Ice Dynamics and Stability Analysis of the Ice Shelf-Glacial System on the East Antarctic Peninsula Over the Past Half Century: Multi-Sensor

Ice dynamics and stability analysis of the ice shelf-glacial system on the east Antarctic Peninsula over the past half century: multi-sensor

observations and numerical modeling

A dissertation submitted to the

Graduate School

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

in the Department of Geography & Geographic Information Science

of the College of Arts and Sciences

Shujie Wang

B.S., GIS, Sun Yat-sen University, China, 2010 M.A., GIS, Sun Yat-sen University, China, 2012

Committee Chair: Hongxing Liu, Ph.D.

March 2018

ABSTRACT

The flow dynamics and mass balance of the Antarctic Ice Sheet are intricately linked with the global climate change and sea level rise. The dynamics of the ice shelf – glacial systems are particularly important for dominating the mass balance state of the Antarctic Ice Sheet. The flow velocity fields of outlet glaciers and ice streams dictate the ice discharge rate from the interior ice sheet into the ocean system. One of the vital controls that affect the flow dynamics of the outlet glaciers is the stability of the peripheral ice shelves. It is essential to quantitatively analyze the interconnections between ice shelves and outlet glaciers and the destabilization process of ice shelves in the context of climate warming. This research aims to examine the evolving dynamics and the instability development of the Larsen Ice Shelf – glacial system in the east Antarctic

Peninsula, which is a dramatically changing area under the influence of rapid regional warming in recent decades. Previous studies regarding the flow dynamics of the Larsen Ice Shelf – glacial system are limited to some specific sites over a few time periods. This research integrates the multi-sensor remote sensing data acquired by various optical and radar satellites and airborne/satellite altimetry missions to study the spatiotemporal variations in ice velocity, ice front and surface elevation. A half-century ice velocity record has been reconstructed over the Larsen

Ice Shelf by processing more than 400 remote sensing images acquired during 1963–2017. Besides, this research implements a physically based ice flow model to investigate the changes in stress conditions prior to the ice-shelf collapse. This integrated perspective of observations and numerical modeling enables to explore the physical processes that lead to the disintegration of an ice shelf.

A four-stage development model (unstable condition initiation stage, enhanced weakening stage, destructing stage and catastrophic disintegration stage) is proposed to elucidate the destabilization process of the northern Larsen Ice Shelf.

In loving memory of my father, Qiang Wang (1959-2016).

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ACKNOWLEDGMENTS

First and foremost, I would like to express my sincere gratitude to my advisor Professor

Dr. Hongxing Liu, who has always been a tremendous mentor to me. This work could not have been done without your immense knowledge, support, patience and encouragement. I appreciate all your contributions of time and effort to make my PhD pursuit productive and enjoyable. I am also thankful for the outstanding example Dr. Liu has provided as a successful scientist and professor. The rigor and enthusiasm that you have for research teaches me how excellent research is done, and inspires me to delve deeper into the core of cryosphere science. Your idea, ‘think in conceptual level and frame a big picture’, not only has a profound influence on my research career, but also has been a beacon for me to go through the toughness of life.

I would also like to thank Professors Dr. Richard Beck, Dr. Tomasz Stepinski, Dr. Kenneth

Hinkel and Dr. Dylan Ward for serving as my committee members and giving me valuable feedbacks and insightful comments. I would particularly like to acknowledge Professor Dr.

Kenneth Jezek from the Ohio State University for improving my work from a more ‘science’ perspective, and Professor Dr. Lei Wang from the Louisiana State University for helping me with the algorithm implementation. I am also thankful to Professors Dr. Lin Liu and Dr. Nicholas

Dunning for their brilliant comments and suggestions during my defense.

Special thanks to the members of the Remote Sensing group. You have contributed enormously to my professional and personal time at UC. The group has been a great source of good advice and collaboration. I am very grateful to Yan Huang, Min Xu, Qiusheng Wu, Bo Yang and Song Shu for their help and support. I would also like to acknowledge Zuoqi Chen, Bin Wu,

Yang Liu, Shengan Zhan, Wenbin Sun, Zhaoxia Ye and Yan Liu, who previously worked with me in this group. Thank you all for the wonderful time we have spent together.

I gratefully acknowledge the funding sources that supported my Ph.D. pursuit. I was funded by the Department of Geography, and was honored to receive the Graduate School Dean’s

Fellowship. My work was also supported by the National Aeronautics and Space Administration.

Last but not least, I am deeply thankful to my family for all your love, encouragement and sacrifice. I dedicate this dissertation to the memory of my father, whose role in my life was and remains immense. Words cannot express how grateful I am to my parents-in-law and mother for the sacrifices that you’ve made to come to United States to look after me and my daughter. To my beloved daughter Shannon Xiadi Li, thank you for coming to this world and being my little precious. The last word of acknowledgement I have saved for my loving, supportive, encouraging and patient husband Jingfei Li, whose faithful support in the past six years means so much to me and is so appreciated. Thank you.

Shujie Wang

University of Cincinnati

March 2018

CONTENTS

ABSTRACT ...... i ACKNOWLEDGMENTS ...... iv CONTENTS ...... vi LIST OF FIGURES ...... viii LIST OF TABLES ...... xiv Chapter 1: Introduction ...... 1 Chapter 2: Revealing the early ice flow patterns with historical Declassified Intelligence Satellite Photographs ...... 7 2.1 Introduction ...... 7 2.2 Data Sets ...... 10 2.2.1 Declassified ARGON Photographs ...... 10 2.2.2 WorldView Imagery ...... 11 2.2.3 Other Data...... 11 2.3 ARGON Image Orthorectification ...... 12 2.3.1 Interior Orientation ...... 12 2.3.2 Exterior Orientation ...... 14 2.3.3 Orthorectification Results and Geolocation Accuracy Assessment ...... 16 2.4 Historical Ice Velocity Fields Over Larsen Ice Shelf ...... 20 2.4.1 Ice Velocity Derivation Results ...... 21 2.4.2 Ice Flow Pattern During the Baseline Period of 1963–1979 ...... 23 2.4.3 Ice Velocity Comparison Between Different Time Periods ...... 24 2.5 Discussion ...... 25 2.6 Conclusions ...... 27 Chapter 3: Half-century ice velocity records reveal the instability development of Larsen Ice Shelf ...... 28 3.1 Main Text ...... 28 3.2 Methods ...... 40 3.3 Supplementary Information ...... 42 3.3.1 Data Description ...... 42 3.3.2 Data processing...... 44

3.3.3 Ice velocity derivation and accuracy assessment ...... 46 3.3.4 Numerical modeling of ice shelf flow ...... 48 3.3.5 Supplementary Tables ...... 53 3.3.6 Supplementary Figures ...... 54 Chapter 4: Investigation of the multidecadal changes of the Larsen B outlet glaciers by integrating multi-source satellite and airborne remote sensing data ...... 64 4.1 Introduction ...... 64 4.2 Study Area ...... 67 4.3 Data and Methods ...... 68 4.3.1 Mapping glacier fronts and surface velocity fields from multitemporal satellite images ...... 68 4.3.2 Detecting surface topographic changes from satellite laser altimetry and airborne LiDAR measurements ...... 74 4.4 Results ...... 79 4.4.1 Glacier front retreat and advance patterns from time-series satellite images ...... 79 4.4.2 Temporal changes of glacier velocity fields from image matching method ...... 81 4.4.3 Temporal evolution of glacier topography from satellite laser altimetry and airborne LiDAR ...... 87 4.5 Discussion ...... 92 4.6 Conclusions ...... 99 BIBLIOGRAPHY ...... 101

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LIST OF FIGURES

Figure 2.1. The Larsen Ice Shelf. The background image is the pan-sharpened red band image of the Landsat Image Mosaic of Antarctica (LIMA) (Bindschadler et al. 2008a). The grounding line is from the MEaSUREs Antarctic Grounding Line (Rignot et al. 2011a). The two dash lines show the partial coastlines of Larsen Ice Shelf in August 1963 and December 2002, respectively. The projection is polar stereographic projection with reference to WGS-84 ellipsoid...... 10

Figure 2.2. Two Landsat-3 MSS scenes (near infrared band) acquired in 1979 ...... 12

Figure 2.3. The arbitrary and translated coordinates of the fiducial marks and estimated principal point for the frame “DS09058A014MC115” acquired in 1963...... 14

Figure 2.4. (a) The ARGON and WorldView image coverage and locations of GCPs and checkpoints on the Landsat Image Mosaic of Antarctica (LIMA). (b and c) The original ARGON photographs and locations of TPs...... 16

Figure 2.5. Orthorectified ARGON KH-5 images ...... 18

Figure 3.1 | Larsen Ice Shelf. a, The geographic setting of Larsen Ice Shelf, the division of flow units (A1 – A4, B1 – B8, C1 – C5, and D1 – D8) and the ice velocity map for the period 2000-

2001. b, The ice front positions of Larsen Ice Shelf and the ice velocity map for the period 2013-

2015...... 31

Figure 3.2 | Time-series velocity profiles along flow direction of nine flow units. Drygalski (A4) flow unit, located at the southern Larsen A, was disintegrated in 1995. Hektoria/Green/Evans (B1),

Jorum/Punchbowl (B3) and Crane (B5) flow units were disintegrated in 2002. Flask (B7) and

Leppard (B8) flow units are part of the southern remnant at SCAR Inlet. Whirlwind Inlet (C3)

viii

flow unit is located at the central Larsen C, and Mobiloil Inlet (C5) flow unit is located at the southern Larsen C. A rapidly propagating rift was developed at the downstream area of C5 and led to the recent major calving on Larsen C in July 2017. The dash lines in graphs a, b, c, d, e and f show the ice front positions in different years...... 32

Figure 3.3 | Inverted ice rigidity and inferred backstress loss of Larsen B. a, Ice rigidity during

1986-1988. b, Ice rigidity during 2000-2001. c, Backstress loss from the period 1986-1988 to the period 2000-2001. The ice rigidity has a high value for ‘stiff’ ice and a low value for ‘soft’ ice.

The weakened rheology bands correspond well to the shear zones that are more easily deformed than those stiffer ice flows from the colder tributary glaciers. The ice rigidity was weakened at the upstream of the collapsed part during 2000-2001...... 34

Figure 3.4 | Numerical modeling results for Larsen C. Graphs a, b, c and d show the inverted ice rigidity and inferred backstress and principal stress fields using the 2013-2015 velocity measurements. Graphs e, f, g and h show the modeled ice velocity fields, backstress and principal stress fields with the new ice front condition following the major calving in July 2017...... 40

Supplementary Figure 3.1 | Time-series ice velocity maps and front positions of Larsen Ice Shelf

(selected time periods). a, Ice velocity maps and front positions of Larsen A and Larsen B from

1979 to 1993. b, Ice velocity maps and front positions of Larsen B from 1993 to 2001. c, Ice velocity maps and front positions of the southern remnant of Larsen B from 2001 to 2014. d, Ice velocity maps and front positions of Larsen C from 1963 to 2015. e, Ice velocity maps and front positions of northern Larsen D from 1992 to 2015. The black dash line in the first graph of each subsection shows the locations of the plotted longitudinal velocity profiles shown in Fig. 2...... 55

Supplementary Figure 3.2 | The ice front changes of Larsen A and Larsen B from August 1963 to December 2014. The bed topography of the grounded glaciers is from the BEDMAP2 (Fretwell

et al. 2013) dataset. The background image is a Landsat TM image acquired on March 1, 1986.

The background image is a Landsat TM image acquired on March 1, 1986. The ice front positions were delineated from the orthorectified satellite images. The retreat of Larsen A began before the

1980s, and the recession rate increased since the late 1980s. The ice front of Larsen A between

Sobral Peninsula and Seal Nunataks progressively retreated in the early 1990s. Larsen B had been advancing until large calving events occurred in 1995 and 1998/1999 (Rott et al. 2002). In the austral summer of 2002, most of Larsen B, fed by Hektoria, Green, Evans, Punchbowl, Jorum and

Crane Glaciers, disintegrated. Two major remnants remain in the north around Seal Nunataks and in the south at SCAR Inlet. The northern remnant is almost stagnant (Rott et al. 1996), while the retreat of the southern remnant fed by Flask and Leppard Glaciers is still on-going (Shuman et al.

2011)...... 56

Supplementary Figure 3.3 | Transverse velocity profiles of the transects T1 (a), T2 (b), T3 (c) and T4 (d) on the collapsed part of Larsen B. The black dash lines in graphs a, b, c and d represent the boundaries between different flow units. The three major lateral shear zones are defined by the shear margins between the B1 unit and the northern Seal Nunataks area, the area upstream of B2 unit at Foyn Point and the area upstream of B6 unit at Disappointment Cape...... 58

Supplementary Figure 3.4 | Lateral shear strain rates and principal stress fields of Larsen B during

1986-1988 (a, b, c) and 2000-2001 (d, e, f). Graphs a and d show the high lateral shear strain rates at suture zones and rifted areas, and the increased magnitude in lateral shearing from the period

1986-1988 to the period 2000-2001. In b and e, the negative values of second principal stress indicate compressive stress regime while the positive values indicate extensive stress regime. The transition boundary where the stress regime changes from the compressive state at the upstream reach to the extensive state at the downstream reach is defined as ‘compressive arch’ (thick black

solid line in b). The ice front after the major calving events in the 1990s passed the ‘compressive arch’. Graphs c and f show the dominant tensile first principal stresses. The frontal portion originally had the first principal stresses oriented perpendicular to the flow directions (Graph c).

After successive terminus retreats, the first principal stresses near the ice front were almost parallel to the flow directions, particularly in the central ice-shelf part (Graph f)...... 59

Supplementary Figure 3.5 | Larsen B suture zone weakening around Disappointment Cape (B6 flow unit). Graph a shows that the suture zone of unit B6 was the transition between the northern collapsed part and the southern remnant. The weakening of this region is illustrated by the satellite images in b, c, d, e and f. Graphs b and c show the formation of new fractures during 1979-1986, which were opened wider in 1988 (d). Graphs e and f show the enhanced fracturing at this zone immediately before the collapse...... 61

Supplementary Figure 3.6 | Comparison between observed and modeled flow velocity fields. a and b, Larsen B during 1986-1988. c and d, Larsen B during 2000-2001. e and f, Larsen C during

2013-2015. The ice velocity maps and scatterplots indicate a good agreement between observed and modeled flow velocities...... 62

Supplementary Figure 3.7 | Fracture development from the northern lateral shear margin of

Larsen B from March 1986 to January 1988. The background images are the near infrared bands of two Landsat TM satellite images acquired in 1986 and 1988. The blue dash line represents the new ice front after the terminus retreat in 1995, which corresponds well with the opened fracture.

...... 63

Figure 4.1. The geographic setting of the study area...... 68

Figure 4.2. The data processing flowchart for deriving the surface velocity measurements from two sequential satellite images...... 73

Figure 4.3. The spatial coverage of the satellite laser altimetry and airborne LiDAR data over the study area. a, The ICESat-1 data tracks during 2003-2009; b, The ATM data coverage from the

Pre-IceBridge and IceBridge missions during 2002-2011; c, The LVIS LiDAR data collected in

2009; and d, The LVIS LiDAR data collected in 2015...... 76

Figure 4.4. The terminus locations of the northern and central Larsen B outlet glaciers between

December 2002 and January 2017. The rectangles in the middle figure show the spatial extents of a (Hektoria, Green and Evans Glaciers), b (Jorum and Punchbowl Glaciers), c (Crane Glacier) and d (Mapple and Melville Glaciers). The central flow lines were used for calculating the retreat and advance distances and plotting the longitudinal profiles of surface velocity and elevation in Figure

4.6, 4.7 and 4.8. The glacier inlets are defined according to the grounding line and calving front positions, which are used as the reference positions to plot the longitudinal velocity and elevation profiles...... 80

Figure 4.5. Surface velocity maps of the Larsen B outlet glaciers and the southern remnant of the

Larsen B Ice Shelf (selected periods)...... 84

Figure 4.6. The longitudinal velocity profiles of the Hektoria, Green, Jorum and Crane Glaciers during 1986-2017...... 85

Figure 4.7. The longitudinal velocity profiles of the Flask and Leppard Glaciers and the corresponding downstream ice-shelf flow units over the period 2000-2017...... 87

Figure 4.8. The along-flow longitudinal surface elevation profiles from the ATM and LVIS

LiDAR data for the Hektoria, Green, Crane, Melville, Flask and Leppard Glaciers. The black-cross marks indicate the locations where the ICESat-1 cross-sections intersect with the along-flow profiles...... 91

xii

Figure 4.9. Transverse profiles from the ICESat-1 surface elevation measurements along the cross-sections of the Green, Evans, Crane, Melville, Flask and Leppard Glaciers. The LVIS data collected in 2009 and 2015 are also included for comparison. The locations of the cross-sections are shown in Figure 4.3...... 92

Figure 4.10. The surface elevation changes of the outlet glaciers between 2009 and 2015 derived from the LVIS elevation grids...... 92

Figure 4.11. Temporal evolution of surface flow velocity and elevation of the Hektoria and Crane

Glaciers...... 95

xiii

LIST OF TABLES

Table 2.1. Horizontal geolocation accuracy assessment of the orthorectified images ...... 19

Supplementary Table 3.1. The satellite images used for velocity derivation ...... 53

Supplementary Table 3.2. Image source, time separation and velocity measurement error ...... 53

Table 4.1. The Landsat and ASTER images used in this study ...... 69

Table 4.2. The Envisat ASAR and ALOS PALSAR images used in this study ...... 71

Table 4.3. Retreat and advance distances and rates of the Larsen B outlet glaciers. The retreat and advance distances were tracked using the time-series images available for each individual glacier.

The rates (m/d) were calculated by dividing the retreat and advance distances (m) of the terminus by the time separation (days) of sequential images. The negative numbers with a gray background indicate glacier retreats...... 81

xiv

Chapter 1: Introduction

Climate change and sea level are intricately linked to the dynamics and mass balance of the polar ice sheets (Shepherd and Wingham 2007). The Greenland and Antarctic ice sheets hold over 99% of fresh water on Earth. Were these two ice sheets to melt completely, the global sea level would rise by more than 70 meters (Alley et al. 2005). Recent studies have shown that the Greenland and

Antarctic ice sheets have contributed to the sea level rise via increased melting and accelerated ice outflux of outlet glaciers and ice streams (Rignot et al. 2011c). Outlet glaciers and ice streams transport ice from the interior ice sheet towards the coastal margins and then discharge ice into the ocean systems. Ice velocity fields of the outlet glaciers and ice streams are essential measurements for quantifying the ice discharge rate and evaluating the mass balance state of an ice sheet (Howat et al. 2007; Rignot and Kanagaratnam 2006; Rignot and Thomas 2002; Thomas et al. 2004). An understanding of the long-term dynamic behavior of the outlet glaciers and ice streams is critical for predicting the future changes of mass balance of the ice sheet and its contribution to sea level.

Over the Antarctic Ice Sheet, the stability of ice shelves affects the flow dynamics and ice discharge of the upstream outlet glaciers (Depoorter et al. 2013; Rignot et al. 2013a). Ice shelves float on the ocean while remaining attached to the grounded ice, which fringe ~75% of the

Antarctica’s coastline. They separate the onshore glaciers from the ocean and regulate their contribution to sea level (Dupont and Alley 2005). Recent ice-shelf disintegrations and thinning trends have revealed their susceptibility to the atmospheric and oceanic changes in the context of climate warming. Although the direct effect of ice-shelf mass loss on sea level is trivial, ice shelves play significant roles in buttressing and stabilizing the grounded glaciers. The important role of ice shelves is emphasized by the rapid accelerations and thinning of the tributary glaciers in

response to the catastrophic collapses of ice shelves in the Antarctic Peninsula (Rignot et al. 2004;

Rott et al. 2002; Scambos 2004).

The Antarctic Peninsula is one of the most rapidly warming regions on Earth, with

3.7±1.6 °C (century)-1 warming rate according to the meteorological records (Vaughan et al. 2003).

The relatively low latitude and warm climate settings make this region particularly sensitive and susceptible to the atmospheric and oceanic conditions. The pronounced regional warming has been accompanied by the rapid shrinkage of peripheral ice shelves (Rott et al. 1996; Scambos et al.

2009; Scambos 2004) and the front retreat of marine glaciers (Cook et al. 2005). The most spectacular change is the catastrophic collapse of the Larsen B Ice Shelf in the austral summer of

2002. This ice shelf has been stable throughout the Holocene and its dramatic collapse is unprecedented over the last 10,000 years (Domack et al. 2005). In only 35 days, a total of approximately 3,250 square kilometers of shelf area was disintegrated into thousands of icebergs drifting in the Weddell Sea (Scambos et al. 2004). Prior to this, its neighboring Larsen A ice shelf was disintegrated in January 1995 with 1600 km2 area loss (Rott et al. 1996). The development of structural weaknesses on an ice shelf are related to its stress system and mechanical properties that essentially determine the ice-shelf flow patterns, while variations in flow velocities modulate the stress conditions. Examination of the spatiotemporal variability in flow velocities over a long period is fundamental for understanding the physical processes leading to ice-shelf instability and disintegration, yet the pre-collapse changes in flow patterns of ice shelves over multi-decadal timescales are still poorly known. The velocity measurements documented by previous studies for

Larsen Ice Shelf (Bindschadler et al. 1994; Rack et al. 1999; Rignot 2004; Skvarca et al. 1999;

Wang et al. 2016) were limited to specific ice-shelf areas or certain time periods.

The disintegrations of the Larsen A and Larsen B ice shelves caused radical flow speedups of their upstream tributary glaciers. Following the collapse of Larsen A, Drygalski Glacier accelerated threefold (Rott et al. 2002), and surges on several glaciers north of Drygalski Glacier were detected as well (De Angelis and Skvarca 2003). The collapse of Larsen B induced an eightfold acceleration of Hektoria, Green and Evans Glaciers, and a threefold acceleration of Jorum and

Crane Glaciers (Rignot et al. 2004). The consequent increase in ice discharge from grounded glaciers has directly contributed to the sea level rise (Berthier et al. 2012; Rott et al. 2007; Wuite et al. 2015). Monitoring long-term flow dynamics, elevation changes and terminus evolutions of the outlet glaciers is essential for better understanding and characterizing the dynamic behaviors of glaciers in response to ice-shelf changes. The flow dynamics of the outlet glaciers immediately following the ice-shelf collapse event have been intensively examined by applying either radar interferometry techniques or feature tracking method to repeat-pass optical and radar images

(Hulbe et al. 2008; Rignot et al. 2004; Rott et al. 2011; Scambos 2004). However, it is still uncertain whether these rapid changes represent long-term trends or transient variations.

Collecting in situ ice velocity measurements is extremely expensive and difficult, whereas remote sensing technologies provide powerful datasets for mapping ice motion over a large geographic area. This research aims to investigate the evolving dynamics and instability development of the Larsen Ice Shelf and to examine the outlet glacier responses to the ice-shelf collapse over decadal timescale, by combining numerical models of ice flow dynamics and a wide range of remote sensing technologies, including the earliest satellite surveillance programs, the multispectral optical remote sensing, the synthetic aperture radar remote sensing and the airborne/satellite altimetry missions.

Chapter 2 presents a new approach to orthorectifying the declassified intelligence satellite photographs over polar regions for mapping ice motion back to the 1960s. The reconnaissance

ARGON satellites collected the earliest images of Antarctica from space dating back to the 1960s, providing valuable historical baseline information for studying polar ice sheets. Those photographs are underutilized for ice motion mapping, due to lack of sufficient ground controls for image orthorectification. In this chapter, the ARGON photographs were orthorectified by fully exploiting the metric qualities of WorldView satellite images: very high spatial resolution and precise geolocation. Through a case study over Larsen Ice Shelf, it is demonstrated that the camera model with bundle block adjustment can achieve geolocation accuracy of better than the nominal resolution (140 m) for orthorectifying ARGON images, with WorldView imagery as ground control source. This enables to extend the ice velocity records of Larsen Ice Shelf back into

1960s~1970s for the first time. The retrospective analysis revealed that acceleration of the collapsed Larsen B occurred much earlier than previously thought.

Chapter 3 presents a comprehensive study to investigate the instability development of

Larsen Ice Shelf by reconstructing time-series velocity fields over the past half century. A numerical ice-shelf flow model was further implemented to examine the evolving ice rheology and stress fields. Based on the retrospective analyses of Larsen A and particularly Larsen B, a four- stage model was proposed to elucidate the physical processes leading to the disintegration of an ice shelf: 1) unstable condition initiation stage triggered by external forcings such as ocean-driven melting; 2) enhanced weakening stage caused by a positive feedback between flow acceleration and structural weakening; 3) destructing stage when radical and extensive acceleration occurs over the entire ice shelf; and 4) catastrophic disintegration stage when the ice shelf fragments rapidly.

The flow velocity is the key indicator for monitoring the instability development of an ice shelf,

and early warning of potential disintegration may be achieved by detecting dramatic acceleration across the whole ice shelf. The modeling analysis suggests that the July 2017 calving event on

Larsen C would not trigger the drastic acceleration as in the destructing stage of Larsen B and

Larsen A. Nevertheless, the localized acceleration and changed stress condition signal that Larsen

C has been in the unstable condition initiation stage. Larsen D had little flow velocity variability in the past decades and is currently stable.

Chapter 4 integrates multi-source remote sensing data acquired by different satellite and airborne missions during 1986-2017 to examine the evolving dynamics of the Larsen B outlet glaciers over a multidecadal timescale. We processed the Landsat and Terra ASTER optical images and the Envisat ASAR and ALOS PALSAR radar images to derive a long-term time series of surface velocity fields before and after the ice-shelf collapse by applying a semi-automated image matching method. The changes of glacier front during the fifteen years after the collapse were tracked from the sequential satellite images. Additionally, we integrated the multitemporal surface elevation measurements collected by the ICESat-1 laser altimetry system and the Pre-

IceBridge and IceBridge airborne LiDAR missions during 2002-2015 to analyze the temporal variations of surface topography. The results indicate that the major outlet glaciers that lost ice- shelf buttressing have experienced the post-collapse stages of acceleration and deceleration, and tend to become stable in recent years. The dramatic glacier speedups have caused the widespread dynamic thinning, with the surface lowering magnitude of hundreds of meters on the northern and central glaciers. The reduction in ice thickness and surface slope due to dynamic thinning has decreased the driving force and slowed down the ice flows. The negative feedback between the velocity increase and the decrease of thickness and slope resulted in the transition from acceleration to deceleration, and eventually to a new equilibrium phase. The time span for a glacier

to reach new equilibrium is potentially affected by the geometric configuration of the glacier outlet.

The flow accelerations of the central glaciers that flow into narrow and deep fjords halted earlier than those northern glaciers that flow into a wide embayment. The dynamics of the Larsen B outlet glaciers are primarily dominated by the stress perturbation effect due to the ice-shelf retreat and disintegration and the glacier terminus changes.

Chapter 2: Revealing the early ice flow patterns with historical

Declassified Intelligence Satellite Photographs

2.1 Introduction

Historical reconnaissance satellite photographs acquired by CORONA, ARGON, and

LANYARD missions (McDonald 1995), known as Declassified Intelligence Satellite Photography

(DISP), provide valuable information about the Earth surface during the early 1960s and 1970s.

Among the three missions, ARGON is the only program collecting frame photographs over

Antarctica between 1961 and 1964 (Bindschadler and Seider 1998). The ARGON photographs are the earliest spaceborne remote sensing images of Antarctica, extending the timeline back into the

1960s beyond the Landsat era. Each photograph provides a unique regional view over an extensive ground area. Some studies (Bindschadler and Vornberger 1998; Kim et al. 2001; Sohn et al. 1998;

Zhou et al. 2002) have utilized those photographs for qualitative analysis about the long-term changes of the Greenland and Antarctic ice sheets. However, little research has been reported on using those early images for quantitative analysis such as ice velocity derivation. Information about the past flow regime is important for understanding the dynamic processes leading to the radical changes of both terrestrial glaciers and floating ice shelves.

The Larsen Ice Shelf (Figure 2.1), spreading along the east coast of the Antarctic Peninsula, has undergone two catastrophic disintegration events in the rapid regional warming context

(Vaughan et al. 2003). The Larsen A disintegrated in January 1995 with 1600 km2 area loss (Rott et al. 1996). The Larsen B collapsed in February 2002 (Scambos 2004), with 3200 km2 area disintegrated as thousands of icebergs in only 35 days. The ice shelf disintegrations have triggered the immediate acceleration and thinning responses of the upstream glaciers (Rignot et al. 2004;

Rott et al. 2002; Scambos 2004). The knowledge of past flow patterns is important for understanding the evolution of flow dynamics and stability of the ice shelf system. Most of the ice velocity measurements over Larsen Ice Shelf are after the mid-1990s with the advent of interferometric synthetic aperture radar technique (Khazendar et al. 2015; Khazendar et al. 2011;

Rack et al. 2000; Rignot et al. 2004; Vieli et al. 2006). The ice velocity records are quite sparse prior to the 1990s and even less before the 1980s.

In the absence of field measurements, the feature tracking method (Bindschadler and

Scambos 1991; Lucchitta and Ferguson 1986) is the only feasible approach to calculating the ice velocity fields from time-sequence images for periods before the 1990s. Sequential images need to be rigorously coregistered in order to accurately derive ice velocity fields. Orthorectification is fundamentally important for quantitative analysis using the DISP images, since precise geographical locations of image pixels must be determined, and inherent geometric distortions need to be corrected. The ARGON missions used a KH-5 panchromatic frame camera to acquire vertical photography of the terrain. The wide field of view induced various geometric distortions, including Earth curvature effect, radial relief displacement, and film distortion. To precisely georeference an image, high-quality ground control points (GCPs) are required to determine the orientation parameters for establishing the relationship between raw arbitrary image coordinates and ground geographical coordinates. However, it has long been a challenge to acquire an adequate number of GCPs in the polar regions. Due to the remote location and hostile environment, it is logistically difficult to acquire GCPs using traditional surveying or Global Positioning System instruments in the field. Many glacial features cannot be selected as GCPs due to their motions over time. Some efforts have been made to develop ground control data sets for the Antarctic Ice

Sheet (Jezek 2008), yet their spatial coverage is quite limited and sparse.

The successful launch of IKONOS satellite in 1999 signaled the advent of the new era of very high resolution (VHR) satellite remote sensing. Since then, a series of new VHR satellite systems have been placed in orbit, routinely offering high-resolution images in both panchromatic and multispectral modes, besides significant swath width and frequent repeat cycle. The very high spatial resolutions make it possible to detect spatial details at the field scale, and stationary features can be visually recognized from the VHR images. More importantly, the attainable horizontal geopositioning accuracies of the newest VHR satellites, such as the WorldView series satellites, have been greatly improved, owing to the ultra-stable three-axis stabilized platform using high- precision attitude sensors and GPS onboard (Anderson and Marchisio 2012; Deilami and Hashim

2011). Without using GCPs, the geolocation accuracy is estimated to be 4 m circular error, 90% confidence (CE90) for WorldView-1 and 3.5 m CE90 for WorldView-2 (http://www. satimagingcorp.com/satellite-sensors/). The high-precision geolocation of the VHR satellite images enables us to derive the comparatively accurate geographical coordinates of recognizable stationary features for orthorectifying coarser resolution historical images.

In this study, we directly utilized the metric qualities of the VHR satellite images in very high spatial resolution and precise georeferencing to derive ground controls, without using any field-measured GCPs, for orthorectifying those ARGON satellite photographs. We demonstrated through the case study over Larsen Ice Shelf that the orthorectification accuracy of ARGON images is better than one nominal resolution cell (140 m), when the bundle block adjustment camera model is used with the GCPs derived from WorldView images. The adequate geolocation accuracy allowed us to derive the earliest ice velocity fields over Larsen Ice Shelf for retrospective analysis of its dynamic behavior.

2.2 Data Sets

2.2.1 Declassified ARGON Photographs

The ARGON missions were equipped with a panchromatic frame camera KH-5 using a

7.62 cm focal length to acquire the photography of the terrain. It was designed to capture vertical photographs with ~60% endlapping area, from the nominal orbit altitude of 322 km above Earth’s surface. The photograph size is 11.43 cm × 11.43 cm, corresponding to ground coverage of approximately 540 km × 540 km. The nominal photo scale is 1:4,250,000, and the nominal ground resolution is 140 m. Three missions (9034A, 9058A, and 9059A) successfully delivered the photographs for Antarctica. We used the photograph frames “DS09058A014MC115” and

“DS09058A014MC116,” which were acquired during the 9058A mission between 29 August and

1 September 1963.

2.2.2 WorldView Imagery

We used 11 WorldView-1 and 8WorldView-2 panchromatic images to derive GCPs. These images were acquired during 2009–2012, provided as Basic Imagery products by Polar Geospatial

Center at the University of Minnesota. The spatial resolution is 0.5m at nadir and 0.55m at 20° off-nadir for the WorldView-1 images and 0.46m at nadir and 0.52m at 20° off-nadir for the

WorldView-2 images. With the vendor-supplied rational polynomial coefficients (RPCs), the

WorldView images were orthorectified using the RPC model (Fraser and Hanley 2005; Tao and

Hu 2001) in PCI Geomatica OrthoEngine software.

2.2.3 Other Data

The Radarsat Antarctic Mapping Project (RAMP) digital elevation model (DEM) version

2 (Liu et al. 1999) was used for image orthorectification. This data set was constructed from a variety of topographical data and has a grid cell size of 200 m. Two Landsat-3 multispectral scanner (MSS) images (Figure 2.2) acquired in 1979 were used with the orthorectified ARGON images to derive the 1960s~1970s ice velocity fields. These two images cover the Larsen A and

Larsen B ice shelves and are the earliest available cloud-free Landsat scenes for this region.

Besides, four Landsat-4/5 thematic mapper (TM) images acquired in 1986 and 1988 were used to derive the 1970s~1980s ice velocity fields.

Figure 2.2. Two Landsat-3 MSS scenes (near infrared band) acquired in 1979

2.3 ARGON Image Orthorectification

The ARGON satellites used a frame camera, and the camera model used in aerial photogrammetry is equally valid to ARGON photographs. The geometric relationship between the camera, image, and ground coordinate systems is based on the photogrammetric collinearity principle (Kraus 1993). The key is to determine the interior and exterior orientation parameters.

2.3.1 Interior Orientation

Interior orientation describes the transformation from image pixel coordinates to image space coordinates, defined by focal length, principal point, fiducial marks, and lens distortion parameters. To perform interior orientation, the principal point location was assumed to coincide with the fiducial center located in the intersection of the lines connecting opposing fiducial marks.

The fiducial marks are located in the middle of the four sides and can be visually identified on the scanned image. The coordinates of the fiducial marks and principal point were measured in arbitrary image coordinate system whose origin is at bottom left corner of each image. The fiducial coordinates were then computed by translating the origin to the principal point. Figure 2.3 shows the calculation results for the frame DS09058A014MC115. With the known fiducial mark coordinates, the image space coordinates of each pixel on the photographs can be computed using affine transformation.

For frame photographs, lens distortion could cause positional errors of the image space coordinates of a given point due to the bending of light rays passing through the lens. Radial lens distortion can be approximated by a polynomial function if the coefficients are provided in the camera calibration report. Unfortunately, the lens distortion parameters for the ARGON KH-5 camera are unknown due to the missing of camera calibration data. However, the impact of lens distortion on ARGON image orientation is considered minimal or negligible according to the relevant declassified documents. The document ‘TECHNICAL EXPLANATION OF PROJECT

ARGON Orbital and Camera Requirements and Data Reduction Procedure’ (Ref: 2 C 0037) archived in the National Reconnaissance Office (NRO) records the distortion (radial & tangential) specification for the KH-5 camera is 0-6 microns. According to the NRO-declassified document

‘HEXAGON (KH-9) MAPPING CAMERA PROGRAM AND EVOLUTION’ and other related records, the KH-5 camera used the Baker-Developed lens Geocon. In the patent documents about the wide angle photogrammetric lens systems Geocon, Baker pointed out that the expected distortion residuals of 3-inch focal length lens did not exceed 5 microns anywhere in the field. The

ARGON KH-5 images have nominal ground resolution of 140 m, corresponding to ~33 microns on the photograph. The positional error induced by lens distortion is expected to be negligible. In

addition, the primary distortion component, the radial lens distortion, increases radially from the principal point to the four corners of the photograph. Most of our focused study area is located at the center of the photographs, and therefore, the influence of lens distortion is considered minimal.

Figure 2.3. The arbitrary and translated coordinates of the fiducial marks and estimated principal

point for the frame “DS09058A014MC115” acquired in 1963.

2.3.2 Exterior Orientation

The accurate determination of exterior orientation requires high-quality GCPs. A single- frame image involves six exterior orientation parameters, and a minimum of three GCPs is required. Two overlapping images allow for the bundle block adjustment, which combines a

limited number of GCPs with tie points (TPs) to refine the exterior orientation parameters for each of two images simultaneously. The TPs, the common features that appear on both images, are complementary to GCPs in solving the exterior parameters. Least squares adjustment method is generally used in bundle block adjustment to estimate the unknowns of the collinearity equations based on the input GCPs and TPs (Kraus 1993; Toutin 2003). The unknowns include six exterior orientation parameters of each image and ground coordinates of the TPs.

The WorldView images contain fine spatial details and rich image texture, which enable visual recognition of stationary features as candidate GCPs. The stationary features include rock outcrops, nunataks, ice rises, peaks of mountains and hills, etc. As the positioning accuracy of

WorldView images is influenced by the off-nadir viewing angles (Aguilar et al. 2013; Åstrand et al. 2012; Wang and Gruen 2012), we gave priority to the images acquired with smaller off-nadir angles. The stationary features in the low-relief regions were preferred, since their geolocations are more accurate on the WorldView images, and the accuracy of their vertical coordinates is less affected by the horizontal and vertical resolutions of DEM. We identified 44 candidate GCPs in total (Figure 2.4). Most of them are located near fjords, where grounded ice drains into ice shelf.

Even though the distribution of the selected GCPs is limited by the spatial coverage of the available cloud-free WorldView images, the radially distributed GCPs from principal point toward image corners are adequate for correcting the displacement distortions associated with the central perspective projection of the frame camera.

The geographical coordinates of those candidate GCPs were extracted from the rectified

WorldView images. Among them, 10 GCPs were used for the frame DS09058A014MC115 and 8

GCPs for DS09058A014MC116, and 30 GCPs were reserved as independent checkpoints for accuracy assessment. To perform bundle block adjustment, 12 TPs were selected (Figure 2.4). In

this bundled block, 14 GCPs (4 in common) and 12 TPs contribute 84 observation equations in total (36 from GCPs and 48 from TPs), with 48 unknowns including 12 exterior orientation parameters of two images and 36 ground coordinates (x, y, and z) of TPs. The degrees of freedom for this bundled solution is 36. Our experiments indicate that the accuracy does not significantly increase, with more GCP input to the model.

Figure 2.4. (a) The ARGON and WorldView image coverage and locations of GCPs and checkpoints on the Landsat Image Mosaic of Antarctica (LIMA). (b and c) The original ARGON

photographs and locations of TPs.

2.3.3 Orthorectification Results and Geolocation Accuracy Assessment

The geometric distortions caused by Earth curvature and relief displacement were also corrected. As the frame photographs captured by ARGON camera system have quite large ground coverage, the geometric distortion caused by Earth curvature effect needs to be addressed. The Earth curvature effect can be calculated by equation (1) (Moffitt and Mikhail 1980)

rH3 r 2 2Rf (1)

ae(1) 2 R  3 222 (1sin)e (2)

ab22 e  2 a (3) where r is the inward radial displacement to be corrected due to Earth curvature, r is the radial distance from the principal point, H is the flying altitude, R is the Earth radius, f is the camera focal length. a is the semi-major axis of the ellipsoid, b is the semi-minor axis of the ellipsoid,

 is the mean latitude. For our study area, the Earth radius was estimated to be 6,378,207.8 meters using the equation (2), with reference to the WGS-84 ellipsoid. Given the orbital altitude of

3 322 km, approximately equals to 4.35 r based on equation (1). On a 4.5-inch photograph, the displacement caused by Earth curvature at the corner points is about 2295 microns, corresponding to the ground distance of 9.8 km.

The relief displacement can be corrected using a digital elevation model (Moffitt and

Mikhail 1980) :

rh r ' H (4)

where r ' is the outward radial displacement due to topography, is the radial distance from the principal point, h is the topographic height, and is the flying altitude.

The ARGON images were orthorectified in the polar stereographic projection with reference to World Geodetic System 84 ellipsoid, and the image pixels were resampled to 60m

(Figure 2.5). The root-mean square error (RMSE) of GCPs was estimated to be 70.8m in x direction, 59.1m in y direction, and 92.2m in total. This RMSE is calculated based on the residuals between the estimated geographical coordinates and the extracted WorldView geographical coordinates. The polynomial transformation method (De Leeuw et al. 1988) and thin plate spline method (Bookstein 1989) have also been evaluated to georeference the frame

DS09058A014MC115 for comparison purpose. Both methods fit the empirical equations to warp the raw image to match the ground coordinates of GCPs, without retrieving the camera orientation parameters.

Figure 2.5. Orthorectified ARGON KH-5 images

The geolocation accuracy of the orthorectified ARGON images was evaluated in two ways.

First, we estimated the residual errors for the 30 independent checkpoints retrieved from the

WorldView images. The overall RMSE is 98.8m (73.6m in x and 66.0m in y) for the bundle block adjustment camera model, which is smaller than the nominal resolution of 140 m. The WorldView images and the checkpoints are mainly distributed over the outlet glaciers and the ice-shelf upstream (Figure 2.4). To further validate the geolocation accuracy, we evaluated the consistency

between the orthorectified ARGON images and the Landsat Image Mosaic of Antarctica (LIMA)

(Bindschadler et al. 2008b). The LIMA was generated from the orthorectified Landsat-7 Enhanced

Thematic Mapper+ scenes acquired during 1999–2003, with geolocation accuracy of 54m

(Bindschadler et al. 2008b; Lee et al. 2004). We identified 25 checkpoints over the motionless regions on the ice shelves from the LIMA, including the promontories, islands, and nunataks between Larsen A and Larsen B ice shelves. The RMSE between the orthorectified ARGON images and the LIMA is 114.8m (85.8m in x and 76.3m in y), less than the nominal resolution

(140 m) as well. The geolocation accuracies of the polynomial transformation and thin plate spline methods were evaluated with the same checkpoints from the WorldView images and the LIMA.

Table 2.1 summarizes the error statistics for the accuracy assessment. The second-order polynomial transformation method has overall RMSE of 214.7 m (146.7 m in X, 156.7 m in Y), and of 539.8 m (289.2 m in X, 455.7 m in Y) comparing with the WorldView images and the

LIMA, respectively. The thin plate spline method has overall RMSE of 133.2 m (112.3 m in X,

71.6 m in Y), and of 225.3 m (115.2 m in X, 193.4 m in Y), respectively. Although the thin plate spline method has better performance than the polynomial transformation method, the RMSEs of both methods are significantly larger than that of the camera model. This indicates that these two empirical methods are not adequate in correcting geometric distortions in ARGON images, and the rigorous camera model with bundle block adjustment is the most suitable with a set of high- quality GCPs derived from the WorldView imagery.

Table 2.1. Horizontal geolocation accuracy assessment of the orthorectified images

CPs from WorldView CPs from LIMA Overall x y Overall x y

Rigorous camera model 98.8 73.6 66.0 114.8 85.8 76.3

Polynomial transformation 214.7 146.7 156.7 539.8 289.2 455.7 Thin plate spline 133.2 112.3 71.6 225.3 115.2 193.4

The orthorectification accuracy of ARGON images is affected by the quality of GCPs and

DEM. The precise georeferencing of WorldView images ensures the horizontal accuracy of GCPs.

To minimize the influence of DEM quality on the vertical accuracy of GCPs, the GCPs were selected near the low-relief ground surface. The accuracy assessment through the checkpoints from

LIMA indicates that the model has achieved satisfactory accuracy over the ice shelf. The topographical source of RAMP DEM v2 over the ice shelf is the ERS-1 radar altimetry data acquired during the 1990s, with vertical accuracy of ±1m (Liu et al. 1999). From the relief displacement equation (equation (4)), 1mvertical error of the DEM may cause ground positional error of ~1.1m on the photograph corner, which is negligible given the nominal resolution of 140m for the ARGON photographs.

2.4 Historical Ice Velocity Fields Over Larsen Ice Shelf

The Larsen Ice Shelf consists of four sections from north to south, referred to as Larsen A,

B, C, and D ice shelves, respectively, and nourished by numerous outlet glaciers draining from the glaciated mountain chain. We focus on the early ice flow patterns of Larsen A and B ice shelves that had undergone dramatic retreats and catastrophic collapses in recent decades. The Larsen A was the smallest section, previously extending from Cape Longing to Robertson Island. The Larsen

B was located between Robertson Island and Jason Peninsula. The northernmost part of Larsen B that merged with Larsen A around Seal Nunataks is almost stagnant (Rott et al. 1996). The northern regions of Larsen B, fed by Hektoria/Green/Evans Glaciers and Jorum/Punchbowl/Crane Glaciers, were disintegrated completely in the summer of 2002 following the large calving events in 1995

and 1998 (Rott et al. 2002). The southern regions of Larsen B fed by Flask and Leppard Glaciers were partially remained as a remnant. The ARGON images provide critical information about the

Larsen Ice Shelf during the early 1960s. Using the orthorectified ARGON images as baseline, we are able to derive ice velocity time series prior to the 1990s in conjunction with the early Landsat images. The retrospective analysis of ice flow dynamics enables us to gain some insights into its changes prior to the disintegration events.

2.4.1 Ice Velocity Derivation Results

We used the feature tracking method to derive the ice velocity fields from ARGON and

Landsat images. This method searches the match points from two sequential images acquired at different times, measures their displacements, and then calculates corresponding flow velocities.

This technique has been widely used and proven effective (Debella-Gilo and Kääb 2011; Heid and

Kääb 2012; Pritchard and Vaughan 2007; Rack et al. 1999; Scambos et al. 1992). The cross- correlation image-matching algorithm can automate the feature tracking process and achieve subpixel-level accuracy in measuring spatial displacements (Scambos et al. 1992). To ensure the image matching accuracy and reliability, several preprocessing procedures were performed, including image co-registration, noise filtering and image enhancement. The two Landsat MSS images were co-registered to the orthorectified ARGON images, and the overall RMSE of the co- registration was estimated to be 54.1 m. An adaptive Wiener filter (Jin et al. 2003) with a 5×5 window was applied to the ARGON images to reduce the film grain noise (Zhou and Jezek 2002).

The Landsat-4/5 TM images acquired in 1986 and 1988 have spatial resolution of 30 m, and have been also co-registered. To enhance the image contrast, we used a water mask to remove the ocean part on the images, and segmented the image pairs into multiple pieces. For each segmented image pair, we enhanced the image contrast by stretching the histogram. This localized image stretching

can highlight the edge features of the low-contrast ice surface features. We performed image matching procedure for each segmented image pair. The spatial consistency in flow velocity and direction was checked for quality control, and spurious matches have been removed. The successfully matched points correspond to persistent crevasses, open rifts, and flow band features.

Figure 2.6 shows the derived ice velocity fields for Larsen A and Larsen B ice shelves during different time periods, including 1963–1979 (Figure 2.6a), 1979–1986 (Figure 2.6b), and

1986–1988 (Figure 2.6c). The 1963–1979 and 1979–1986 velocity fields do not completely cover the Larsen B downstream area, because of the limited coverage of the 1979 Landsat images. The derived velocities represent the average flow speed during each time period. The velocity grids shown in Figure 2.6 were generated by interpolating the valid velocity measurements from the feature tracking after filtering the erroneous match points. To examine the temporal variations of ice flows, we plot the longitudinal velocity profiles of different time periods (Figure 2.6d) along the Crane Glacier flow unit located at the central Larsen B. On each profile, the velocity values were calculated at the sampling distance of 1 km by averaging the valid velocity measurements within each distance interval. For comparison, Figure 2.6d also includes the in-situ differential

GPS-based velocities at the stakes measured by the Instituto Antártico Argentino Glaciology

Division (Rack et al. 2000; Skvarca et al. 2004; Skvarca et al. 1999) for the periods of 1996–1997,

1997–1999, and 1999–2001.

2.4.2 Ice Flow Pattern During the Baseline Period of 1963–1979

Figure 2.6a shows the ice velocity fields derived from the ARGON and Landsat MSS images for the baseline period of 1963–1979. The time separation between the sequential images is ~15 years. The error budget for measuring spatial displacements includes image-matching errors

(subpixel level of 30 m) and image coregistration errors (one-pixel level of 60 m). The uncertainty in measuring velocities is estimated to be ~6 m/yr.

The derived velocity field for Larsen A covers two regions: the ice-shelf upstream fed by

Drygalski Glacier (229 ± 3 m/yr) and the northern ice-shelf front (251 ± 9 m/yr). The 1963–1979 velocity field for Larsen B has better spatial coverage owing to the presence of more trackable features. At the upstream of northern regions, the average velocity was 278 ± 12 m/yr for the flow unit fed by Hektoria/Green/Evans Glaciers and 319 ± 19 m/yr for the flow unit fed by

Jorum/Punchbowl/Crane Glaciers. In comparison, the southern regions flowed slower than the northern regions. The average velocity was 213 ± 27 m/yr at the upstream of the “suture zone”

(Glasser and Scambos 2008b) around the Disappointment Cape and 215 ± 12 m/yr at the upstream of the flow unit fed by Flask and Leppard Glaciers. The fastest ice flow over Larsen B during

1963–1979 was approximately at its central part fed by Jorum/Punchbowl/Crane Glaciers.

2.4.3 Ice Velocity Comparison Between Different Time Periods

For Larsen A, the comparison between the periods of 1963–1979 and 1979–1986 shows no significant velocity changes at the upstream of the flow unit fed by Drygalski Glacier and a slight velocity increase at the northern ice-shelf front from 251 m/yr to 275 m/yr. Bindschadler et al. (1994) estimated the velocity of 220 m/yr (1975–1986) for the upstream of Drygalski Glacier flow unit from Kosmos and Landsat images, which is close to our derived baseline velocity of 229

± 3 m/yr (1963–1979). This suggests the stable flow regime in this region during 1963–1986. By comparing Figure 2.6b with Figure 2.6c, it is quite clear that flow acceleration occurred at the

upstream of Drygalski Glacier flow unit from 1979–1986 to 1986–1988, while the acceleration magnitude decreased rapidly along the flow direction toward downstream. This flow pattern was likely attributed to the lateral drag from shear margin of the near-stagnant Seal Nunataks and the backstress from Lindenberg Island (Rack et al. 1999; Rott et al. 1998). The flow velocity of the northern ice front near Sobral Peninsula increased by 11.5% from 1979–1986 to 1986–1988, comparable to the 15% velocity increase from 1975–1986 to 1986–1989 reported by Bindschadler et al. (1994). The northernmost part in Larsen Inlet had considerable velocity increase (by 34.8%) between these two periods, accompanied by the front retreat of Larsen A between 1979 and 1988

(Figure 2.6).

For Larsen B, we have derived an additional ice velocity field during 1963–1986 using the

ARGON image and Landsat TM image, which covers the entire downstream area of Larsen B.

The velocity at the ice front was ~400 m/yr during 1963–1986 and ~490 m/yr during 1986–1988

(increased by ~21%). Figure 2.6d includes the 1963–1986 velocity profile of the Crane Glacier flow unit. The velocity profiles clearly indicate that the Crane Glacier flow unit at the central

Larsen B had a velocity increase at the upstream from 1963–1979 to 1979–1986, and a more significant velocity increase occurred from 1979–1986 to 1986–1988. By comparing the entire longitudinal velocity profiles between the periods of 1963–1986 and 1986–1988, it is evident that widespread accelerations occurred throughout the upstream and downstream, with an average velocity increase of 45.6 m/yr (by ~14.7%).

2.5 Discussion

The radical retreat of ice shelves in the Antarctic Peninsula has been linked to the rapid regional warming since the 1950s (King 1994; Vaughan et al. 2003). Precollapse flow dynamics provide an important clue to investigate the physical mechanisms leading to the ice-shelf

instability. Previous studies (Rignot 2004; Skvarca et al. 2004) reported the ice flow speedups on

Larsen B during the late 1990s, immediately before the collapse in 2002. However, little research has been conducted on the dynamic behavior of Larsen B prior to the 1990s due to the difficulty in reconstructing earlier ice velocity records. Our retrospective analysis above reveals that the flow accelerations of the collapsed Larsen B initiated well before the 1990s, much earlier than previously thought.

Many factors could induce the ice-shelf flow accelerations, including the boundary condition change, tributary glacier speedups, ice-shelf thickness change, and ice rheological property change (Vieli et al. 2007). The boundary conditions involve the geometries and locations of ice front, lateral shear margins, and ice rises. Satellite data showed that the Larsen B had been gradually advancing since 1963 until January 1995 when a large tabular iceberg (~1700 km2) calved off (Cook and Vaughan 2010; Survey and Ferrigno 2008). The accelerations from the 1980s to the 1990s may associate with this calving event which reduced the constraining effect on the upstream ice flows. However, the detected accelerations of Larsen B between the 1960s~1970s and the 1980s cannot be explained by ice front retreat. During 1963–1988, the Larsen B ice front advanced by ~10 km. Shepherd et al. (2003) observed the progressive thinning of Larsen B from

1992 to 2001. Although the thickness changes during the 1960s~1980s are unknown for Larsen B, the perturbation experiments by Vieli et al. (2007) indicated that the Larsen B flow dynamics were insensitive to its thickness variations. Previous studies (Khazendar et al. 2007; Vieli et al. 2007) suggested that ice rheology may play the critical role in affecting the Larsen B flow dynamics. The ice rheology could be changed through ice softening by warming and mechanical weakening due to rift opening, enhanced shearing, or basal fracturing. Ice weakening could be further enhanced by increased surface melting by atmospheric warming, melting water percolating through ice

crevasses, and reduced basal marine ice by oceanic forcing. It needs more rigorous simulation studies with the time series velocity data before the 1990s to determine the predominant processes causing the detected acceleration pattern.

2.6 Conclusions

This research has demonstrated that the VHR satellite images are well suited to support orthorectification of moderate resolution historical DISP images over polar regions owing to the high spatial resolution and precise geolocation. The exploitation of the VHR satellite imagery as the potential ground control source would greatly promote the widespread use of the DISP data as the baseline in various polar environmental studies. Our case study shows that with the WorldView images as ground control source, the camera model with bundle block adjustment can achieve subpixel level (better than 140 m) accuracy for orthorectifying ARGON images.

Using the orthorectified ARGON images and Landsat images, we mapped the ice velocity fields of Larsen Ice Shelf during 1963–1979 for the first time. This represents the earliest view of ice flow pattern over the Larsen Ice Shelf and provides important baseline information to understand its flow regime dynamics with reference to more recent velocity measurements. With the derived baseline velocity during 1963–1979 and multitemporal velocity fields during 1980s, we concluded that the flow acceleration of the collapsed Larsen B occurred much earlier than previously thought. The initiation of the flow acceleration of Larsen B might be attributed to the changes of ice rheology properties. A better understanding of the predominant processes causing the Larsen B flow accelerations needs further investigations.

Chapter 3: Half-century ice velocity records reveal the instability

development of Larsen Ice Shelf

The Antarctic ice shelves restrain and stabilize the ice discharge from the grounded ice sheet into the ocean system (Dupont 2005; Pritchard et al. 2012). Recent ice-shelf disintegrations

(Braun and Humbert 2009; Rott et al. 1996; Scambos 2004) on the Antarctic Peninsula reveal the vulnerability of ice shelves to atmospheric and oceanic changes (Vaughan et al. 2003). The catastrophic collapses of the northern Larsen Ice Shelf triggered immediate acceleration and thinning of the upstream glaciers (Rignot 2004; Scambos 2004). Such rapid responses highlight the importance of understanding the underlying mechanism responsible for disintegration (Doake et al. 1998; MacAyeal et al. 2003; Shepherd et al. 2003) and assessing the stability of other ice shelves (Jansen et al. 2010; Khazendar et al. 2015). Here we reconstruct time-series velocity fields for Larsen Ice Shelf over the past half century to investigate the instability development process, and implement an ice-shelf flow model to examine the stress conditions. The retrospective analyses of Larsen A and Larsen B reveal four development stages leading to disintegration: unstable condition initiation stage, enhanced weakening stage, destructing stage and catastrophic disintegration stage. Radical and extensive acceleration may signal the destructing stage and portend subsequent disintegration. Numerical modeling suggests that the July 2017 calving event on Larsen C would not trigger drastic acceleration as in the destructing stage of Larsen A and

Larsen B. Nevertheless, the localized accelerations and the changed stress condition suggest that

Larsen C has been in the unstable condition initiation stage.

3.1 Main Text

The Larsen Ice Shelf, extending along the east coast of the Antarctic Peninsula, was

formerly composed of Larsen A, B, C and D from north to south (Figure 3.1). The Larsen A disintegrated in 1995, and the Larsen B collapsed in 2002 with a Rhode Island-sized area broke into thousands of icebergs. The Larsen C experienced major calving events in 1986 and 2005

(Cook and Vaughan 2010), and recently, a giant iceberg twice the size of Luxembourg calved off

Larsen C on July 11, 2017. The Larsen D had advanced in the past decades (Cook and Vaughan

2010). The radical disintegrations of Larsen A and Larsen B have been attributed to the atmospheric warming effect (Scambos et al. 2003; Scambos et al. 2000). Meteorological records indicate a rapid regional warming on the Antarctic Peninsula since the 1950s (Vaughan et al.

2003). High air temperatures and intense surface melting (van den Broeke 2005) were observed in

1995 and 2002 prior to the disintegration events. This led to the prevailing hypothesis that ice- shelf collapse was caused by enhanced fragmentation due to extensive surface meltwater percolating through ice crevasses (MacAyeal et al. 2003). Other alternative hypotheses include stress system destabilization induced by ice front geometry change (Doake et al. 1998) and crevasse-fracturing through sustained ice-shelf thinning (Shepherd et al. 2003). These mechanisms were proposed based on preexisting lines of weakness on ice shelves and short-term observations regarding pre-collapse changes in ice-shelf conditions.

The development of structural weaknesses on an ice shelf are related to its stress system and mechanical properties that essentially determine the ice-shelf flow patterns, while variations in flow velocities modulate the stress conditions. Examination of the spatiotemporal variability in flow velocities over a long period is fundamental for understanding the physical processes leading to ice-shelf instability and disintegration, yet the pre-collapse changes in flow patterns of ice shelves over multi-decadal timescales are still poorly known. The velocity measurements documented by previous studies for Larsen Ice Shelf (Bindschadler et al. 1994; Rack et al. 1999;

Rignot 2004; Skvarca et al. 1999; Wang et al. 2016) were limited to specific ice-shelf areas or certain time periods. Here we reconstruct the time-series velocity records (Figure 3.2 and

Supplementary Figure 3.1) for Larsen Ice Shelf from 1963 to 2015 by processing over 400 satellite images (see Methods). The overall velocity uncertainty was estimated to be in the range of 4 m/yr to 35 m/yr, depending on the spatial resolution and time separation of sequential images (see

Supplementary Information). We implement a physically based ice-shelf flow model (MacAyeal

1989) to infer the ice-shelf stress condition changes (see Methods).

Figure 3.1 | Larsen Ice Shelf. a, The geographic setting of Larsen Ice Shelf, the division of flow units (A1 – A4, B1 – B8, C1 – C5, and D1 – D8) and the ice velocity map for the period 2000-

2001. b, The ice front positions of Larsen Ice Shelf and the ice velocity map for the period 2013-

2015.

The time-series velocity data show the distinct flow patterns of each ice-shelf section at different temporal stages. The temporal evolution of the pre-collapse velocity fields of Larsen B can be subdivided into three stages. At the first stage from the early 1960s to the late 1980s, Larsen

B had slight and localized acceleration at the ice front (Figure 3.2b) and the central part (Figure

3.2c-d). At the second stage during the 1990s, Larsen B had sustained downstream acceleration on the collapsed part (Figure 3.2b-d). The acceleration magnitude and extent significantly increased and expanded at this stage along with the terminus retreats (Supplementary Figure 3.2). At the third stage during the early 2000s, dramatic and widespread acceleration occurred through the whole ice shelf immediately before the collapse in 2002 (Figure 3.2b-f). Larsen B had over 50% average velocity increase from the period 1997-2000 to the period 2000-2001. Larsen A experienced similar velocity evolution stages, although each stage occurred earlier than Larsen B.

At the first stage before the middle 1980s, the northern unit A2 had a velocity increase of 9.6% near the ice front from the period 1963-1979 to the period 1979-1986. At the second stage in the late 1980s, significant acceleration occurred at the downstream area of units A2 and A3

(Supplementary Figure 3.1). At the third stage in the early 1990s, the major part of Larsen A between Sobral Peninsula and Seal Nunataks had a drastic acceleration throughout the upstream and downstream reaches (Figure 3.2a and Supplementary Figure 3.1), and the flow velocity increased by 23% on average from the period 1988-1990 to the period 1992-1993, before its final disintegration in 1995. The northernmost part at Larsen Inlet (A1) entered the dramatic

acceleration stage even earlier than the southern units (A2-A4). Unit A1 had accelerated by 35% from the period 1979-1986 to the period 1986-1988 before its complete disappearance between

1992 and 1993.

Figure 3.2 | Time-series velocity profiles along flow direction of nine flow units. Drygalski

(A4) flow unit, located at the southern Larsen A, was disintegrated in 1995. Hektoria/Green/Evans

(B1), Jorum/Punchbowl (B3) and Crane (B5) flow units were disintegrated in 2002. Flask (B7)

and Leppard (B8) flow units are part of the southern remnant at SCAR Inlet. Whirlwind Inlet (C3) flow unit is located at the central Larsen C, and Mobiloil Inlet (C5) flow unit is located at the southern Larsen C. A rapidly propagating rift was developed at the downstream area of C5 and led to the recent major calving on Larsen C in July 2017. The dash lines in graphs a, b, c, d, e and f show the ice front positions in different years.

The early flow accelerations on Larsen B before the terminus retreat might be related with the weakening of suture zones. The flow domains fed by those large and active glaciers were connected by the slow-moving ice flows originating from Foyn Point (B2), Caution Point (B4) and

Disappointment Cape (B6). These bands received less glacier ice input, hence being thinner and more susceptible to change. The transverse velocity profiles (Supplementary Figure 3.3) and lateral shear strain rates (Supplementary Figure 3.4) show three major lateral shear zones for the collapsed part. The increased transverse strain rates at these suture zones, particularly before the collapse, indicate the enhanced lateral shearing between the active flow domains. This was manifested by the pronounced development of open-rift systems upstream of units B2 and B6 in the years preceding the collapse (Glasser and Scambos 2008a). The satellite images

(Supplementary Figure 3.5) show the expansion of tensional fractures of the B6 unit between 1979 and 1988, suggesting the early mechanical weakening of the Larsen B suture zones before the

1990s.

Based on the ice-shelf flow model, we computed the ice rigidity parameters through an iterative optimization process by minimizing the differences between modeled and observed velocities (Supplementary Figure 3.6). The inverted ice rigidity field for the period 1986-1988

(Figure 3.3a) shows an exceptionally ‘soft’ area between the central flow domain and B1 unit, yet fractures were barely observed there. This may lend credence to the hypothesis that the Larsen B

suture zones contained marine ice. Marine ice forms when plumes of buoyant meltwater from deep meteoric inflows rise and refreeze to the ice-shelf base at a shallower depth. The presence of marine ice reduces the ice stiffness because of distinct crystallographic structure and salinity content, which can prevent fracture propagation and mitigate mechanical weakening caused by heterogeneous velocities of neighboring ice flows (McGrath et al. 2014). Although direct observations were absent for Larsen B, oceanographic modeling (Holland et al. 2009) has suggested the likely presence of marine ice at the suture zones of B2 and B6 units. Satellite altimetry measurements indicated the progressive thinning of Larsen B during the 1990s (Shepherd et al. 2003). If the thinning began before the 1990s, the decline of marine ice due to ocean-driven melting may have initiated the observed weakening at suture zones and the early acceleration of the central part, and thus triggered the instability development. The flow accelerations of those active units could further deteriorate the stability of the vulnerable suture zones.

Figure 3.3 | Inverted ice rigidity and inferred backstress loss of Larsen B. a, Ice rigidity during

The weakened rheology bands correspond well to the shear zones that are more easily deformed

than those stiffer ice flows from the colder tributary glaciers. The ice rigidity was weakened at the upstream of the collapsed part during 2000-2001.

There was a strong correspondence between terminus retreat (Supplementary Figure 3.2) and flow acceleration in the 1990s (Figure 3.2b-d). The expansion of rifts and large calving events were accompanied by flow speedups and steep along-flow velocity gradients. The 1992-1993 velocity profile of B1 unit (Figure 3.2b) shows an abrupt velocity increase at the downstream location ~78 km away from the grounding line, where a fracture developed during 1986-1988

(Supplementary Figure 3.7) and triggered the later calving in 1995. Similar patterns can be observed on the 1995-1997 profiles of B1, B3 and B5 units. Formation and propagation of rifts are related to the tensile longitudinal stresses. The increased velocity gradients and fracture development indicate the enhanced longitudinal stretching towards the ice front before the calving events. Previous studies (Doake et al. 1998; Kulessa et al. 2014) suggested that an ice shelf tends to be unstable when its terminus retreat overpasses the ‘compressive arch’ that defines the transition from compressive to tensile second principal stresses. The first principal stress determines local strain rate and relates to fracture opening. A frontal portion with a large stress- flow angle close to 90° is more likely to stabilize an ice shelf, while a near-zero stress-flow angle tends to destabilize the ice shelf (Kulessa et al. 2014). The terminus retreat between 1998 and 1999 went beyond the ‘compressive arch’ (Doake et al. 1998) (Supplementary Figure 3.4). The ice front shape changed from convex to concave, and the stress-flow angle between first principal stress and flow direction became near-zero at the ice front (Supplementary Figure 3.4). The successive calving events in the 1990s made the Larsen B stress system to an actively unstable state.

The flow acceleration immediately before the disintegrations occurred throughout the upstream and downstream reaches (Figure 3.2a-f). Correspondingly, the compressive ice flow

(indicated by negative downstream velocity gradients) at the upstream area of B1 unit changed into tensile ice flow during 2000-2001 (Figure 3.2b), and the numerical modeling reveals the large- scale backstress loss (Figure 3.3c). The backstress mainly originates from the lateral shear stresses against side margins, and generally decreases towards the ice front, unless other confinements

(e.g., ice rises, ice rumples) are encountered. The disintegrated part had larger decrease in backstress (Figure 3.3c), indicating its pre-collapse decoupling from the lateral shear margins. The weakening and fracturing at the shear zones were enhanced by persistent flow accelerations, and the intense surface melting (van den Broeke 2005) could further lower the ice rigidity through hydrofracturing processes.

The retrospective analyses suggest that the collapse of Larsen B was preconditioned by the long-term gradual weakening driven by the interplay between the exogenous forcing of climatic and oceanic warming and the endogenous adjustments of flow velocity, stress condition, and ice rheology. A stable ice-shelf system is characterized by steady velocity field and sturdy geometry condition to maintain mass balance and force balance. External forcing factors may trigger the instability development of an ice shelf and induce short-term or long-term adjustment of internal conditions, which may exceed the critical limit to retain the system equilibrium. We generalize the instability development process of an ice shelf towards disintegration into four stages:

I. Unstable condition initiation stage: Atmospheric and oceanic warming initiates the unstable condition within the ice shelf. Ice-shelf thinning and marine ice reduction due to ocean- driven melting make the ice shelf vulnerable. Fractures may emerge at those weak zones (e.g. suture zones and ice front). Sporadic flow acceleration occurs at the central and frontal parts of the ice shelf.

II. Enhanced weakening stage: A positive feedback cycle forms between flow acceleration and structural weakening. The accelerated and spatially heterogeneous ice flows increase the lateral shearing and longitudinal stretching, leading to further weakening and subsequent front retreat. Significant and sustained flow acceleration occurs over a large area of the ice-shelf downstream reach.

III. Destructing stage: The accumulated weakening exceeds the critical point to maintain system equilibrium. The prolonged fracturing and weakening lead to the decoupling of the ice shelf from the lateral shear margins and the rapid loss of backstress. This causes radical and widespread flow accelerations over the entire ice shelf, heralding its ultimate collapse.

IV. Catastrophic disintegration stage: The enhanced longitudinal tensile stresses trigger the rapid and extensive fragmentation of the ice shelf. Successive calving of elongate icebergs occurs rapidly, and the ice shelf catastrophically breaks up into ice rubble and small icebergs. The ice- shelf disintegration triggers the rapid surges of the tributary glaciers.

The four-stage model provides a conceptual framework of the evolutionary process of an ice shelf towards instability and disintegration, therefore shedding some light on understanding the future fate of other ice shelves. The instable conditions of an ice shelf are manifested by flow velocity, stress field, ice rheology and structural weakness. It is difficult to directly observe and quantify the stress field, ice rheology and structural weakness, however, the flow velocity can be measured frequently at a high precision over a large spatial scale and thus can serve as a key indicator for the ice-shelf instability development. Dramatic and extensive flow acceleration across the entire ice shelf can be regarded as the harbinger of imminent disintegration, which can be closely monitored using remote sensing techniques. In the context of increasing warming, an ice

shelf may evolve from one stage to the next towards disintegration, and each stage is characterized by different spatial extents and magnitudes of flow acceleration. Due to the lower latitude and warmer climatic setting, Larsen A apparently started the instability evolutionary process earlier than Larsen B. With the warming trend spreading further southward (Cook and Vaughan 2010), more ice shelves at higher latitudes (e.g. Larsen C and Larsen D) would be susceptible to the instability evolutionary process as predicted by Mercer (Mercer 1978).

We examined the spatio-temporal variability of the flow velocity fields on Larsen C and

Larsen D. The flow velocities of these two ice shelves had much less temporal variations. The southern Larsen C (C5 unit) has accelerated at the downstream reach since the period 2008-2010

(Figure 3.2h). The localized acceleration has coincided with a northerly developed rift from Gipps

Ice Rise. This rift had propagated rapidly since 2012 (Jansen et al. 2015) and eventually led to the major calving event on Larsen C in July 2017. The velocity profiles of C5 unit (Figure 3.2h) are similar to those of B1 unit before the major calving on Larsen B in 1995 (Figure 3.2b). Both were characterized by compressive ice flows along the upstream reach and the increased longitudinal stretching along the downstream reach, and were associated with a rift developed from lateral shear margins that caused later front calving. Larsen C was most likely at the unstable condition initiation stage before the July 2017 calving event, and will probably enter the enhanced weakening stage.

In contrast, Larsen D had little velocity variability in the past decades, and even a slight deceleration occurred from the period 2000-2002 to the period 2004-2006 (Figure 3.2i). This suggests that Larsen D is currently in a stable state.

The July 2017 calving event has raised the concern about the possible dramatic consequences for Larsen C. Using the ice-shelf flow model, we inferred the ice rigidity and stress tensor of Larsen C using the 2013-2015 velocity measurements, and conducted a perturbation

experiment based on the new ice front position after the calving event. The modeling results

(Figure 3.4) indicate that the recent calving event would not trigger drastic acceleration as in the destructing stage of Larsen A and Larsen B. Although the retreat of Larsen C caused by the recent calving did not go beyond the ‘compressive arch’, the tensile first principal stresses on the central ice front after the calving align with the flow directions, potentially undermining the stability of

Larsen C. It has been argued that the suture zones play a significant role in regulating the stability of Larsen C (Kulessa et al. 2014). Airborne and ground radar measurements have confirmed the marine ice content underneath the Larsen C suture zones (Jansen et al. 2013; McGrath et al. 2014).

Reduction of marine ice due to basal melting may trigger the ice-shelf instability. Oceanographic observations (Nicholls et al. 2012) reveal that the temperature of the water mass interacting with the Larsen C base is at surface freezing point as controlled by sea ice formation process. Increasing basal melting requires higher production rates of high salinity shelf water entering the sub-ice shelf cavity, which have not been observed for Larsen C yet (Nicholls et al. 2012). Due to the sensitive nature of ice shelves, any processes that undermine the sturdy condition of suture zones may alter the flow patterns as well. Regular velocity monitoring is therefore essential for assessing the stability of ice shelves and predicting possible disintegrations.

3.2 Methods

We applied an image-matching based feature tracking method (Liu et al. 2012; Scambos et al. 1992) to satellite images to derive the time-series flow velocity fields of the Larsen Ice Shelf during the past half century. The rationale is to track common features on temporally sequential images. The derived velocity field represents the average flow speed and direction during the period between acquisition dates of two sequential images. The images used in the velocity

derivation include historical Declassified Intelligence Satellite Photographs (DISP) from ARGON missions in the 1960s, Landsat MSS, TM, and ETM+ images since the 1970s, and synthetic aperture radar (SAR) images from ERS-1/2, Envisat, Radarsat-1 and ALOS satellites since the

1990s. To ensure measurement accuracy, the images were rigorously and precisely orthorectified and co-registered. Quality control of the velocity measurements was performed through directional and statistical filters, and manual inspection and editing.

We used a numerical ice-shelf model (MacAyeal 1989) to compute the ice rigidity and stress tensor of Larsen B and Larsen C. The model is based on shallow shelf approximation, which assumes hydrostatic equilibrium and depth-invariant horizontal velocities. We implemented the model using the Ice Sheet System Model (ISSM) (Larour et al. 2012) based on a finite element scheme. The ice rigidity parameters were inverted through an iterative optimization process to minimize the differences between modeled and observed flow velocities. The boundary condition at the ice calving front was given by the longitudinal stress that balances the difference between the hydrostatic pressure of ice and ocean water. The observed flow velocities were used as the interior boundary condition. Model inputs include the model spatial domain constrained by grounding line and ice front positions, surface elevation, ice thickness, observed flow velocities, and initialized ice rheology parameters. Model outputs include the optimally inverted ice rigidity, modeled flow velocities, two-dimensional strain rates and stress fields, and projected strain rates and stress fields in principal directions. For Larsen B, we used the Radarsat Antarctic Mapping

Project (RAMP) Digital Elevation Model Version 2 (Liu et al. 2001) for surface elevation, and for

Larsen C, we used the Antarctic Digital Elevation Model from Combined ERS-1 Radar and ICESat

Laser Satellite Altimetry (Bamber et al. 2009). The ice thickness was calculated from the surface elevation based on the hydrostatic equilibrium condition. The grounding line positions were

determined by combining the MEaSUREs Antarctic Grounding Line (Rignot et al. 2011b) and the

RAMP ground ice mask data (Jezek 2002). The backstress was calculated using the analytical solution of ice-shelf creep (Cuffey and Paterson 2010; Thomas 1973). The northern part of Larsen

D was included in the ice-shelf modeling as well. The perturbation experiment was conducted by updating the model spatial domain and setting the new ice front boundary condition. The optimally inverted ice rigidity values in the period 2013-2015 were used as the ice rigidity parameters, and the boundary condition of the interior ice shelf was set to be the observed flow velocities of 2013-

2015. The model ran in the diagnostic mode under the condition of steady state.

3.3 Supplementary Information

This supplementary information file includes:

Data description

Data processing

Ice velocity derivation and accuracy assessment

Numerical modeling of ice shelf flow

Supplementary Figures 3.1-3.7

Supplementary Tables 3.1-3.2

3.3.1 Data Description

We used both optical and radar images acquired by various satellite sensors since the 1960s to derive the ice velocity fields and to map the ice-shelf margins (Supplementary Table 3.1). The image data include the Declassified Intelligence Satellite Photographs (DISP) from the reconnaissance ARGON missions in the 1960s, the Landsat MSS/TM images during 1970s –

1980s, the synthetic aperture radar (SAR) images from European Space Agency (ESA) ERS-1/2

Satellites and Canadian Space Agency’s Radarsat-1 Satellite in the 1990s, the Landsat-7 ETM+ images between 1999 and 2003, the SAR images from ESA’s Envisat Satellite and Japanese

Advanced Land Observation Satellite (ALOS) PALSAR (Phased Array type L-band Synthetic

Aperture Radar) during 2002-2010, and the Landsat-8 OLI images since 2013.

The ARGON satellite photographs were acquired by a panchromatic frame camera KH-5 that used a 3-inch focal length to capture vertical photographs of the terrain (Wang et al. 2016).

The photograph size is 4.5 inches by 4.5 inches, corresponding to ground coverage of approximately 540 km by 540 km. The nominal photo scale is 1:4,250,000, and the nominal ground resolution is 140 m. The films were scanned at 7 µm resolution into digital images and distributed by the United States Geological Survey (USGS) data center.

The Landsat images were provided as Level-1G (L1G) or Level-1GT (L1GT) products at the USGS EROS data center. The L1G product is radiometrically calibrated and systematically georeferenced. The L1GT product is radiometrically calibrated and orthorectified using the

Radarsat Antarctic Mapping Project Digital Elevation Model Version 2 (RAMP DEM v2). The near infrared band of Landsat MSS (60 m resolution) and Landsat TM images (30 m resolution) and the panchromatic band (15 m resolution) of the Landsat-7 ETM+ and Landsat-8 OLI images were used for deriving the ice velocity fields and tracking the ice front changes.

The ERS-1/2 SAR and Envisat ASAR images were obtained from the ESA’s Earth Online website (https://earth.esa.int/). The ERS-1/2 SAR and Envisat ASAR both operate in the C band.

The ERS-1/2 SAR image data are Level-0 Raw Image Product (SAR_IM_0P) with the SAR telemetry data and the required auxiliary data. The Envisat ASAR images are provided as the

ASAR Image Mode Precision Image Product (ENVISAT.ASA.IMP_1P). These images are multi- look ground range data processed from Level-0 data, which have a spatial resolution of 30 m in

both range and azimuth directions. The ALOS PALSAR L-band SAR images were obtained from the Alaska Satellite Facility data portal, which are the ground range Level 1.5 Product and have been geocoded by Japan Aerospace Exploration Agency (JAXA). We used the Radarsat-1 SAR images collected in 1997 and 2000 for the Radarsat Antarctic Mapping Project (RAMP), which have been orthorectified and mosaiced at the Byrd Polar Research Center of the Ohio State

University (Jezek 2003; Liu and Jezek 2004). The C-band SAR image mosaics are in polar stereographic map projection with reference to WGS-84 ellipsoid, with a spatial resolution of 25 m.

To avoid short-term interannual variability, flow velocities were measured from the sequential images with time separation of 1~3 years. Two epochs of 1963-1979 and 1979-1986 are an exception, during which the sequential images have a longer time separation due to the limited availability of cloud-free image data.

3.3.2 Data processing

The basic requirements for the feature tracking method to derive reliable and accurate velocity measurements are precise co-registration of sequential images, detectable surface features and sufficient image resolution. Several data preprocessing operations were performed, including image orthorectification and co-registration, image noise filtering, and image feature enhancement.

The ARGON satellite photographs were orthorectified using the camera model and bundle block adjustment, with high-precision ground control points identified from WorldView satellite images (Wang et al. 2016). The geolocation accuracy of the orthorectified ARGON photographs was estimated to be better than the nominal ground resolution of 140 m. We applied the adaptive

Wiener filter to reduce the film grain noise of the orthorectified ARGON images. The Landsat

MSS images acquired during the 1970s were co-registered to the orthorectified ARGON images,

and the overall Root Mean Square Error (RMSE) of the co-registration was estimated to be better than the image resolution (60 m). The Landsat TM, ETM+ and OLI images are provided as L1G or L1GT products, which have been georeferenced and orthorectified at the USGS EROS Data

Center. To further improve geolocation accuracy, we used a two-step co-registration strategy to preprocess the Landsat images. First, a set of stationary ground control points identified from the high-resolution WorldView Images were used as GCPs to geocode the images through the polynomial transformation. Second, an image-to-image co-registration was conducted between two sequential images of each pair based on a set of stationary tie points. The earlier image in the pair was used as the reference to co-register the later image using the first-order polynomial transformation. The overall co-registration RMSE for each image pair was estimated to be at a subpixel level.

The ERS-1/2 SAR images and the Envisat ASAR images were geocoded and orthorectified with the RAMP DEM and the auxiliary precise orbit data using the SARscape software package.

The precise orbit data and other auxiliary data for ERS-1/2 and Envisat satellites are obtained from the ESA’s Earth Online website. PRARE Precise Orbit Product provides precise orbital information for ERS-1/2 SAR, including the satellite ephemeris (position and velocity vector) data.

DORIS Precise Orbit State Vectors provide precise orbital information for Envisat ASAR, and auxiliary ASAR XCA files contain external calibration data. Using the precise orbit correction procedure, the geolocation accuracy of the orthorectified ERS-1/2 SAR images and Envisat ASAR images was estimated to be better than one pixel (25 m). Radar images from different satellite SAR sensors or different orbital passes may have different geometric distortion patterns and radiometric properties. To ensure reliable image matching quality, we selected two SAR images acquired by similar SAR sensors (C band or L band) on the same ascending or descending orbit passes to form

the sequential image pair for the velocity derivation. An image-to-image co-registration was also conducted between the SAR images in each pair using a set of stationary tie points.

Gamma and median filters were applied to suppress data noise. To enhance the surface features, we performed various image contrast stretching operations prior to the image matching computation. We subdivided the image pairs into multiple image segments. For each image segment, we performed a histogram stretching operation to enhance the surface features. In addition, a Gaussian stretching operation was applied to optical images, and logarithmic stretching was applied to SAR images. Edge enhancement filters were also applied to further highlight subtle surface features after noise reduction.

3.3.3 Ice velocity derivation and accuracy assessment

The feature tracking method was used to derive the ice flow velocity fields from sequential satellite images acquired at different times. The rationale is to track the moving and persistent surface features such as crevasses, rifts, flow bands and meltwater ponds, measure the spatial displacements of these features over time and calculate the corresponding flow velocities. The cross-correlation based image matching algorithm was used to automate the feature tracking process. This algorithm is widely applied to search match (conjugate) points between images, which has been proven effective for both radar and optical images (Heid and Kääb 2012; Liu et al.

2012; Rack et al. 1999; Scambos et al. 1992). The cross-correlation method calculates the cross- correlation surface to evaluate the similarity between the image chips of two sequential images, and its matching accuracy can reach sub-pixel level (Scambos et al. 1992). Fast Fourier

Transformation can greatly speed up the computation process of the cross-correlation coefficients.

Conventionally, prior knowledge of flow velocities is required to initialize the image matching parameters such as the location and size of the search window, however, uniform settings of the

search window may generate spurious matches for the areas with heterogeneous ice flows (Liu et al. 2012).

To take into account the heterogenous ice flows, we used a semi-automated image matching approach (Liu et al. 2012; Zhan et al. 2016). This semi-automated method starts with a small number of match points that are interactively identified through visual inspection of two sequential images on computer screen. These manually identified match points are used to compute the optimal search space for the subsequent automated area-based image matching operation to derive a dense set of match points for velocity computation. For the automated image matching operation, we used a regular grid of points with a spacing interval of 300 m as match candidate points, and the matching chip window size was set to be 64 by 64 pixels. For the quality control of velocity measurements, we used directional filters (Scherler et al. 2008) and local statistical filters (Liu et al. 2012) to detect and remove the erroneous matches. Those matches that deviate greatly from flow directions were regarded as mismatches. Local statistical filters were applied to the two-dimensional displacement measurements on the assumption that ice motion changes continuously and smoothly over a local neighborhood. The mean (μ) and standard deviation (σ) of the x-direction displacements and the y-direction displacements were computed respectively over a local neighborhood with a specific radius. The matches whose x-direction displacement or y-direction displacement drastically deviates from the mean value were discarded as erroneous measurements. The matching results were visually inspected and edited after the automated filtering. The valid matches are mainly distributed over the areas with crevasses, rifts and flow band features.

The accuracy of velocity measurements is evaluated by considering the image-matching accuracy, the co-registration accuracy of sequential images and the time separation of each

sequential image pair. The cross-correlation image matching algorithm reaches a sub-pixel level of accuracy for the matched points from the two co-registered images. The image orthorectification and co-registration accuracy is estimated to be less than one pixel. The overall error magnitude for the spatial displacement measurement of the matched points is estimated to be 1.5 pixels, which corresponds to 90 m for Landsat MSS images, 45 m for Landsat TM images, 37.5 m for ERS-1/2

SAR images, Radarsat-1 SAR images and Envisat ASAR images, and 22.5 m for Landsat ETM+ and OLI images and ALOS PALSAR images. The corresponding error estimates for velocity measurements are listed in Table 3.2, in terms of specific time period for each ice-shelf section.

The ice velocity grids (fields) were generated using the ordinary Kriging interpolation method based on the valid velocity measurements, and the spatial extent of interpolation was defined by the boundary of valid velocity measurements for each time period. The longitudinal velocity profiles were plotted along the flow direction of each flow unit from the groundling line to the ice-shelf front. For each profile, the velocity values were calculated with an interval of 1 km by averaging the valid velocity measurements within the distance of 3 km from the central flow line.

3.3.4 Numerical modeling of ice shelf flow

We adopted a finite element ice-shelf flow model, which is constructed using the Ice Sheet

System Model (ISSM) software. In this model, the ice rigidity parameters and stress fields are calculated based on the following ice-shelf flow equations (MacAyeal 1989):

휕 휕푢 휕휗 휕 휕푢 휕휗 휕푠 (2푣ℎ(2 + )) + (푣ℎ( + )) = 𝜌𝑔ℎ (5) 휕푥 휕푥 휕푦 휕푦 휕푦 휕푥 휕푥

휕 휕휗 휕푢 휕 휕푢 휕휗 휕푠 (2푣ℎ(2 + )) + (푣ℎ( + )) = 𝜌𝑔ℎ (6) 휕푦 휕푦 휕푥 휕푥 휕푦 휕푥 휕푦

where 푥 and 푦 are the horizontal Cartesian coordinates, 푢 and 휗 are the vertically averaged velocities in 푥 and 푦 directions, 𝑔 is the gravitational acceleration (9.81 m/s2), ℎ is the ice thickness, 푠 is the surface elevation, 𝜌 is the density of ice, and 푣 is the effective viscosity, given by

1 휕푢 휕휗 휕푢 휕휗 1 휕푢 휕휗 푣 = 퐵̅[( )2 + ( )2 + + ( + )2](1−푛)/2푛 (7) 2 휕푥 휕푦 휕푥 휕푦 4 휕푦 휕푥

1 1 푧푠 − 퐵̅ = ∫ 퐴 푛 푑푧 (8) ℎ 푧푏 where 퐵̅ is a depth averaged value of the flow law rate constant 퐴, representing the ice rigidity (or hardness). 푛 is the flow law exponent in Glen’s flow law. This model assumes that the basal shear stress is zero and the horizontal flow is independent of the vertical coordinate.

The critical steps of the ice-shelf flow modeling include model spatial domain definition, mesh generation, model parameterization, ice rigidity inversion and stress fields calculation. The model spatial domain was confined by the groundling line, the ice shelf front and the spatial extent of valid velocity measurements. The model spatial domain includes Larsen B, Larsen C, and the northern Larsen D between the Gipps Ice Rise and the Hearst Island. The grounding line positions were determined by combining the MEaSUREs Antarctic Grounding Line (Rignot et al. 2011b) and the RAMP ground ice mask data (Jezek 2002). The ice fronts were delineated from the orthorectified satellite images for each ice-shelf section in different time periods. The ice-shelf geometry was further prescribed by the ice thickness and the surface elevation. The Radarsat

Antarctic Mapping Project (RAMP) Digital Elevation Model Version 2 (Liu et al. 2001) was used for the surface elevation of Larsen B, and the Antarctic Digital Elevation Model from Combined

ERS-1 Radar and ICESat Laser Satellite Altimetry (Bamber et al. 2009) was used for the surface elevation of Larsen C. The thickness of the floating ice shelf was inferred from the surface elevation based on the hydrostatic equilibrium assumption:

휌′ ℎ = ( ) × 푠 (9) 휌′−휌 where ℎ is the ice thickness, 푠 is the surface elevation, 𝜌′ is the sea water density (1028 kg/m3) and 𝜌 is the ice density (917 kg/m3).

The numerical mesh net nodes used for the ice-shelf modeling computation were generated using the anisotropic mesh adaptation method (Hecht 1998). This method starts from a regular triangular net covering the model spatial domain, and optimizes the mesh resolution spatially to minimize the interpolation error of a predefined metric. The ice velocity measurements were interpolated into raster grids using the Kriging interpolation method, which were used to adapt and refine the mesh sizes. After the mesh is generated, the raster grids of ice thickness, surface elevation and ice velocity were interpolated onto the mesh net nodes. Kinematic boundary conditions were specified at the interior boundary of the ice shelves, and dynamic boundary conditions were specified at the ice-shelf front. For the ice rheological properties, the flow law exponent 푛 was set to a fixed value of 3, and the depth-averaged ice rigidity 퐵̅ was initialized to be 1.2*108 Pa s1/3 for Larsen B (corresponding to an ice temperature of about -10 °C) and 1.5*108

Pa s1/3 for Larsen C (corresponding to -15 °C).

Using the observed velocities as constraints, the ice rigidity parameter 퐵̅ was inversely solved by using an iterative optimization procedure. The cost function of the optimization is defined as a weighted sum of the differences between the observed and modeled velocities and the gradient of the derived rigidity parameter in each iteration which penalizes the oscillations of the derived parameter fields 퐵̅. The M1QN3 optimization algorithm (Gilbert and Lemaréchal 1989) was used to solve the parameter fields by minimizing the defined cost function. As shown in

Supplementary Figure 3.6, the modeled velocity fields after the optimization process match the observations very well. In comparison with the observed velocities, the RMSE of the modeled

velocities is estimated to be 16 m/yr for Larsen B during 1986-1988, 23 m/yr for Larsen B during

2000-2001, and 11 m/yr for Larsen C during 2013-2015, which are comparable with the measurement error of the feature tracking method.

The strain rate tensor and deviatoric stress tensor in the Cartesian system and in the principal directions are computed using the optimized ice rigidity fields 퐵̅ and the modeled velocity fields. In a horizontal Cartesian system, the strain rate fields (휖푥푥̇ , 휖푦푦̇ , 휖푥푦̇ ) are calculated based on the modeled velocity fields:

휕푢 휖̇ = (10) 푥푥 휕푥

휕휗 휖̇ = (11) 푦푦 휕푦

1 휕푢 휕휗 휖̇ = ( + ) (12) 푥푦 2 휕푦 휕푥 and the corresponding deviatoric stress tensor (휏푗푘) is calculated as below:

휏푗푘 = 2푣휖푗푘̇ (13) where 푣 is the effective viscosity in Equation 7. The strain rate tensor and deviatoric stress tensor in principal directions are obtained by calculating the eigenvalues and eigenvectors of the matrices

휖̇ 휖̇ 휏푥푥 휏푥푦 [ 푥푥 푥푦] and [ ]. 휖푥푦̇ 휖푦푦̇ 휏푥푦 휏푦푦

The backstress (Cuffey and Paterson 2010) (𝜎푏) is inferred from strain rates 휖푥푥̇ and 휖푦푦̇ :

1 휌 𝜎 = 𝜌𝑔 (1 − ) ℎ − 2푣(2휖̇ + 휖̇ ) (14) 푏 2 휌′ 푥푥 푦푦

Using the scaling parameters (Thomas 1973) in Equation (10), the backstress is calculated as:

1 휌 (2+푎)|휖̇ |1/(푛−1)휖̇ 𝜎 = 𝜌𝑔 (1 − ) ℎ − 퐵̅ 푥푥 푥푥 (15) 푏 2 휌′ (1+푎+푎2+푏2)(푛−1)/2푛

where 푎 = 휖푦푦̇ /휖푥푥̇ , 푏 = 휖푥푦̇ /휖푥푥̇ . The backstress values are calculated along the flow direction and along the principal direction separately.

The perturbation experiment was conducted for Larsen C and northern Larsen D by using the ice front position after the recent major calving on Larsen C in July 2017. The kinematic boundary condition for the interior ice shelf was specified using the velocity measurements during

2013-2015. The ice rigidity parameter was set to be the optimally inverted 퐵̅ for Larsen C during

2013-2015. The ice-shelf flow equations were solved diagnostically to simulate the impact of the major calving event in July 2017 on the ice velocity fields. The strain rate tensor, deviatoric stress tensor and backstress fields were also simulated, given the new ice shelf geometry after this major calving event.

3.3.5 Supplementary Tables

Supplementary Table 3.1. The satellite images used for velocity derivation

Satellite sensor Acquisition year Resolution Data source Optical Imagery ARGON KH-5 1963 140 m U.S. Geological Survey Landsat-3 MSS 1979 60 m U.S. Geological Survey Landsat-4/5 TM 1984, 1986, 1988, 1989, 1990, 1991 30 m U.S. Geological Survey Landsat-7 ETM+ 2000, 2001, 2002 15 m U.S. Geological Survey Landsat-8 OLI 2013, 2014, 2015 15 m U.S. Geological Survey Radar Imagery ERS-1/2 SAR 1992, 1993, 1995, 1997 25 m European Space Agency RADARSAT-1 SAR 1997, 2000 25 m Radarsat Antarctic Mapping Project Envisat ASAR 2004, 2005, 2006 25 m European Space Agency ALOS PALSAR 2006, 2008, 2010 6.25 m Alaska Satellite Facility

Supplementary Table 3.2. Image source, time separation and velocity measurement error

Time Velocity Displacement Period Image source separation uncertainty Area uncertainty (m) (yr) (m/yr) 08/1963-02/1979 DISP, Landsat MSS 90 15.5 5.8 Larsen A, B 08/1963-03/1986 DISP, Landsat TM 90 22.5 4.0 Larsen B, C 02/1979-03/1986 Landsat MSS, TM 45 7.0 6.4 Larsen A, B 03/1986-01/1988 Landsat TM 45 1.9 23.7 Larsen A, B, C 11/1984-01/1988 Landsat TM 45 3.2 14.1 Larsen D 01/1988-02/1990 Landsat TM 45 2.1 21.4 Larsen A, B, D 11/1989-02/1991 Landsat TM 45 1.3 34.6 Larsen C 07/1992-08/1993 ERS SAR 37.5 1.2 31.3 Larsen A, B 07/1992-11/1995 ERS SAR 37.5 3.3 11.4 Larsen D 08/1993-10/1995 ERS SAR 37.5 2.2 17.0 Larsen B 10/1995-07/1997 ERS SAR 37.5 1.7 22.1 Larsen B 11/1995-07/1997 ERS SAR 37.5 1.7 22.1 Larsen D 10/1997-11/2000 Radarsat SAR 37.5 3.1 12.1 Larsen B 10/1997-10/2000 Radarsat SAR 37.5 3.0 12.5 Larsen C 09/1997-10/2000 Radarsat SAR 37.5 3.1 12.1 Larsen D 02/2000-12/2001 Landsat ETM+ 22.5 1.8 12.5 Larsen B 01/2000-12/2001 Landsat ETM+ 22.5 1.9 11.8 Larsen C, D 12/2001-12/2002 Landsat ETM+ 22.5 1.1 20.5 Larsen B 03/2004-03/2005 Envisat ASAR 37.5 1.1 34.1 Larsen B 04/2005-12/2006 Envisat ASAR 37.5 1.7 22.1 Larsen B 07/2004-05/2006 Envisat ASAR 37.5 1.9 19.7 Larsen D 06/2006-11/2008 ALOS PALSAR 22.5 2.4 9.4 Larsen B, C 07/2006-10/2008 ALOS PALSAR 22.5 2.3 9.8 Larsen D 11/2008-10/2010 ALOS PALSAR 22.5 2.0 11.3 Larsen B, C 10/2008-10/2010 ALOS PALSAR 22.5 2.0 11.3 Larsen D 10/2013-12/2014 Landsat OLI 22.5 1.2 18.8 Larsen B 11/2013-04/2015 Landsat OLI 22.5 1.5 15.0 Larsen C, D

3.3.6 Supplementary Figures

Supplementary Figure 3.1 | Time-series ice velocity maps and front positions of Larsen Ice

Shelf (selected time periods). a, Ice velocity maps and front positions of Larsen A and Larsen B from 1979 to 1993. b, Ice velocity maps and front positions of Larsen B from 1993 to 2001. c, Ice velocity maps and front positions of the southern remnant of Larsen B from 2001 to 2014. d, Ice velocity maps and front positions of Larsen C from 1963 to 2015. e, Ice velocity maps and front positions of northern Larsen D from 1992 to 2015. The black dash line in the first graph of each subsection shows the locations of the plotted longitudinal velocity profiles shown in Fig. 2.

Supplementary Figure 3.2 | The ice front changes of Larsen A and Larsen B from August

1963 to December 2014. The bed topography of the grounded glaciers is from the BEDMAP2

(Fretwell et al. 2013) dataset. The background image is a Landsat TM image acquired on March

1, 1986. The background image is a Landsat TM image acquired on March 1, 1986. The ice front positions were delineated from the orthorectified satellite images. The retreat of Larsen A began before the 1980s, and the recession rate increased since the late 1980s. The ice front of Larsen A between Sobral Peninsula and Seal Nunataks progressively retreated in the early 1990s. Larsen B had been advancing until large calving events occurred in 1995 and 1998/1999 (Rott et al. 2002).

In the austral summer of 2002, most of Larsen B, fed by Hektoria, Green, Evans, Punchbowl,

Jorum and Crane Glaciers, disintegrated. Two major remnants remain in the north around Seal

Nunataks and in the south at SCAR Inlet. The northern remnant is almost stagnant (Rott et al.

1996), while the retreat of the southern remnant fed by Flask and Leppard Glaciers is still on-going

(Shuman et al. 2011).

Supplementary Figure 3.4 | Lateral shear strain rates and principal stress fields of Larsen B during 1986-1988 (a, b, c) and 2000-2001 (d, e, f). Graphs a and d show the high lateral shear strain rates at suture zones and rifted areas, and the increased magnitude in lateral shearing from the period 1986-1988 to the period 2000-2001. In b and e, the negative values of second principal stress indicate compressive stress regime while the positive values indicate extensive stress regime.

The transition boundary where the stress regime changes from the compressive state at the upstream reach to the extensive state at the downstream reach is defined as ‘compressive arch’

(thick black solid line in b). The ice front after the major calving events in the 1990s passed the

‘compressive arch’. Graphs c and f show the dominant tensile first principal stresses. The frontal

portion originally had the first principal stresses oriented perpendicular to the flow directions

(Graph c). After successive terminus retreats, the first principal stresses near the ice front were almost parallel to the flow directions, particularly in the central ice-shelf part (Graph f).

Supplementary Figure 3.5 | Larsen B suture zone weakening around Disappointment Cape

(B6 flow unit). Graph a shows that the suture zone of unit B6 was the transition between the northern collapsed part and the southern remnant. The weakening of this region is illustrated by the satellite images in b, c, d, e and f. Graphs b and c show the formation of new fractures during

1979-1986, which were opened wider in 1988 (d). Graphs e and f show the enhanced fracturing at this zone immediately before the collapse.

Supplementary Figure 3.6 | Comparison between observed and modeled flow velocity fields. a and b, Larsen B during 1986-1988. c and d, Larsen B during 2000-2001. e and f, Larsen C during

2013-2015. The ice velocity maps and scatterplots indicate a good agreement between observed and modeled flow velocities.

Supplementary Figure 3.7 | Fracture development from the northern lateral shear margin of Larsen B from March 1986 to January 1988. The background images are the near infrared bands of two Landsat TM satellite images acquired in 1986 and 1988. The blue dash line represents the new ice front after the terminus retreat in 1995, which corresponds well with the opened fracture.

Chapter 4: Investigation of the multidecadal changes of the Larsen

B outlet glaciers by integrating multi-source satellite and airborne

remote sensing data

4.1 Introduction

Changes in global climate and sea level are intricately linked to the dynamics and mass balance of the polar ice sheets (Shepherd and Wingham 2007). According to the IPCC assessment reports (AR4 and AR5), the Antarctic and Greenland ice sheets probably contributed to the sea level rise at an average rate of 0.4 mm/yr over the period 1993-2003, and the ice loss rates substantially increased over the period 2002-2011 (Pachauri et al. 2014; Solomon 2007). Outlet glaciers and ice streams transport grounded ice from the interior ice sheet toward coastal margins and discharge into ice shelves or ocean systems. A large proportion of the mass loss from the grounded ice sheet flows through a small number of outlet glaciers and ice streams (Bamber 2000;

Bentley 1987). One of the vital controls affecting the dynamics of the Antarctic outlet glaciers is the buttressing effect from the peripheral ice shelves (Dupont 2005; Mercer 1978). An ice shelf exerts buttressing force that stabilizes the ice flow of upstream glaciers, thus regulating the discharge rate from grounded ice into ocean. The thinning and disintegrations of the Antarctic ice shelves in the past decades reveal their vulnerability to climate changes (Doake and Vaughan 1991;

Paolo et al. 2015; Pritchard et al. 2012; Rignot et al. 2013b; Rott et al. 1996; Scambos et al. 2009;

Scambos 2004). It is crucial to understand the long-term responses of upstream outlet glaciers to ice-shelf changes for better estimating the mass balance of ice sheets and predicting the future sea level rise.

The Antarctic Peninsula warmed at a rate of 3.7±1.6 °C per century since the 1950s

(Vaughan et al. 2003). The rapid regional warming has been accompanied by the dramatic disintegrations of ice shelves (Cook and Vaughan 2010; Rott et al. 1996; Scambos et al. 2009) and the widespread retreat of marine-terminating outlet glaciers (Cook et al. 2005). The collapses of the Larsen A and Larsen B ice shelves triggered an immediate acceleration and thinning response of the upstream glaciers (Rignot et al. 2004; Rott et al. 2002; Scambos et al. 2004). The disintegration of the Larsen A Ice Shelf in 1995 caused a threefold acceleration of the Drygalski

Glacier (Rott et al. 2002) and surges on several glaciers north of the Drygalski Glacier (De Angelis and Skvarca 2003). The Larsen B Ice Shelf underwent a catastrophic and unprecedented collapse event in the austral summer of 2002 with a 3200 km2 area broken into thousands of icebergs during a 35-day period. This rapid collapse induced an eightfold acceleration of the Hektoria, Green and

Evans Glaciers, and a threefold acceleration of the Jorum and Crane Glaciers (Rignot et al. 2004).

The consequent increase in ice discharge from these outlet glaciers directly contributed to the sea level rise (Berthier et al. 2012; Rott et al. 2007; Wuite et al. 2015).

Previous studies (Rignot et al. 2004; Rott et al. 2007; Scambos 2004) have documented the immediate accelerations of the Larsen B outlet glaciers following the ice-shelf collapse by applying either the radar interferometry technique or the feature tracking method to repeat-pass optical and radar images. Rott et al. (2011) used high-resolution TerraSAR-X radar images to map the ice motion of the Larsen B glaciers between 2008 and 2009, and found that these glaciers had similar ice flow acceleration patterns. Berthier et al. (2012) evaluated the mass loss of the Larsen

B tributaries over the period 2006-2011 by mapping the elevation changes from optical stereo images. They concluded that the mass loss rate during 2006-2011 was nearly the same as that during 2001/2002-2006 reported by Shuman et al. (2011). Khazendar et al. (2015) investigated the

evolving surface velocities and elevations of the southern ice-shelf remnant and its upstream glaciers. It should be noted that these studies were mainly based on short-term observations over multi-year periods. Recently, Wuite et al. (2015) mapped the multitemporal surface velocities of the Larsen B glaciers over the period 1995-2013. They examined the evolution of surface velocities and ice discharges of the Larsen B tributaries by applying the offset tracking or the SAR interferometry to the repeat-pass SAR data with a time span ranging from 1 to 46 days. The measured velocity fields from SAR data represent the near-instantaneous motion of the glaciers, which are potentially subject to seasonal variability compared with the annually averaged velocity fields. In their work, surface elevation and slope changes due to flow speedups were not examined.

Despite many interesting findings from previous studies, it is still uncertain whether the flow velocity and surface topography of the Larsen B outlet glaciers will reach a new steady state after the dramatic acceleration and thinning stage.

This paper presents a comprehensive time-series analysis of the dynamic behavior of the

Larsen B outlet glaciers before and after the ice-shelf collapse in 2002. We integrated multi-source remote sensing data dating back to 1986 to examine the spatiotemporal variations of the glacier front, flow velocity, and surface topography over the period 1986-2017. The satellite images acquired by Landsat-4/5 TM, Landsat-7 ETM+, Landsat-8 OLI, Terra ASTER, Envisat ASAR and

ALOS PALSAR were processed to track the ice front changes and examine the surface velocity fields over time. A semi-automated image matching method was employed to derive the velocity measurements from temporally sequential image pairs. The changes of surface topography during the period 2002-2015 were examined using satellite laser altimetry and airborne LiDAR data. We analyzed the long-term impact of the ice-shelf collapse on the dynamics of the outlet glaciers over decadal timescales in terms of ice flow behavior and surface topographic change.

4.2 Study Area

The Larsen Ice Shelf (Figure 4.1) spreads along the east coast of the Antarctic Peninsula.

It was composed of the Larsen A, B, C and D ice shelves from north to south. Figure 4.1 shows the front positions of the Larsen B Ice Shelf in different years on the Landsat Image Mosaic of

Antarctica (LIMA) (Bindschadler et al. 2008a), in which the image colors are coded according to the bed topography (Fretwell et al. 2013). The Larsen A Ice Shelf disintegrated in January 1995 with an area loss of 1600 km2. The Larsen B Ice Shelf underwent large calving events in 1995 and

1998/1999 (Rott et al. 2002) before its collapse in 2002. The Larsen B Ice Shelf, fed by the

Hektoria, Green, and Evans glaciers in the northern part, and by the Punchbowl, Jorum and Crane

Glaciers in the central part, broke up entirely during February-March 2002. The northernmost part around Seal Nunataks and the southern part at SCAR Inlet remained as two major remnants of the ice shelf. The ice-shelf area around Seal Nunataks is almost stagnant (Rott et al. 1996), while the retreat of the southern remnant is still ongoing (Khazendar et al. 2015). This study examines the dynamic changes of the Hektoria, Green, Evans, Punchbowl, Jorum, Crane, Mapple, Melville,

Flask and Leppard Glaciers as well as the southern remnant ice-shelf area at SCAR Inlet.

Figure 4.1. The geographic setting of the study area.

4.3 Data and Methods

4.3.1 Mapping glacier fronts and surface velocity fields from multitemporal satellite images

The Landsat-4/5 TM, Landsat-7 ETM+, Landsat-8 OLI and Terra ASTER images acquired during 1986-2017 were used to track the changes of glacier terminus and to derive the time-series surface velocity fields of the study area. The Landsat images over the Antarctica were processed to Level-1G (L1G) or Level-1GT (L1GT) products at the USGS EROS Data Center. Both the L1G and L1GT products were radiometrically calibrated. The L1G products were georeferenced, and the L1GT products were orthorectified using the Radarsat Antarctic Mapping Project Digital

Elevation Model Version 2 (RAMP DEM v2) (Liu et al. 1999). The Terra ASTER images archived by the EROS Data Center’s Land Processes Distributed Active Archive Center (LP-DAAC) were processed to Level-1A (L1A) and Level-1B (L1B) products. The L1A products are unprocessed

instrument data, including the original image data, radiometric and geometric coefficients and other auxiliary data. The L1B products are radiometrically calibrated and geometrically corrected by applying those coefficients. We used the L1A products since the availability of L1B data over the study area is very limited.

In total, we used 31 Landsat images and 33 ASTER images (Table 1). The near infrared bands of the Landsat-4/5 images (band 4, 30-m resolution) and the ASTER images (band 3N, 15- m resolution) were used for velocity derivation since they are sharper and less influenced by atmospheric backscattering in comparison with the other bands. The panchromatic bands of the

Landsat-7 and Landsat-8 images were used owing to the better spatial resolution (15 m). We calibrated and orthorectified the ASTER L1A data using the auxiliary coefficients and the RAMP

DEM v2 with the ENVI 4.8 software. The Landsat and ASTER images were further co-registered to the Landsat Image Mosaic of Antarctica (LIMA) (Bindschadler et al. 2008a) using the stationary features as ground control points. The LIMA is composed of more than 1,000 cloudless orthorectified Landsat-7 ETM+ images acquired during 1999-2003. These images were pan- sharpened to a spatial resolution of 15 m. The co-registration accuracy was estimated to be at subpixel level. Piecewise histogram stretching and high-pass filtering were performed to enhance the images and to sharpen the detectable features. The glacier fronts were manually delineated from the orthorectified images assembled for the period 2002-2017.

Table 4.1. The Landsat and ASTER images used in this study

Landsat image scenes Date ASTER image scenes Date

L5217106_10619860301 1986/03/01 AST_L1A_00301062001132724_20151001145943_6669 2001/01/06 L4219105_10519891126 1989/11/26 AST_L1A_00301062001132733_20151001145933_6629 2001/01/06 L4219106_10619891126 1989/11/26 AST_L1A_00301062001132742_20151001145933_6622 2001/01/06 LT52191051991040XXX03 1991/02/09 AST_L1A_00301062001132750_20151001145933_6627 2001/01/06 LT52191061991040XXX03 1991/02/09 AST_L1A_00311222001131915_20151001145933_6616 2001/11/22 LT52181061997033XXX02 1997/02/02 AST_L1A_00311222001131924_20151001145933_6617 2001/11/22 L71217106_10620000127 2000/01/27 AST_L1A_00311222001131933_20151001145923_6549 2001/11/22

L71219105_10520000226 2000/02/26 AST_L1A_00311222001131942_20151001145923_6547 2001/11/22 L71219106_10620000226 2000/02/26 AST_L1A_00311072002132843_20151001145913_6494 2002/11/07 L71218105_10520011206 2001/12/06 AST_L1A_00311072002132835_20151001145923_6532 2002/11/07 L71218106_10620011206 2001/12/06 AST_L1A_00311072002132826_20151001145923_6542 2002/11/07 LE72191052002030AGS00 2002/01/30 AST_L1A_00302022003133434_20151001145913_6482 2003/02/02 LE72191062002030AGS00 2002/01/30 AST_L1A_00302022003133443_20151001145913_6477 2003/02/02 LE72171062002352EDC00 2002/12/18 AST_L1A_00302022003133452_20151001145903_6437 2003/02/02 LE72181062006034EDC00 2006/02/03 AST_L1A_00309272004131419_20151001145903_6425 2004/09/27 LE72181062007021EDC00 2007/01/21 AST_L1A_00309272004131427_20151001150023_8107 2004/09/27 LE72181062007053EDC00 2007/02/22 AST_L1A_00309272004131436_20151001150023_8105 2004/09/27 LE72181062007325EDC00 2007/11/21 AST_L1A_00309272004131445_20151001150023_8100 2004/09/27 LE72181062008360EDC00 2008/12/25 AST_L1A_00311242005132033_20151001150023_8095 2005/11/24 LE72181062010349EDC00 2010/12/15 AST_L1A_00311242005132042_20151001150023_8090 2005/11/24 LC82181062013301LGN00 2013/10/28 AST_L1A_00312082005133232_20151001150003_7001 2005/12/08 LC82191052013324LGN00 2013/11/20 AST_L1A_00312082005133241_20151001145943_6679 2005/12/08 LC82191062013324LGN00 2013/11/20 AST_L1A_00312082005133250_20151001145923_6537 2005/12/08 LC82171062014313LGN00 2014/11/09 AST_L1A_00311252006133252_20120404201926_5374 2006/11/25 LC82171062015044LGN00 2015/02/13 AST_L1A_00311252006133300_20120404201936_5449 2006/11/25 LC82181052015307LGN00 2015/11/03 AST_L1A_00311252006133309_20120404201916_5299 2006/11/25 LC82181062015307LGN00 2015/11/03 AST_L1A_00311252006133318_20120404201916_5300 2006/11/25 LC82181062016326LGN00 2016/11/21 AST_L1A_00302252008132724_20151001150013_7614 2008/02/25 LC82191052016365LGN00 2016/12/30 AST_L1A_00302252008132733_20151001150013_7612 2008/02/25 LC82191062016365LGN00 2016/12/30 AST_L1A_00302252008132742_20151001150013_7607 2008/02/25 LC82171062017001LGN00 2017/01/01 AST_L1A_00312152010132707_20120404133151_14017 2010/12/15 AST_L1A_00312152010132716_20120404133130_13719 2010/12/15 AST_L1A_00312152010132725_20120404133140_13802 2010/12/15

Due to the failure of the Scan Line Corrector (SLC), Landsat-7 ETM+ images have ~22% data gap since 2003. To compensate the inadequacy of optical images, the Synthetic Aperture

Radar (SAR) images from Envisat ASAR and ALOS PALSAR during 2004-2010 were utilized to derive the surface velocity fields over the southern ice-shelf remnant (Table 2). The Envisat ASAR

C-band images are provided as the ASAR Image Mode Precision Image Product

(ENVISAT.ASA.IMP_1P) at the European Space Agency’s Earth Online data portal. The ALOS

PALSAR L-band SAR images were obtained from the Alaska Satellite Facility data portal, which are ground range Level 1.5 Products and have been geocoded by the Japan Aerospace Exploration

Agency (JAXA). The DORIS Precise Orbit State Vectors (available at earth.esa.int) provide precise orbital information for the Envisat ASAR, and the auxiliary ASAR XCA files contain external calibration data. The Envisat ASAR images were geocoded and orthorectified using the precise orbital data and the RAMP DEM v2. The geolocation accuracy of the orthorectified SAR

images was estimated to be less than one pixel (25 m). Radar images from different satellite SAR sensors or different orbital passes may have different geometric distortion patterns and radiometric properties. The SAR images acquired by similar SAR sensors (C band or L band) on the same ascending or descending orbit passes were selected to form the sequential image pair for velocity derivation. Image co-registration was conducted between the SAR images in each pair using a set of stationary tie points. Gamma and median filters were applied to suppress the speckle noise of

SAR images, and logarithmic histogram stretching was performed to enhance the surface features on SAR images.

Table 4.2. The Envisat ASAR and ALOS PALSAR images used in this study

Envisat ASAR images Date ALOS PALSAR images Date

ASA_IMP_1PNDPA20040303_122211_000000162024_00424_ 2004/03/03 ALPSRP025545790-L1.5 2006/07/18 10498_2188 ALPSRP025545800-L1.5 2006/07/18 ASA_IMP_1PNDPA20050427_122221_000000162036_00424_ 2005/04/27 ALPSRP149095810-L1.5 2008/11/11 16510_2189 ALPSRP253245820-L1.5 2010/10/27 ASA_IMP_1PNDPA20050706_122209_000000162038_00424_ 2005/07/06 ALPSRP253245830-L1.5 2010/10/27 17512_2182 ALPSRP253245840-L1.5 2010/10/27 ASA_IMP_1PNDPA20061204_035403_000000162053_00290_ 2006/12/04 ALPSRP252225810-L1.5 2010/10/19 24893_2137

The image matching method (Bindschadler et al. 1994; Liu et al. 2012; Scambos et al.

1992) was applied to derive the surface velocity fields from temporally sequential images. This method searches matching points from co-registered sequential images acquired at different dates, measures the spatial displacements of those matching points over time, and calculates the corresponding surface flow velocities. Previous studies (Heid and Kääb 2012; Liu et al. 2012;

Rack et al. 1999; Scambos et al. 1992) have demonstrated its effectiveness for velocity derivation from both optical and radar images. The cross-correlation algorithm is commonly used for numerically identifying matching points between two images, and the matching accuracy can reach sub-pixel level (Scambos et al. 1992). The Fast Fourier Transformation can speed up the cross-

correlation computation. With the traditional method, prior knowledge of possible flow speed is required to set the initial parameters (e.g., the location and size of search window) for the image matching operation. However, a uniform setting of search parameters often generates spurious matches, particularly for the areas with heterogeneous ice flows (Liu et al. 2012).

We employed a semi-automated image matching method (Wang et al. 2016; Zhan et al.

2017) to derive the surface velocity fields. As shown in Figure 4.2, this method starts with a small number of matching points that are interactively identified through visual inspection of two sequential images. Those manually identified matching points are used to compute the optimal search space for the subsequent automated area-based image matching operation to derive a dense set of matching points for velocity computation. This method takes advantage of the high reliability of human-based visual recognition and the high efficiency and precision of computer-based automated image matching, hence particularly effective for the regions with heterogeneous ice flow patterns. For the derivation of ice velocity measurements, we used a regular grid of points with a spacing interval of 300 m as candidate matching points, and the matching chip window size was set to 64 by 64 pixels. The directional filters (Scherler et al. 2008) and local statistical filters

(Liu et al. 2012) were used for quality control to detect and remove the erroneous matches. Those matches deviating greatly from the flow directions were regarded as mismatches. The local statistical filters were applied to the two-dimensional displacement measurements on the assumption that ice motion changes continuously and smoothly over a local neighborhood. The mean (μ) and standard deviation (σ) of the x-direction displacements and the y-direction displacements were computed respectively over a local neighborhood with a specific radius. The matches whose x-direction displacement or y-direction displacement drastically deviates from the mean value were discarded. The matching results were visually inspected and verified after the

automated filtering. The valid matches are mainly distributed over the areas with surface features such as crevasses, rifts and flow band texture. The valid matches are spatially interpolated using an ordinary Kriging method to create flow velocity fields.

Figure 4.2. The data processing flowchart for deriving the surface velocity measurements from two sequential satellite images.

The subpixel level of image co-registration accuracy ensures the geolocation error of mapped glacier front to be less than 15 m. The measurement error of surface displacement by feature tracking method is influenced by image co-registration and image matching of sequential images. The co-registration accuracy of the sequential images is better than one pixel. The cross- correlation image matching algorithm can reach an accuracy of better than 0.5 pixel (Scambos et al. 1992). The total error budget for measuring the spatial displacements between matching points is estimated to be in the order of 1.5 pixels, corresponding to 45 m for Landsat-4/5 TM images,

37.5 m for Envisat ASAR images and 22.5 m for Terra ASTER, Landsat-7 ETM+, Landsat-8 OLI and ALOS PALSAR images. The velocity uncertainty varies with the displacement measurement

error and the time span of each measurement period. Most of the velocity fields were measured over 1~3 years. The velocity uncertainty is estimated to be in the range of 8.0~34.8 m/yr.

4.3.2 Detecting surface topographic changes from satellite laser altimetry and airborne LiDAR measurements

The surface elevation and slope changes of the outlet glaciers during 2002-2015 were measured using the satellite altimetry data collected by the NASA’s Ice, Cloud and Land Elevation

Satellite (ICESat-1) laser altimetry and the airborne LiDAR data collected by the NASA’s

Airborne Topographic (ATM) and Land, Vegetation and Ice Sensor (LVIS). Figure 4.3 shows the spatial coverage of each data source.

The ICESat-1, launched in 2003, carried the Geoscience Laser Altimeter System (GLAS) onboard and successfully collected high-precision laser altimetry data during a series of operational periods (campaigns) from 2003 to 2009 (Zwally et al. 2002a). GLAS emitted laser pulses toward the Earth’s surface at a frequency of 40 Hz. The laser pulses illuminated a series of footprints of ~70 m in diameter, with an along-track spacing of 170 m and an across-track spacing of ~20 km at 70° S. The vertical accuracy and precision were estimated to be ~14 cm and ~2 cm, respectively (Shuman et al. 2006). The horizontal geolocation accuracy of laser footprint could be less than 4 m on an ideal condition (Baghdadi et al. 2011; Luthcke et al. 2005). The ICESat GLA12

Version 34 data product archived in the National Snow & Ice Data Center (NSIDC) provides the surface elevation measurements for ice sheets. The measurements available for our study area span from October 2003 to November 2008. As shown in Figure 4.3a, most of the repeat ICESat tracks cross over the Larsen B outlet glaciers, forming topographic cross-section profiles.

The NASA’s Operation IceBridge (OIB) mission began in 2009, and the ATM and LVIS are two major airborne laser instruments developed for OIB missions. ATM is a conical laser

scanning system operating at a wavelength of 532 nm, and measures surface elevation at a nominal altitude of 500 m above the ground with an off-nadir scan angle of 15° (Krabill et al. 2002). The accuracy and precision were estimated to be ~6.6 cm and ~3 cm, respectively (Martin et al. 2012).

We used the Level-2 ATM data (ILATM2) acquired during October/November 2009, November

2010, and November 2011. In addition, the Pre-IceBridge mission collected the ATM data

(BLATM2) during November/December 2002, November 2004 and October 2008 over the study area. Most of the ATM flight lines were along the glacier valleys (Figure 4.3b).

LVIS is an airborne LiDAR laser scanning system operating at a wavelength of 1064 nm

(Blair et al. 1999). It collected data from an altitude of up to 10 km above the ground at a scanning angle of ~12°. The nominal footprint is 25 m in diameter, with an along-track spacing of ~25 m and an across-track spacing of ~10 m (Blair et al. 1999; Hofton et al. 2008). The accuracy of the

LVIS surface elevation measurements is better than 12 cm in comparison with the in situ DGPS measurements (Brunt et al. 2017). The OIB mission collected LVIS altimetry data over the

Antarctic Peninsula in November 2009 and October 2015. We used the Level-2 LVIS data

(ILVIS2) that were processed from the waveform-based measurements. The LVIS data collected in 2009 have a wide spatial coverage over the Hektoria, Green, Evans, Jorum and Crane Glaciers

(Figure 4.3c), and those collected in 2015 have more extensive spatial coverage yet with data gaps between the flight tracks (Figure 4.3d).

Figure 4.3. The spatial coverage of the satellite laser altimetry and airborne LiDAR data over the study area. a, The ICESat-1 data tracks during 2003-2009; b, The ATM data coverage from the Pre-IceBridge and IceBridge missions during 2002-2011; c, The LVIS LiDAR data collected in 2009; and d, The LVIS LiDAR data collected in 2015.

The ICESat-1, ATM and LVIS data were adjusted with the vertical reference to the EGM96

Geoid model to measure the surface elevation and slope changes. The ATM and LVIS measurements are less influenced by clouds and weather conditions, since the airborne flights were generally scheduled to take place in clear-sky conditions. We selected the ATM and LVIS

measurements within 200 m from the central flow line of each glacier to generate the along-flow elevation profiles of different years. The sampling distance is 100 m along the flow lines. The measurements within each distance interval were averaged to obtain the elevation value of each sampling point on the profile. Owing to the dense sampling of the LVIS data, two spatially- continuous surface elevation grids were generated for 2009 and 2015 using the ordinary Kriging interpolation method. The interpolated grids have a spatial resolution of 30 m. The surface elevation change grid was generated by subtracting the 2009 elevation grid from the 2015 elevation grid.

The accuracy of ICESat-1 data could be affected by various factors, such as forward scattering by clouds or wind-blowing snow (Duda et al. 2001; Mahesh et al. 2002; Palm et al.

2011), sensor saturation (Fricker et al. 2005), errors induced by waveform re-tracking algorithms

(Borsa et al. 2014) and topographical effect (Duan and Bastiaanssen 2013). We filtered the potentially bad data points using a combination of the data quality indicators defined by the

GLAS/ICESat science team (http://nsidc.org/data/docs/daac/glas_altimetry/data_dictionary.html).

Only the measurements that meet all the following criteria were retained for subsequent analysis.

The criteria include attitude quality indicator (i_sigmaatt=0), number of peaks (i_numPk=1), range offset quality/use flag (i_rng_UQF=0), altimeter frame quality flag (i_FrameQF<4), and saturation correction flag (i_satCorrFlg<=2). The saturation correction values (i_satElevCorr) were applied to the remaining valid measurements.

The repeat-track ICESat-1 measurements were used to examine the cross-section surface elevation changes of certain glaciers. Nevertheless, the repeat tracks from different campaigns are not exactly coincident in location, and they may be several hundred meters apart. The elevation differences between the repeat track measurements contain not only real temporal elevation

changes but also the contributions from glacier surface slopes between repeat tracks. To remove the slope effect, a reference track was selected for each site, and the repeat tracks that are within

500 m from the reference track were retained. The long-wavelength topographic information

(Slobbe et al. 2008) was considered to estimate the slope contribution on elevation differences between tracks, which can be calculated based on a trigonometric equation:

훥ℎ = 푡푎푛(훼) × 퐿 (16) where 퐿 is the distance from the reference track, and α is the long-wavelength slope estimated from the ATM elevation profiles along the glacier valley. We used the derived ATM elevation profiles to estimate the long-wavelength slope along the glacier flow direction. The ATM profile data that are within 3 km above and below the reference track were extracted for each site overpassed by

ICESat-1. The extracted ATM profiles were fitted using a linear function. The slope 훼 in Equation

(1) for each ICESat-1 data track was calculated using the estimated slope of the fitted line for the

ATM profile data of the closest acquisition date with the ICESat data. The slopes of the selected transects are in the range of 0.7 ~ 1.7 degrees, corresponding to the elevation adjustment of 1.2 ~

3.0 m when the transect is 100 m away from the reference track.

The estimation error of surface elevation change is determined from the accuracy of elevation measurements and the firn compaction. The elevation measurement accuracies of the

ICESat-1, ATM and LVIS data are better than 14 cm, 6.6 cm and 12 cm, respectively. In addition to the elevation measurement error, the accuracy in tracking real surface elevation changes is also affected by the variability in firn compaction rate, which is further controlled by accumulation, temperature and surface melting (Khazendar et al. 2015; Ligtenberg et al. 2011; Scambos et al.

2014). Scambos et al. (2014) estimated the effect of firn compaction on surface elevation change to be -19~12 cm/yr for the grounded ice of the northern Antarctic Peninsula. According to the

propagation principles of uncertainty, the uncertainty of the elevation change measurements is estimated to be less than 27.4 cm.

4.4 Results

4.4.1 Glacier front retreat and advance patterns from time-series satellite images

Figure 4.4 shows the terminus changes of the northern and central Larsen B outlet glaciers from December 2002 to January 2017. We calculated the distances and rates of retreat and advance for the terminus locations in different years along the central flow line (Table 3).

After the collapse of Larsen B Ice Shelf, most of the northern and central glaciers reached the minimum glacier area in February 2012, while the Crane Glacier reached its minimum earlier in February 2007. The Hektoria, Green and Evans Glaciers converged downstream into the ice shelf before the collapse, and then experienced similarly alternating patterns of advance and retreat: advanced during 2002-2006, 2007-2008 and 2012-2017 and retreated during 2006-2007 and 2008-2012. The most rapid retreat occurred during February-November 2006, at a recession rate of 20.2 m/d on the Hektoria Glacier, 31.4 m/d on the Green Glacier and 23.7 m/d on the Evans

Glacier. The sudden loss of ice-shelf buttressing force caused the significant advances of these three glaciers between 2002 and 2005 as a result of immediate adjustment of glacier front in response to the change in stress conditions. The dynamic thinning and increased longitudinal stretching in downstream near the terminus enhanced the formation and propagation of crevasses, preconditioning the rapid retreat in 2006. During 2008-2012, the Hektoria and Green Glaciers retreated by more than 3 km, and then advanced by 5.7 km and 9.3 km respectively during 2012-

2017.

Unlike the Hektoria, Green and Evans Glaciers, the central glaciers retreated immediately after the ice-shelf collapse and then persistently advanced. The Crane Glacier retreated by more

than 10 km during 2002-2007, and then was in advancing phase during 2008-2017, with the glacier terminus moving forward by 5.9 km. The Jorum, Punchbowl, Mapple and Melville Glaciers showed the general retreat pattern before 2012 and advance pattern between 2012 and 2017. The

Jorum and Punchbowl Glaciers retreated by 7.4 km and 2.4 km respectively between 2002 and

2012. The Jorum Glacier advanced by 1.6 km during 2012-2015, followed by a slight recession during 2015-2017. The Mapple and Melville Glaciers have less active ice flows, and the front retreat in the years immediately after the collapse was due to the sustained ice loss of the ice-shelf remnant. After 2004, the major change of the Mapple Glacier was the recession occurred during

2008-2010.

Figure 4.4. The terminus locations of the northern and central Larsen B outlet glaciers between December 2002 and January 2017. The rectangles in the middle figure show the spatial extents of

a (Hektoria, Green and Evans Glaciers), b (Jorum and Punchbowl Glaciers), c (Crane Glacier) and d (Mapple and Melville Glaciers). The central flow lines were used for calculating the retreat and advance distances and plotting the longitudinal profiles of surface velocity and elevation in Figure 4.6, 4.7 and 4.8. The glacier inlets are defined according to the grounding line and calving front positions, which are used as the reference positions to plot the longitudinal velocity and elevation profiles.

Table 4.3. Retreat and advance distances and rates of the Larsen B outlet glaciers. The retreat and advance distances were tracked using the time-series images available for each individual glacier. The rates (m/d) were calculated by dividing the retreat and advance distances (m) of the terminus by the time separation (days) of sequential images. The negative numbers with a gray background indicate glacier retreats.

Time Hektoria Green Evans Jorum Punchbowl Crane Mapple Melville

m m/d m m/d m m/d m m/d m m/d m m/d m m/d m m/d Dec 2002 Feb 2003 220 4.7 615 13.1 561 11.9 -942 -20.0 -459 -9.8 -945 -20.1 -496 -10.6 -2173 -46.2 Sep 2004 1128 1.9 -203 -0.3 1583 2.6 -4010 -6.6 -1259 -2.1 -7120 -11.8 -4090 -6.8 -6100 -10.1 Dec 2005 70 0.2 4440 10.1 2341 5.3 -1439 -3.3 -230 -0.5 -803 -1.8 -34 -0.1 -1675 -3.8 Feb 2006 70 1.2 456 7.9 -275 -4.7 -605 -10.4 -151 -2.6 -262 -4.5 Nov 2006 -6056 -20.2 -9426 -31.4 -8473 -23.7 -316 -1.1 -395 -1.1 -102 -0.3 -160 -0.5 -306 -1.0 Feb 2007 -1156 -13.4 -320 -3.7 -514 -6.0 183 3.4 -767 -14.2 -25 -0.5 -201 -3.7 Feb 2008 40 4.4 650 1.8 621 1.7 -350 -0.9 918 2.3 -145 -0.4 -415 -1.0 Dec 2008 387 1.3 -432 -1.4 637 2.1 188 0.6 -538 -1.8 97 0.3 -383 -1.3 Dec 2010 -1790 -2.5 -2600 -3.6 -623 -0.9 -202 -0.3 3 0.0 761 1.1 -776 -1.1 -338 -0.5 Feb 2012 -1796 -4.1 276 0.6 -1305 -3.0 -217 -0.5 -21 0.0 16 0.0 -320 -0.7 -443 -1.0 Nov 2013 1856 2.9 4929 7.7 833 1.3 218 0.3 175 0.3 1923 3.0 -23 0.0 283 0.4 Nov 2014 1550 4.4 1317 3.7 320 0.9 687 1.9 59 0.2 499 1.4 115 0.3 152 0.4 Nov 2015 1603 4.5 1639 4.6 353 1.0 718 2.0 -100 -0.3 1340 3.7 62 0.2 156 0.4 Jan 2017 735 1.7 1371 3.2 -436 -1.0 153 0.4 1366 3.2 56 0.1 352 0.8

4.4.2 Temporal changes of glacier velocity fields from image matching method

By applying the semi-automated image matching method to sequential satellite images, we have derived the time-series surface velocity fields for the Hektoria, Green, Evans, Jorum, Crane,

Flask and Leppard Glaciers during 1986-2017 and for the southern ice-shelf remnant during 2000-

2017. The ice velocities prior to the Larsen B collapse in 2002 were mapped over four epochs, including 1986-1989, 1989-1991, 1997-2000, 2000-2001. The extensive data coverage after 2002

allows to derive temporally dense velocity measurements over a continuous period with a time separation of 1~2 years between sequential images. Figure 4.5 shows the ice velocity maps for the periods of 2001-2002, 2013-2014/2015, and 2015-2017. The longitudinal velocity profiles extending from the upper reach to the ice front along the central flow line of each glacier were plotted to examine the temporal variations of velocity fields (Figure 4.6 and Figure 4.7). The velocity profiles for the Flask and Leppard Glaciers include the downstream flow units on the ice- shelf remnant as well. The velocity values on each profile were computed at a sampling distance of 250 m by averaging the valid measurements within each distance interval. The data gaps on the profiles are due to the absence of detectable surface features or radical change in surface texture.

The comparison of the longitudinal velocity profiles for the four epochs prior to the ice- shelf collapse shows that the outlet glaciers had no significant temporal variations in flow velocity throughout the entire glacier stretch, indicating stable ice motion of the outlet glaciers before the collapse event. The ice-shelf collapse triggered immediate flow speedups on the Hektoria, Green,

Evans, Jorum and Crane Glaciers, as also documented by previous studies (Rignot et al. 2004;

Scambos et al. 2004). Comparing the pre-collapse period February 2000-December 2001 with the post-collapse period December 2001-December 2002, the Hektoria and Green Glaciers accelerated by 73% (140 m/yr) and 109% (322 m/yr) on average at the upstream location of 5 to 10 km from the reference inlets, respectively. The Jorum and Crane Glaciers had 35% and 55% velocity increase near the calving front, respectively.

The northern Hektoria and Green Glaciers had almost simultaneous changes of surface velocity. Both glaciers accelerated for a decade during 2002-2012 and then decelerated during

2012-2017 (Figure 4.6a and b). The detected peak flow velocities occurred during 2010-2012. The average velocity was 1443 m/yr at the upstream distance of 10-15 km on the Hektoria Glacier

during 2010-2012, which was increased by 708 m/yr (96%) compared with the previous period

2008-2010. Afterwards, the average velocity of the same region was decreased to 879 m/yr during

2012-2013, 632 m/yr during 2013-2014, 510 m/yr during 2014-2015, and 487 m/yr during 2015-

2017. The flow decelerations between 2012 and 2015 occurred throughout the upstream and downstream reaches, and the maximum deceleration magnitude was 39% from the period 2010-

2012 to the period 2012-2013. The velocity profile for the period 2015-2017 shows the insignificant changes in the upstream reach and the slight slowdown near the calving front compared with the previous period 2014-2015. The Green Glacier had similar acceleration and deceleration patterns, and the most recent velocity measurements over the period 2015-2017 indicate much smaller velocity variations than the previous years. From the front to the upper reach of 10 km, the average velocity along the central flow line of the Green Glacier was 1494 m/yr during 2013-2014, 1280 m/yr during 2014-2015, and 1262 m/yr during 2015-2017, which were nearly twice as fast as the velocity of 688 m/yr during December 2001-December 2002, and corresponding to a fourfold~fivefold acceleration comparing with the pre-collapse periods.

The slowdown of the central Jorum and Crane Glaciers began earlier than the northern

Hektoria, Green and Evans Glaciers. The acceleration of the Jorum Glacier immediately following the ice-shelf collapse was confined to the lower floating part near the calving front. The continued retreat from 2002 to 2004 induced the acceleration propagating upstream as a consequence of stress perturbation. Figure 4.6c indicates that the Jorum Glacier reached a peak flow velocity during 2006-2008, followed by constant deceleration during 2008-2015. The Crane Glacier showed an acceleration pattern from 2002 to 2007 and a deceleration pattern from 2007 to 2017

(Figure 4.6d). The deceleration magnitude was greatly reduced after 2014. The average velocity was about 1200 m/yr near the calving front during 2014-2017, which roughly doubled the pre-

collapse velocity. The maximum measured flow velocity on the Crane Glacier occurred in the summer season of 2007 (November 2006-February 2007), during which the terminus velocity reached 4350 m/yr and the spatial extent of flow acceleration extended about 40 km up-glacier.

Figure 4.6d shows the steep along-flow velocity gradient extending for 18 km up-glacier from its terminus. The along-flow strain rate of this section of the galcier was 0.25 yr-1 on average, suggesting the strong longitudinal stretching in the downstream area of the Crane Glacier.

Figure 4.5. Surface velocity maps of the Larsen B outlet glaciers and the southern remnant of the Larsen B Ice Shelf (selected periods).

Figure 4.6. The longitudinal velocity profiles of the Hektoria, Green, Jorum and Crane Glaciers during 1986-2017.

Surface velocities of the southern Flask and Leppard Glaciers over the period 2000-2017 are shown in Figure 4.7. The longitudinal velocity profiles of these glaciers are extended to include the corresponding flow units on the ice-shelf remnant. The southern ice-shelf remnant fed by the

Flask and Leppard Glaciers continued retreating and accelerating after the collapse. Due to calving events, the total area of the southern remnant was reduced by about 1100 km2 (35%) during 2002-

2017. An iceberg with an area of 600 km2 calved off in early 2006 (Shuman et al. 2011). The ice- shelf remnant had persistently accelerated during 2001-2015, while the flow velocity was decreased from the period 2013-2015 to the period 2015-2017. The ice-shelf flow velocity was

365 m/yr during 2000-2001 at the downstream distance of 20 km on the flow unit fed by the Flask

Glacier, which increased to 730 m/yr during 2013-2015 and then decreased to 615 m/yr during

2015-2017. In comparison, the ice-shelf flow unit fed by the Leppard Glacier had smaller velocity variations after the calving event in 2006, which could be attributed to the lateral dragging effect from the near-stagnant ice-shelf area in the north of Jason Peninsula.

The primary velocity changes of the Flask and Leppard Glaciers occurred near the grounding line (inlet). Both glaciers accelerated significantly since the period 2005-2006, which was concurrent with the large calving event of the ice-shelf remnant. The Flask Glacier had a higher magnitude of velocity increase, which was about 200 m/yr near the grounding line over the entire observational periods, in comparison with the velocity increase by about 100 m/yr near the grounding line of the Leppard Glacier. The flow velocity of the Flask Glacier was 512 m/yr at the upstream distance of 2 km during 2004-2005, and was increased to 580 m/yr during 2005-2006.

Afterwards, the Flask Glacier continued accelerating, with a velocity of 683 m/yr at the same location during 2013-2015. The flow acceleration of the Leppard Glacier was most pronounced during 2005-2006. Although the velocity continued increasing in later periods, the increase rate was much less than that of the Flask Glacier.

Figure 4.7. The longitudinal velocity profiles of the Flask and Leppard Glaciers and the corresponding downstream ice-shelf flow units over the period 2000-2017.

4.4.3 Temporal evolution of glacier topography from satellite laser altimetry and airborne LiDAR

The flow accelerations of the outlet glaciers have not only increased the ice discharge into the ocean, but also changed the surface topography and ice thickness. The variations in surface topography and ice thickness would change the driving forces of the glaciers, which in turn provides a feedback mechanism to adjust the ice flow pattern. Figure 4.8 shows the temporal

changes of surface topography along the flow directions of the Hektoria, Green, Crane, Melville,

Flask and Leppard Glaciers derived from the airborne ATM and LVIS LiDAR data. The ICESat-

1 and LVIS topographic transverse profiles across the Green, Evans, Melville, Flask and Leppard

Glaciers were plotted in Figure 4.9. The locations of the cross-sections for the transverse profiles are shown in Figure 4.3a and marked as black crosses in Figure 4.8. The cross-sections generated by ICESat-1 data tracks are roughly perpendicular to the flow directions of the outlet glaciers.

Both the longitudinal profiles in Figure 4.8 and the transverse profiles in Figure 4.9 indicate that the Hektoria, Green, Evans, and Crane Glaciers had experienced dramatic thinning due to flow acceleration after turning into marine-terminating glaciers. Between 2004 and 2015, the Hektoria

Glacier thinned up to 210 m at the location of 17 km upstream (Figure 4.8a), and the Green Glacier thinned about 170 m at the location of 14 km upstream (Figure 4.8b). The ice surface of the Evans

Glacier was lowered by 38.5m (at the rate of 8.6 m/yr) on average along the cross-section overpassed by ICESat-1 during 2004–2008 (Figure 4.9b). The Crane Glacier thinned about 172 m at the location of 11 km upstream during 2002–2015 (Figure 4.8c).

The along-flow longitudinal elevation profiles reveal that the northern outlet glaciers had a different thinning pattern from the central outlet glaciers (Figure 4.8a, b, c and d). The surface elevation of the Hektoria and Green Glaciers had been constantly decreased, except the downstream area near the calving front where the elevation was increased recently due to glacier advancing. The location of maximum thinning on the Hektoria Glacier has migrated upstream, which was at the upstream location of 13 km during 2004–2008 (with a thinning rate of 20.6 m/yr),

17 km during 2010–2011 (with a thinning rate of 53.1 m/yr) and 21 km during 2011–2015 (with a thinning rate of 15.3 m/yr). The most rapid thinning of the Hektoria Glacier occurred during 2010–

2011 immediately before the time of minimum glacier area and maximum flow velocity. The

Green Glacier had the fastest thinning during 2008–2009, with a thinning rate of 23.5 m/yr at the upstream location of 15 km. Most of the thinning on the Crane Glacier occurred at the downstream area near the calving terminus, and the thinning amplitude decreased gradually with the distance to the terminus (Figure 4.8c). The Crane Glacier had the highest thinning rate during October 2004

– February 2005, which was 118.7 m/yr at the upstream location of 10 km. After 2008, the thinning of the Crane Glacier was much reduced, being consistent with the phase of front advancing and flow deceleration. Other glaciers in the central section like the Melville glacier had relatively small thinning rate.

In comparison, the southern Flask, and Leppard Glaciers had much less surface lowering

(Figure 4.8e and f). Overall, the Flask and Leppard Glaciers thinned only about 22 m and 31 m near the grounding line, respectively. The highest thinning rate on the Flask Glacier occurred during 2008–2009, estimated to be 13.5 m/yr near the grounding line. Afterwards, the maximum thinning location propagated upstream, and the downstream area near the grounding line was thickened at a rate of 2.3 m/yr during 2009–2011. The thinning rate of the Leppard Glacier was

8.8 m/yr near the grounding line during 2008–2009, which was decreased to 1.4 m/yr during 2009–

2015.

The densely-sampled airborne LVIS LiDAR data provide a regional view of the surface elevation change between 2009 and 2015 over the Hektoria, Green, Evans, Punchbowl, Jorum,

Crane, Mapple and Melville Glaciers (Figure 4.10). The thinning amplitude of these outlet glaciers decreased from north to south in general, with the most widespread and radical thinning occurred on the Hektoria and Green Glaciers. The average changes of surface elevation from 2009 to 2015 were -58.0 m (Hektoria), -47.2 m (Green), -19.9 m (Evans), -4.5 m (Punchbowl), -7.4 m (Jorum),

-9.4 m (Crane), 0.0 m (Mapple) and -1.0 m (Melville), respectively. The smaller magnitude of

surface elevation reduction in the downstream area of the Hektoria, Green and Crane Glaciers indicates the dynamic thinning propagating upstream after the rapid retreat and thinning in the first few years following the ice-shelf collapse.

The dynamic thinning of the outlet glaciers has not only reduced the ice thickness but also changed the surface slope. Figure 4.8a and b show that the surface slopes of the lower trunks of the Hektoria and Green Glaciers were greatly reduced in 2015 compared with previous years. This reduction is consistent with the observation of ice slowdown and stabilization of the flow velocities in recent years. We calculated the long-wavelength surface slopes of different years by subdividing the ATM longitudinal elevation profiles into different sections from upstream to downstream based on the general trend of surface topography. The driving force is positively related to the surface slope (sin 휃). On the Green Glacier (Figure 4.8b), the estimated sin 휃 for the downstream section extending 17 km from the calving terminus is 0.020 in 2004, 0.019 in 2008, 0.026 in 2009, and 0.010 in 2015. The ice surface was steepened over time due to the thinning near the terminus before 2009, which corresponded to the flow acceleration stage. With continued ice loss, flow acceleration and ice thinning propagated upstream and gradually flattened the whole downstream area. If we assume that the change of ice thickness is negligible compared with the total ice thickness, the reduced surface slope would decrease the driving force by half in 2015. Similarly, the surface slope of the downstream area of the Hektoria Glacier was much reduced as well (Figure

4.8a). The sin 휃 of the downstream extending about 10 km from the terminus was decreased from

0.019 in 2004 to 0.005 in 2015. On the Crane Glacier (Figure 4.8c), the surface slope of the downstream increased from 2002 to 2004 and then decreased, and in contrast, the surface slope of the upstream had been increasing from 2002 to 2015. The flow deceleration and the tendency to

be stable could be explained by the decrease of ice thickness and surface slope because of the mutual adjustment between flow velocity and surface topography.

Figure 4.8. The along-flow longitudinal surface elevation profiles from the ATM and LVIS LiDAR data for the Hektoria, Green, Crane, Melville, Flask and Leppard Glaciers. The black-cross marks indicate the locations where the ICESat-1 cross-sections intersect with the along-flow profiles.

Figure 4.10. The surface elevation changes of the outlet glaciers between 2009 and 2015 derived from the LVIS elevation grids.

4.5 Discussion

We extended the ice velocity for the Larsen B outlet glaciers back to 1986, and the pre- collapse velocity measurements over four epochs indicate that those outlet glaciers were stable without significant velocity variations before the collapse event, suggesting that they were in equilibrium state. The collapse of the northern and central Larsen B Ice Shelf in 2002 resulted in the abrupt loss of ice-shelf buttressing force for the outlet glaciers, which broke down their equilibrium and triggered the immediate and widespread flow accelerations. The glaciers previously feeding the collapsed parts turned into marine-terminating glaciers, and became more sensitive to the atmospheric and oceanic warming. Our time-series velocity measurements reveal a decade-long acceleration of the northern Hektoria and Green Glaciers after the ice-shelf collapse.

The flow acceleration of the central Crane Glacier lasted until 2007, five years after the collapse.

Our observations of the initial acceleration phase are consistent with previous studies. Scambos et al. (2004) and Rignot (2004) documented the near-instantaneous flow accelerations of the glaciers in response to the ice-shelf collapse. Rott et al. (2011) mapped the glacier velocities in the years

2007 to 2010 from TerraSAR-X images and compared with the pre-collapse velocities in 1995 and

1999 retrieved from ERS-1/2 SAR images. They concluded that the Larsen B tributaries experienced significant acceleration during 2007-2010 and showed no signs of slowing down.

Further, we found that both northern and central glaciers entered the deceleration phase after their flow velocity reached peak value. The deceleration of the northern Hektoria and Green Glaciers was persistent between 2012 and 2015 (Figure 4.11a), while the central Crane Glacier started decelerating in 2007 (Figure 4.11b).

The detected deceleration pattern is in agreement with the study by Wuite et al. (2015) who mapped the post-collapse velocity fields of the glaciers mainly for the period from 2007 to 2013 and observed the deceleration of the Crane Glacier since mid-2007. Our study further extended the

temporal coverage of the velocity measurements up to 2017. The velocity measurements for the most recent four years show that the flow velocity of the Crane Glacier has been stabilized without much variations during 2014-2017, and that the deceleration rates of the Hektoria and Green

Glaciers have been decreasing and their flow velocities tend to be stable (Figure 4.11). This indicates that these northern and central outlet glaciers have been close to a new equilibrium state.

The time-series velocity data over the past three decades reveal the dynamic evolution processes of the outlet glaciers: initial pre-collapse equilibrium phase, post-collapse acceleration phase, post- collapse deceleration phase, and new post-collapse equilibrium phase. Figure 4.11 indicates that the velocities of the outlet glaciers in new equilibrium state are significantly higher than those in original equilibrium prior to the ice-shelf collapse.

Figure 4.11. Temporal evolution of surface flow velocity and elevation of the Hektoria and Crane

Glaciers.

Glacier accelerations are generally explained by melting percolation (Zwally et al. 2002b) and stress perturbation (Thomas 2004) mechanisms. The melting percolation mechanism attributes the glacier acceleration to the enhanced basal sliding when surface meltwater percolates through ice crevasses and reaches glacier bed with the increased atmospheric warming. The stress

perturbation mechanism suggests that the glacier terminus retreat and/or ice-shelf disintegration reduce the buttressing force at downstream and thus lead to glacier flow speedups. Previous studies suggested that the effect of surface melting on the flow dynamics of the Larsen B glaciers was trivial, as seasonal variations in velocity were barely detected (Rott et al. 2011). The immediate and widespread acceleration responses of the northern and central glaciers to the ice-shelf collapse indicate that the stress perturbation due to the failure and collapse of the ice shelf is the primary trigger initiating the dramatic changes of the outlet glaciers. These outlet glaciers were mostly retreating during the years following the collapse and became advancing in recent years, except for the Hektoria, Green and Evans Glaciers that experienced alternating patterns of retreat and advance. The temporal analyses on glacier fronts and flow velocities reveal a strong correspondence between front retreat and flow speedup as well as between front advance and flow deceleration. The terminus recession of the outlet glaciers after becoming marine-terminating generally coincided with the flow acceleration. This suggests that the stress perturbation due to the change in glacier terminus also considerably influenced the glacier flow dynamics.

The temporal change analysis of the glacier front, flow velocity and surface topography allows to investigate the negative feedback mechanism for the outlet glaciers to self-regulate their dynamic behaviors and to reach new equilibrium state. The dramatic glacier accelerations immediately after the ice-shelf collapse induced the widespread thinning. The northern and central outlet glaciers had much higher thinning rates than those southern glaciers. The maximum surface elevation reduction is over 210 m for the Hektoria Glacier, and over 170 m for the Green and Crane

Glaciers. The flow acceleration and ice thinning propagated along the glacier channel upstream.

Overall, the accumulated thinning magnitude decreases from the downstream reach to the upstream reach. For the northern glaciers, the significant thinning occurred throughout the entire

channel. For the central glaciers like the Crane Glacier, the major thinning concentrated in the downstream reach. The southern glaciers did not experience dramatic thinning. The dynamic thinning process led to the reduction of ice thickness of the outlet glaciers. In addition, the analysis of the along-flow longitudinal profiles shows that the variable thinning rate along the glacier valley has changed the surface slope. The longitudinal surface slopes of the outlet glaciers became smaller in later periods, particularly in the downstream reaches. The decrease in ice thickness and surface slope of the outlet glaciers considerably reduced the driving force, thus serving as a negative feedback mechanism to slow down the ice motion. The self-regulations and adjustments of the outlet glaciers, including the decrease of ice thickness and surface slope, and the advance of glacier front, provide negative feedback effects, driving the glaciers to slow down.

Our analysis also suggests that the time span for an outlet glacier to reach a new steady state is probably controlled by the geometric configurations of the outlet glacier. The wide-bay geometric setting makes the northern Hektoria and Green Glaciers more vulnerable to the stress perturbations than the central Jorum and Crane Glaciers that terminate in deep and narrow fjords.

The side walls exert more lateral shear stresses to balance the driving force on the glaciers that are confined in deep valleys than on the glaciers that flow into wide bays. The front retreat and ice thinning near the calving front would make the wide-bay glaciers more sensitive to the stress condition change, thus leading to flow speedups propagating more rapidly up-glacier. The prolonged flow speedups caused the dramatic thinning of the outlet glaciers, as evidenced by the time-series surface elevation measurements. The maps of surface elevation change between 2009 and 2015 (Figure 4.10) indicate the most widespread and dramatic lowering of the Hektoria, Green and Evans Glaciers over the entire drainage basins. Figure 4.11 shows that the variations of surface velocity and ice thickness converged faster on the Crane Glacier, suggesting the importance of the

geometric configuration of the glacier embayment in affecting the time to reach new steady state.

The glacier bed may be another factor in influencing the time span to reach the new steady state.

Glaciers resting on a retrograde bed are more inclined to the unstable and irreversible retreat

(Weertman 1974), for instance, the glaciers flowing into the Amundsen Sea sector in West

Antarctica (Favier et al. 2014; Joughin et al. 2014; Rignot 2001). The available information about the bed topography of the Larsen B outlet glaciers is limited, and the effect of the glacier bed condition needs to be examined in the future with better bed data set.

The continued retreat and speedup of the southern ice-shelf remnant hint at its evolving instability towards its ultimate demise. The southern remnant was also characterized by enhanced fracturing (Khazendar et al., 2015) and thinning (Fricker and Padman 2012) after the collapse of the northern and central parts. Khazendar et al. (2015) investigated its stress condition changes using numerical modeling, and revealed the weakening of shear margins and the reduction of ice- shelf buttressing force. The enduring speedups of the southern remnant could be explained by the decoupling of the flow units fed by the Flask and Leppard Glaciers, due to mechanical weakening along the shear margins. The decrease in backstress due to front retreat and ice-shelf weakening induced the flow accelerations of the Flask and Leppard Glaciers. Both glaciers had accelerated significantly during the period 2005-2006, which coincided with the large calving event occurred at the ice front of the southern remnant. This observation confirms the ice-shelf buttressing effect on the upstream outlet glaciers. Since 2007, the Flask and Leppard Glaciers behaved differently.

The Flask Glacier continued accelerating near the grounding line, while the Leppard Glacier had much smaller velocity variations. Such dissimilarity of flow behavior has been attributed to the different bed topographies and different degrees of grounding (Farinotti et al. 2013; Khazendar et al. 2015).

4.6 Conclusions

Investigating glacier dynamics in response to ice-shelf retreat and disintegration is fundamentally important for assessing and predicting the mass balance of the Antarctic Ice Sheet in the context of climate warming. This study examined the temporal evolution of the Larsen B outlet glaciers and the southern ice-shelf remnant over three decades, mainly after the catastrophic collapse of the Larsen B Ice Shelf. The multi-source remote sensing data (i.e., Landsat and ASTER optical images, Envisat ASAR and ALOS PALSAR radar images, ATM and LVIS LiDAR data, and ICESat-1 altimetry measurements) over the past three decades were integrated to investigate the changes of calving front, flow velocity and surface topography.

The time-series velocity data reveal the evolving flow dynamics of the Larsen B outlet glaciers before the after the ice-shelf collapse. The northern and central outlet glaciers that became marine-terminating have experienced the pre-collapse equilibrium, post-collapse acceleration, post-collapse deceleration stages, and are close to new equilibrium state after the collapse. The post-collapse acceleration phase of the northern Hektoria and Green Glaciers had lasted for a decade. In contrast, the central Jorum and Crane Glaciers had accelerated for about five to six years before the post-collapse deceleration stage. In the recent two years, the flow velocities of these outlet glaciers tend to be stabilized, although they are significantly higher than those in pre- collapse equilibrium phase. The southern Flask and Leppard Glaciers flowing into the ice-shelf remnant at SCAR Inlet had accelerated and thinned in response to the reduction of buttressing force caused by the continued retreat and weakening of the ice-shelf remnant. The observed strong correspondence between the glacier flow speedup and the ice-shelf retreat/collapse and the glacier terminus retreat suggests the predominating role of stress perturbation in affecting the flow dynamics of the Larsen B outlet glaciers.

The change analysis of the flow velocities and surface elevations indicates the self- adjustment process of the glaciers to regulate the ice flows in response to the rapid change in stress conditions through a negative feedback mechanism between flow speedup and dynamic thinning.

The larger outlet glaciers in the northern and central parts have lowered for hundreds of meters, while the smaller and southern outlet glaciers have very modest changes in surface elevation. The dynamic and differential thinning of the outlet glaciers changed the spatial distribution of ice thickness and surface slope. The decrease in ice thickness and surface slope due to the sustained flow speedups eventually reduced the driving force and induced the slowdown of ice motion. The comparison between the northern and central outlet glaciers suggests that the geometric configuration of the glacier outlet, where the grounded ice flows into the ocean, probably affects the time span for an outlet glacier to reach a new equilibrium after the ice-shelf collapse. The northern Hektoria, Green and Evans Glaciers that flow into a wide bay exhibited an alternating pattern of retreat and advance, and had the most dramatic thinning in comparison with other glaciers. The Hektoria and Green Glaciers had been decelerating and advancing since 2012, while the flow acceleration of the central Crane and Jorum Glaciers that flow into deep and narrow fjords had halted much earlier.

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