ice exists (Figure 4.7d). While typically internal heating only constitutes a small amount of basal melting (Cuffey and Paterson, 2010), in the Petermann catchment these deformed structures are both wide (5 – 10 km) and thick (200 – 1100 m). Uplifting of warm basal ice would lower the temperature gradient in the bottom ice column, allowing less heat to conduct away and more heat to be used for basal melting (Cuffey and Paterson, 2010; Wolovick et al., 2014). Thus, it is possible that the ice deformation has led to significant strain heating within the Petermann catchment that could explain the widespread basal water I observed in the ice sheet interior. This internal heating from the deformed basal ice bodies is not currently represented in the thermomechanical model. While my calculations included a mixture of Holocene and LGM ice composition, this exercise only accounts for the effect of anisotropic composition on ice conductivity but not for its effect on ice velocity. A softer glacial ice would be easier to deform (Bons et al., 2016; Dahl-Jensen et al., 2013), resulting in more basal melting underneath Petermann than the model predictions.

4.6.2 Relation between water and deformation at the onset region

I examine the relationship between water and ice deformation further by focusing on the onset region of Petermann Glacier (Figure 4.4c, black box). The onset of Petermann, defined by the shift in the ice velocity contour spacing, begins at 160 km from the grounding line (Figure 4.4c, black arrow). The position of the Petermann’s margin is not defined by any distinctive basal troughs, unlike other topographically confined glaciers in southeast Greenland (Bamber et al., 2013a; Morlighem et al., 2014). Mechanisms other than topographic focusing are thus likely responsible for localizing the Petermann ice flow. I suggest that there are two potential candidates that could explain why the onset of Petermann is located where it is (Figure 4.9). The first one is related to the presence of widespread basal water. The onset of Petermann is coincident with the inception of widespread basal water along the center profile (Figure 4.9b). The hydrological routing model predicts that this drainage network is fed by an upstream catchment that extends 80 km further inland from the onset region (Figure 4.6c, blue dotted area). Coalescing CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 82 and focusing of upstream water into the center of the glacier may have contributed to the onset of Petermann. Another potential candidate for the onset of Petermann could be related to the ice rheology. The onset is spatially coincident with a 20 km wide and 800 m high folding in the ice stratigraphy (Figure 4.9b, red line). Notably, although a similar deformation was found along the western sector of Petermann ice trunk (Figure 4.9c, red line), the height of that deflection is only half of the uplift observed at the onset region. The origin of these ice deformation structures has been extensively studied in the Petermann catchment. The proposed theories are generally divided into three camps relating to the variations in subglacial hydrology (Bell et al., 2014; Wolovick and Creyts, 2016; Wolovick et al., 2014), rheology contrast between glacial and interglacial ice (Dahl- Jensen et al., 2013) or the strong convergence and shearing of Petermann ice flow (Bons et al., 2016). I suggest that these processes are not necessary independent of each other. Strong convergence forced by the narrow fjord at the ice sheet margin can cause the soft glacial ice to deform and buckle along flow. The subsequent uplift of basal ice can increase strain heating in the lower ice column, lowering the temperature gradient near the base and generating water along the ice sheet base. Basal melting, in turn, may lead to a spatially variable slip along the bed that could enhanced ice deformation (Wolovick et al., 2014). Together, ice deformation and its feedback with basal meltwater, enhance and maintain the fast flow in the interior of the Petermann catchment. Petermann underwent a major calving event in 2010 that broke off 25% of its floating tongue (Falkner et al., 2011). Such calving episodes are expected to increase as the polar oceans and atmosphere continue to warm due to climate changes (Nick et al., 2012). A complete disintegration of the ice tongue would have far reaching impacts on the subglacial hydrologic system in the ice sheet interior. Melting along the ice base may increase as reduction of back-stress at the grounding line enhances sliding and deformational processes upstream. Enhanced water generation along the ice bed could further reduce the basal resistance along the ice flow, causing the region of Petermanns fast flow to migrate inland. CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 83

4.7 Conclusion

I identified widespread basal water underneath the accumulation zone of the Petermann Glacier in northern Greenland using a combined modeling and radar sounding technique. Three distinctive basal water distributions are found along the canyon and underneath the western and center sections of the Petermann ice trunk. Intermittent drainage along the 800 – 1000 m deep canyon indicating that basal water originating from the ice sheet interior is locally stored in the canyon. Underneath the Petermann ice trunk, there is a close relationship between basal water, ice velocity, and internal deformation. Close to the ice sheet margin, more than half of basal water bodies observed are associated with the increased viscous heating driven by the fast ice motion. In the interior region, I have also identified basal water that is produced by heat generated from ice deformational processes. The onset of concentrated flow in the Petermann catchment is spatially coincident with the headwater of the basal water tributaries and localized uplift of warm ice into the ice sheet. Uplift lowers temperature gradients of the basal ice, thereby leaving more heat for basal melting. Together, the interaction between deformation and basal water enhances and sustains fast flow in the interior of the Petermann catchment. Incorporating the coupling between non-uniform rheology and basal melting into numerical ice sheet model is vital to produce realistic velocity structure for fast flowing glaciers in northern Greenland. CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 84

Figure 4.7: Estimated basal melt rates from a thermomechanical model along (a) the canyon. (b) the western section (c) the center section along the main basin. CHAPTER 4. WATER PRODUCTION IN NORTHERN GREENLAND 85

Figure 4.8: (a) Measured ice speed above the basal water bodies showing over 60% of the water bodies are in region of fast ﬂow. (b) Modeled basal melt rates interpolated at the location of the basal water bodies showing water mostly occurs in regions with high melt rates.

Figure 4.9: Development of subglacial water network and uplift of basal ice close to the onset of fast flow in the Petermann catchment (a) Close-up of the onset of concentrated flow with basal water bodies in dark blue. Color map shows the mapped Holocene-LGM horizon elevation. (b – c) Ice sheet profiles along the center and western sections of the Petermann basin crossing the region of onset (arrow) with basal water locations (blue squares) and the horizon elevation (red line). Grey shaded area highlights the uplift regions where the warm basal ice was moved to higher elevations. CHAPTER 5. CONCLUSION 86

Chapter 5

Conclusion

The purpose of this dissertation was to examine the variability of basal hydrology as a potential mechanism in causing rapid changes around the Greenland Ice Sheet. The work was motivated by the need of the glaciology community to extend our current observations from a localized borehole scale to an ice-sheet wide scale. A continent wide study of Greenland is critical to understanding the determining factors that control the coupling between the ice and water flow. The work presented in this dissertation is the first attempt to combine hydrological routing and ice sheet models with radar sounding techniques to address this challenge. Particularly, this work focused on investigating 1) spatial variability of basal water within the ice catchment, 2) temporal variability of this water throughout the seasons, and 3) geographical variability of the subglacial drainage behavior across Greenland. In chapter 2, I addressed the first research objective and examined the spatial variability of basal water in western Greenland. I found that large-scale reorganization of subglacial drainage can occur in Greenland. Water can be rerouted 100s of km between neighboring glaciers. While similar subglacial water piracy has been observed beneath West Antarctica (Anandakrishnan and Alley, 1997; Carter et al., 2013; Vaughan et al., 2008), Greenland drainage has been thought to be more topographically confined and thus incapable of massive rerouting. I provided evidence from hydrological model simulations to show that this is not the case. Greenland, in fact, is similar to West Antarctica and its subglacial drainage system is very prone to piracy. In chapter 2, I CHAPTER 5. CONCLUSION 87 made the case that this sensitivity lies in the glacier geometry and more specifically, the ratio between the ice surface and bed slopes. Away from the first 10 – 20 km from the ice sheet margin, the ice surface flattens rapidly towards the ice sheet interior. Further upstream, bed slopes become progressively more important in steering basal water flow For glaciers where the local bed slope is oblique to the general ice flow direction, like in the case for Alángordliup Sermia in West Greenland, the bed topography can divert basal waters to adjacent outlet glaciers at the right basal water pressure condition. In the case of Antarctic ice streams, water piracy is thought to have caused ice flow stagnation along the Siple Coast (Anandakrishnan and Alley, 1997; Carter et al., 2013) and in Carlson Inset (Vaughan et al., 2008) in West Antarctica. I suggested that rerouting of water underneath Greenland can have a similar effect on modifying the ice velocity pattern on an annual time scale. Particularly, water piracy can help to explain the year-to-year difference in ice velocity speedup patterns observed around the time of supraglacial lake drainage events. The work presented in Chapter 3 provided a better understanding of the temporal variability of the subglacial hydrological system. Measurements of basal water pressure from boreholes and observations of ice surface velocity from Global Positioning System (GPS) offer an important glimpse into the variability of basal hydrology on a local scale (Andrews et al., 2014; Bartholomaus et al., 2008; Stevens et al., 2015; van de Wal et al., 2008). In chapter 3, I expanded this view and demonstrated, for the first time, that the seasonal distribution of basal water varies across an entire ice catchment. I illustrated that this variation in water distribution is strongly controlled by the material properties of the ice sheet base. Impermeable bedrock enables water to build up along the bed at the end of the melt season as the subglacial drainage system shuts down. These isolated subglacial ponds maintain high basal water pressures over the course of the winter. In contrast, the more permeable basal troughs allow water to continuously recharge the underlying aquifer, leaving behind a relatively drained bed surface. Together, these varying basal conditions across the ice catchment set up contrasting hydrological states that could lead to differing ice velocity response to surface melting in the following melt season (Fitzpatrick et al., 2013; Palmer et al., 2011). The results in this chapter highlight the CHAPTER 5. CONCLUSION 88 need to extend observations on subglacial drainage beyond a single melt season, in order to fully understand the coupling between ice velocity speed-up and water drainage across Greenland. Both Chapter 2 and 3 focused on hydrologic systems that are primarily fed by surface melting. In chapter 4, I extended this study to include a basal-melt driven system at Petermann Glacier in northern Greenland. Together, these results allowed me to examine the geographical variability of subglacial hydrology across Greenland. The results in Chapter 4 demonstrated that widespread basal water could exist even in regions where surface melt input is scarce. I found that in a basal melt driven system, water is primarily generated by two sources. Near the margin, the fast ice motion generates water through viscous heating. In the interior, substantial basal water is produced by strain heating related to internal ice deformation (Bell et al., 2014; Wolovick et al., 2014). While in most ice sheet regions, deformational heating only constitutes a minor amount for water generation, in the case of northern Greenland massive ice deformation provided a perfect condition for extensive basal melting to occur (Wolovick et al., 2014). Taken together, the research in this dissertation represents the first step in characterizing the variability of subglacial hydrology active around the entire Greenland Ice Sheet. The results presented in this work provide information about how the subglacial drainage behavior may change in the future. As climate continues to warm in the coming century, surface melting is projected to migrate further into the ice sheet interior, where melting of snow would decrease the surface albedo creating a feedback with ablation (Box and Colgan, 2013; Fettweis et al., 2011; Tedesco et al., 2011). Increased surface melting will lead to stronger seasonal variations in both water flux and pressure in the ice sheet interior than observed in present. Further, glacier velocity is also expected to increase due to enhanced dynamic thinning with the greatest changes expected for glaciers that terminate in the oceans (e.g. Joughin et al., 2008; Rignot and Kanagaratnam, 2006). Glacier acceleration, in turn, will enhance the amount of frictional and deformational heating inside the ice sheet. All in all, both surface and basal melting are expected to increase over a large portion of the Greenland Ice Sheet. CHAPTER 5. CONCLUSION 89

The work in this dissertation indicates that different sectors across Greenland may respond to this increased meltwater input variably, depending on the geometry of the glaciers, the material properties of the bed and the rate of the water production. In the southern and eastern sectors, as surface meltwater input migrates upstream onto the more resistant bedrock (Rippin, 2013; Swift et al., 2005), we expect to see an increasing amount of winter subglacial storage underneath these regions. Ice discharge along this sector of Greenland will likely be strongly controlled by the connectivity between these upstream storage regions and the downstream subglacial valleys. By contrast, glaciers in the northern and western sectors are localized in deep subglacial troughs that extend far into the ice sheet interior. Their drainage behavior will likely be very similar to those observed in the present day, where the bed channels will continue to act as low-pressure sinks that draw water from the surrounding regions. Elsewhere, however, as meltwater migrates upstream into the flatter ice sheet interior, bed slope will exert an increasingly dominant role in steering basal water flow. The drainage pathways that the water take to reach the ice sheet margin will be very different from today. A large-scale reorganization of subglacial drainage may promote ice piracy between adjacent glaciers by changing the spatial distribution of basal sliding, at least until the ice surface adjusts to a new equilibrium. To fully understand the role of subglacial hydrology in promoting rapid changes around Greenland, future work will need to expand the integrated approaches developed in this dissertation to the rest of the continent. More analysis should also be done to link the hydrological observations to other observed changes in seasonal ice velocity and surface elevations. The increasing availability of frequent ice velocity measurements from Landsat 8 (e.g Fahnestock et al., 2016), along with altimetry observations from CryoSat-2 and the future ICESat-2 mission (e.g. Csatho et al., 2014; Helm et al., 2014) are valuable to link the water and ice flow variability in Greenland. Furthermore, additional analyses should also utilize the full characteristics of the radar bed echo, to investigate the influence of bed roughness and the scattering effect on the radar reflectivity. Overall, the work presented in this dissertation is a first but crucial step in providing an integrated model and observational technique that would eventually allow us to quantify the amount of CHAPTER 5. CONCLUSION 90 subglacial water and its variability beneath Greenland. BIBLIOGRAPHY 91

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