An Integrated Approach to Determining Short-Term and Long-Term Patterns of Surface Change and Flow Characteristics for a Polythermal Arctic Glacier

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2013-07-15 An Integrated Approach to Determining Short-Term and Long-Term Patterns of Surface Change and Flow Characteristics for a Polythermal Arctic Glacier

Whitehead, Kenneth Lindsay

Whitehead, K. L. (2013). An Integrated Approach to Determining Short-Term and Long-Term Patterns of Surface Change and Flow Characteristics for a Polythermal Arctic Glacier (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24905 http://hdl.handle.net/11023/812 doctoral thesis

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UNIVERSITY OF CALGARY

An Integrated Approach to Determining Short-Term and Long-Term Patterns of Surface Change and Flow Characteristics for a Polythermal Arctic Glacier

Kenneth Lindsay Whitehead

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES

IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF GEOGRAPHY

CALGARY, ALBERTA

JULY, 2013

A combination of remote sensing and in-situ data collection techniques were used

to characterise the surface dynamics, as well as the seasonal and long-term melt patterns

of Fountain Glacier, a polythermal arctic glacier located on Bylot Island in Canada's

Nunavut Territory. The techniques used are presented as part of an integrated system,

designed to measure key parameters relating to the overall health of the glacier system

and to establish long and short-term trends.

This work contributes to the knowledge-base for arctic research in that it provides

an integrated and logical approach to gathering information aimed at establishing both

spatial and temporal patterns of change. By making use of ground-based time-lapse

photography to measure the surface elevations of targets on the glacier surface, detailed

patterns showing the seasonal changes in ice thickness were revealed. By combining this

with the longer-term picture obtained from comparing surface elevations from historical

aerial photography long and short-term patterns of surface change were established.

A number of other innovative techniques were also used, including the use of an

Unmanned Aerial Vehicle (UAV) to produce detailed orthophotos and surface elevations for the glacier terminus region, as well as the production of a left-looking RADARSAT-2

interferogram, which made it possible to determine the full 3D-motion field over most of

the glacier.

ii The techniques used in this analysis are naturally complementary and are

optimised for the study of slow-moving arctic glaciers. Similar studies can be used to provide much-needed data on glacier-health throughout the Canadian Arctic, with little modification being required. Such information will help to fill in gaps in contemporary knowledge with respect to the short and long-term effects of climate change in this rapidly-changing region.

iii Acknowledgements

Producing a PhD thesis is not a trivial undertaking. This project has been my main focus over the last few years. Most of that time I have been working as well, trying to come to some kind of balance between the conflicting demands of academia, income generation, and family. That this thesis has seen the light of day at all is testament to many compromises made, and also the help and support of many people.

Firstly I would like to thank my supervisor, Dr Brian Moorman for his support and encouragement. In particular I thank him for taking a gamble that someone working from home in the wilds of British Columbia, who had last been in university in 1987, would one day mange to produce a completed PhD thesis. This is a condition I believe few other potential supervisors would have been willing to entertain. Brian’s enthusiasm for this project, and his support and guidance at all stages were essential in ensuring a successful outcome.

I would like to thank the members of my graduate committee; Dr John Yackel, Dr

Shawn Marshall, and Dr Ayman Habib for their contributions. By providing advice and critical feedback on my initial proposal, and at the final thesis defence, they helped to ensure the scientific integrity of this thesis and the overall success of the project. I would also like to thank my external examiner Dr Roger Wheate from the University of

Northern BC for his comments and input, which also served to improve the quality of the

iv final version. Above all, simply having feedback from everyone involved during the final defence has given me the confidence to submit this thesis in its current form.

I also wish to thank my fellow student (now Dr) Pablo Wainstein for his informal advice, for his collaboration on numerous different projects, and above all for the time spent in the field on Bylot Island, which has definitely been a highlight of the past few years.

I owe a debt of gratitude to the following organisations, which provided me with financial or in-kind support:

• The Natural Sciences and Engineering Research Council (NSERC), who funded

much of the research presented in this thesis through their grant provided to Dr

Brian Moorman.

• The Institute for Sustainable Energy, Environment, and Economy (ISEEE) who

provided a salary to me for two years of this project, and who’s generosity

enabled the purchase of a dedicated InSAR processor.

• The Northern Science Training Program (NSTP), who provided financial support

for travel and accommodation in the field.

• The Polar Continental Shelf project (PCSP), who provided logistical support for

our time in the arctic.

• Parks Canada, and in particular the personnel of Sirmilik National Park, who

provided us with logistical support, and took a personal interest in the work we

carried out.

v • Accuas Services inc., who introduced me to the potential of Unmanned Aerial

Vehicles (UAVs), provided me with access to high-end photogrammetric

software, and who were brave enough to provide me with a UAV to take to Bylot

Island.

Lastly I would like to acknowledge my long-suffering wife La, and my children

James and Lindsay. More than anyone else my family were impacted by my studies, and yet I could not have completed this thesis without their support. I thank them for their patience and apologise for all the things that the last few years have not brought; the house maintenance, the stability of a regular income, free weekends, and vacations that don’t involve tents, to name but a few. I hope that the next few years will prove that their patience was justified.

vi Table of Contents

Abstract ...... ii

Acknowledgements ...... iv

Table of Contents ...... vii

Table of Figures...... xii

List of Tables ...... xv

List of Acronyms used ...... xvii

Chapter 1: Introduction ...... 1

1.1 Synopsis ...... 1 1.2 Background ...... 1 1.3 Overall objectives ...... 8 1.4 Structure of thesis ...... 10 1.5 Description of study area ...... 12

Chapter 2: Determination of Surface Thinning and Surface Dynamics Using Aerial Photogrammetry ...... 18

2.1 Introduction ...... 18 2.1.1 Feature tracking...... 19 2.1.2 On-demand photogrammetric surveys ...... 21 2.2 Outline ...... 22 2.3 Methodology ...... 23 2.3.1 1982 photography ...... 23 2.3.2 1958 photography ...... 26 2.3.3 UAV survey ...... 29 2.3.4 Helicopter survey ...... 31 2.3.5 Data comparisons ...... 34 2.3.6 Ice flow analysis using feature tracking ...... 34 2.3.7 Accuracy estimates...... 35 2.4 Results ...... 38 2.4.1 Terminus region ...... 40

vii 2.4.2 Ice flow ...... 45 2.5 Discussion ...... 47 2.6 Conclusions ...... 52

Chapter 3: Using Oblique Photogrammetry to Monitor the Seasonal Decay of a Proglacial Icing ...... 55

3.1 Introduction ...... 55 3.2 Objectives ...... 62 3.3 Photogrammetric theory ...... 63 3.3.1 Single-photo resection ...... 66 3.3.2 Inner orientation ...... 67 3.3.3 Determination of 2D-photo and 3D-ground positions for a single photo 69 3.4 Methodology ...... 70 3.4.1 Camera set up ...... 70 3.4.2 Photo retrieval and control survey ...... 72 3.4.3 Camera calibration ...... 73 3.4.4 Processing ...... 74 3.4.4.1 Orientation of the reference photographs ...... 74 3.4.4.2 Determination of orientation parameters for the remaining photographs ...... 77 3.4.4.3 Orthophoto generation ...... 78 3.5 Verification ...... 83 3.6 Results ...... 83 3.6.1 Assessment of the rotational instabilities for each camera station...... 85 3.6.2 Variations in focal length over time...... 86 3.7 Discussion and conclusions...... 89

Chapter 4: Using Oblique Photogrammetry to Characterise Glacier Surface Dynamics and Elevation Changes ...... 93

4.1 Introduction ...... 93 4.1.1 Stereo photogrammetry ...... 93 4.1.2 The effect of baseline length and convergence on measurement accuracy ...... 96 4.1.3 Elevation measurement from a single photograph ...... 98 4.1.4 Focal length and principal point drift ...... 98 4.1.5 Analysis strategy for determining accurate relative target positions ..... 100 4.2 Objectives ...... 101

viii 4.3 Methodology ...... 102 4.3.1 Fieldwork ...... 102 4.3.1.1 August 2008 ...... 102 4.3.1.2 June / July 2009 ...... 104 4.3.1.3 June / July 2010 ...... 105 4.3.1.4 June 2011 ...... 107 4.3.2 Data retrieved ...... 107 4.3.3 Data Processing ...... 108 4.3.3.1 Measurement year one: 20 August 2008 - 20 June 2009 ...... 108 4.3.3.2 Measurement year two: 24 June 2009 – 29 June 2010 ...... 112 4.3.3.3 Measurement year three: 10 July 2010 - 29 June 2011 ...... 115 4.3.4 Calculating three year surface elevation changes ...... 118 4.3.4.1 Estimation of surface melt rates ...... 119 4.3.4.2 Compensation for the vertical component of down-glacier motion ...... 120 4.3.5 Measuring horizontal motion ...... 121 4.4 Results ...... 122 4.4.1 GT1 ...... 122 4.4.2 GT2 ...... 124 4.4.3 GT3 ...... 130 4.4.4 GT4 ...... 130 4.4.5 GT5 ...... 134 4.4.6 GT6 ...... 139 4.4.7 GT7 ...... 142 4.4.8 GT8 ...... 145 4.4.9 GT9 ...... 149 4.4.10 GT10 ...... 152 4.4.11 Comparing measurement year two and three elevation changes for each target ...... 152 4.4.12 DEM generation and comparison ...... 161 4.5 Accuracy Assessment and Sources of Error ...... 165 4.5.1 Photo measurement errors ...... 165 4.5.2 The effect of baseline length on the accuracy of intersected positions ... 166 4.5.3 The effect of errors in XY position on elevation ...... 168 4.5.4 The effect of focal length variations...... 169 4.5.5 Stability of camera stations ...... 170 4.5.6 Snow cover and poor visibility ...... 171 4.5.7 GPS errors ...... 173 4.5.8 Target lean and target collapse ...... 174 4.5.9 Atmospheric effects ...... 175 4.5.10 Overall accuracy ...... 175

ix 4.5.11 Potential errors in the DEMs produced...... 176 4.6 Discussion and conclusions...... 177

Chapter 5: Using a Combined SAR Interferometry and Feature Tracking Approach to Measure Glacier Surface Displacement ...... 181

5.1 Introduction ...... 181 5.1.1 Single-pass interferometry ...... 182 5.1.2 Repeat-pass interferometry ...... 183 5.1.3 Generation of interferograms ...... 184 5.1.4 Image pair selection ...... 185 5.1.5 Interferogram unwrapping...... 186 5.1.6 InSAR geometry ...... 186 5.1.6.1 Extracting topography ...... 188 5.1.6.2 Extracting LOS displacement ...... 190 5.1.7 Sources of error associated with SAR interferometry ...... 191 5.1.7.1 Effects of DEM and baseline errors on displacement estimates ...... 191 5.1.7.2 Errors arising from atmospheric conditions ...... 193 5.1.7.3 Variations in penetration depth ...... 194 5.1.7.4 Spatial and temporal decorrelation ...... 194 5.1.8 Deriving motion vectors from LOS displacements ...... 195 5.1.8.1 Determination of the full 3D displacement field using interferograms from multiple look directions ...... 197 5.1.9 Feature tracking...... 200 5.1.10 Radar satellites suitable for interferometry ...... 202 5.2 Research using InSAR and feature tracking for the study of glacial motion 208 5.3 Objectives ...... 214 5.4 Methodology ...... 215 5.4.1 Imagery used ...... 215 5.4.2 ERS-1 processing ...... 220 5.4.3 TerraSAR-X processing ...... 224 5.4.4 RADARSAT-2 processing...... 228 5.4.5 Determining the full 3D motion field for Fountain Glacier using multi- track interferometry ...... 231 5.4.6 Feature tracking of TerraSAR-X amplitude images ...... 234 5.4.7 Feature tracking of SPOT-5 panchromatic images ...... 235 5.4.8 Determining changes in horizontal and vertical motion ...... 236 5.5 Results ...... 239 5.5.1 3D motion analysis ...... 239

x 5.5.2 Feature tracking...... 242 5.5.3 Projection of centre-line displacements...... 245 5.5.3.1 Projected residual vertical displacements ...... 249 5.6 Error assessment ...... 253 5.6.1 Acquisition errors ...... 253 5.6.2 DEM errors ...... 253 5.6.3 Phase unwrapping errors ...... 255 5.6.4 Errors affecting the determination of the vertical displacement ...... 256 5.6.5 Combined error for InSAR measurements ...... 257 5.6.6 Errors associated with feature tracking ...... 258 5.7 Discussion and conclusion ...... 260

Chapter 6: Integrating Data from Different Sources ...... 263

6.1 Introduction ...... 263 6.2 Comparison of results obtained through independent measurements ...... 265 6.2.1 Comparison of down-glacier flow estimates...... 266 6.2.2 Comparison of surface elevation change between 2010 and 2011...... 271 6.3 Combining information from multiple sources to provide a description of glacial processes...... 273 6.3.1 Seasonal flow variations and melt patterns ...... 274 6.3.2 Detection of a possible subglacial water body ...... 278 6.3.3 Marginal lake drainage event ...... 282 6.4 Summary of glacier characteristics ...... 287 6.5 Summary of techniques used ...... 289 6.6 Summary of new knowledge obtained on glacial processes ...... 292 6.7 Suggestions for further work ...... 293 6.8 Meeting overall Objectives ...... 295 6.9 Conclusion...... 297

References ...... 301

xi Table of Figures

Figure 1.1: Location of the study area ...... 13 Figure 1.2: Active calving from the main southern calving face in August 2008...... 17 Figure 2.1: Orthophoto generated from 1982 photography...... 25 Figure 2.2: Orthophoto generated from 1958 photography...... 28 Figure 2.3: Orthophoto mosaics generated from 2010 and 2011 photo surveys...... 33 Figure 2.4: Points used for feature tracking...... 35 Figure 2.5: 3D perspective views of Fountain Glacier ...... 38 Figure 2.6: Ice loss between 1958 and 1982 ...... 39 Figure 2.7: Change in surface elevation along profile AA’ ...... 40 Figure 2.8: Position of Fountain Glacier Terminus in 1958, 1982, and 2010 ...... 41 Figure 2.9: Average annual ice loss for the terminus region ...... 42 Figure 2.10: Surface elevations for profiles AA', BB', and CC' ...... 43 Figure 2.11: Average ice flow measured between 1 July 2010 and 2 July 2011 ...... 46 Figure 3.1: The Geometry of perspective projection...... 64 Figure 3.2: The relationship between object and image coordinates ...... 65 Figure 3.3: Location of Camera Station 1and Camera Station 2...... 71 Figure 3.4: Camera Station 2...... 72 Figure 3.5: Targets and reference points as seen from Camera 1 and Camera 2 ...... 75 Figure 3.6: Source photographs and orthophotos obtained from Camera 1...... 79 Figure 3.7: Reference photo and associated orthophoto for Camera 1 ...... 80 Figure 3.8: Source photographs and orthophotos obtained from Camera 2 ...... 81 Figure 3.9: Reference photo and associated orthophoto for Camera 2 ...... 82 Figure 3.10: Movement of Camera 1 check point ...... 84 Figure 3.11: Movement of Camera 2 check point...... 85 Figure 3.12: Variation in rotational parameters for Camera 1...... 87 Figure 3.13: Variation in rotational parameters for Camera 2...... 88 Figure 4.1: Point measurement from two cameras using intersecting rays ...... 96 Figure 4.2: The effect of baseline length and convergence on accuracy ...... 98

xii Figure 4.3: Camera station and target positions for measurement years one and two. 103 Figure 4.4: (a): View from Camera Station 1, (b): View from Camera Station 2 ...... 104 Figure 4.5: Camera station and target positions for measurement year three...... 106 Figure 4.6: (a): View from Camera Station 1 (b): View from Camera Station 3...... 107 Figure 4.7: Autumn 2008 Rotational parameters for Camera 1 and Camera 2...... 110 Figure 4.8: Rotational parameters for Camera 2 for May and June 2009...... 111 Figure 4.9: Camera rotations for measurement year two of the study...... 114 Figure 4.10: Camera rotations for measurement year three...... 117 Figure 4.11: Elevation change at GT1 over measurement year two...... 123 Figure 4.12: Surface elevation change for measurement years two and three at GT2. . 126 Figure 4.13: Change in horizontal position for GT2 over measurement year three...... 128 Figure 4.14: Surface elevation change for measurement years one and two at GT4. ... 131 Figure 4.15: Change in horizontal position for GT4 over measurement year one...... 133 Figure 4.16: Three year surface elevation change at GT5...... 136 Figure 4.17: Change in horizontal position of GT5 for years one and three...... 138 Figure 4.18: Elevation change at GT6 for measurement year three...... 140 Figure 4.19: Change in horizontal position at GT6 over measurement year three...... 141 Figure 4.20: Measurement year three elevation changes measured at GT7...... 143 Figure 4.21: Change in horizontal position at GT7 over measurement year three...... 144 Figure 4.22: Elevation changes at GT8 over all three years...... 146 Figure 4.23: Change in horizontal position of GT8 for years one and three...... 148 Figure 4.24: Elevation changes at GT9 over all three measurement years...... 150 Figure 4.25: Change in horizontal position at GT9 for years one and three...... 151 Figure 4.26: Slope-corrected elevation changes for all targets over year two...... 153 Figure 4.27: Slope-corrected elevation changes for all targets over year three...... 155 Figure 4.28: Comparison of slope-corrected elevations for year two and year three .. 157 Figure 4.29: Averaged year two and year three profiles...... 158 Figure 4.30: Plots of averaged minimum and maximum temperatures...... 160 Figure 4.31: Differences between computed DEMs ...... 162 Figure 4.32: Profiles across photogrammetrically-generated DEMs ...... 164 Figure 4.33: Variation of camera focal length over year three...... 170

xiii Figure 5.1: Formation of a displacement interferogram...... 185 Figure 5.2: InSAR Geometry...... 187 Figure 5.3: Workflow for measuring down-glacier flow from ERS-1 imagery...... 221 Figure 5.4: Measurement of displacement from ERS-1 interferogram ...... 222 Figure 5.5: Geometry of the five interferograms used to determine 3D motion ...... 232 Figure 5.6: Obtaining the vertical component of motion ...... 238 Figure 5.7: Computed down-glacier displacement ...... 240 Figure 5.8: Displacement along centre-line profile AA' ...... 241 Figure 5.9: Comparison of displacement estimates from InSAR and feature tracking .. 243 Figure 5.10: Comparison between centre-line horizontal down-glacier displacements 244 Figure 5.11: Projected ascending-pass displacements...... 247 Figure 5.12: Projected descending-pass displacements ...... 248 Figure 5.13: Residual ascending-pass vertical displacements...... 250 Figure 5.14: Residual descending-pass vertical displacements ...... 251 Figure 5.15: 2009 vertical centre-line profiles...... 252 Figure 6.1: Difference between InSAR and manual feature tracking displacements ..... 270 Figure 6.2: Comparison of annual displacement along centre-line profile BB'...... 270 Figure 6.3: 2008 SPOT image of Fountain Glacier showing flow striping ...... 275 Figure 6.4: The extents of the vertical anomaly ...... 279 Figure 6.5: Interpreted GPR trace showing the region of the anomaly ...... 281 Figure 6.6: Fountain Glacier terminus in July 2008 and June 2010...... 284 Figure 6.7: Observed changes in glacier surface elevation ...... 285 Figure 6.8: Spring visible on northern terminus from 15 – 24 July 2009...... 286

xiv List of Tables

Table 2.1: Maximum ice thickness, ice loss, and cross-sectional areas for profile BB’. . 44 Table 2.2: Maximum ice thickness, ice loss, and cross-sectional areas for profile CC’. . 45 Table 3.1: Error measured at each target...... 76 Table 4.1: Elevation change at GT1 over measurement year two...... 124 Table 4.2: Horizontal motion for GT1 over measurement year two...... 124 Table 4.3: Elevation change at GT2 over measurement years two and three...... 126 Table 4.4: Horizontal motion for GT2 over measurement years two and three...... 129 Table 4.5: Vertical motion for GT4 over measurement years one and two...... 132 Table 4.6: Horizontal motion for GT4 over measurement years one and two...... 134 Table 4.7: Three year surface elevation change for GT5...... 136 Table 4.8: Horizontal motion for GT5 over all three years of the study...... 139 Table 4.9: Elevation differences at GT6 for measurement year three...... 140 Table 4.10: Horizontal motion at GT6 for measurement year three...... 142 Table 4.11: Elevation differences at GT7 for measurement year three...... 143 Table 4.12: Horizontal motion at GT7 for measurement year three...... 145 Table 4.13: Elevation differences at GT8 over all three years of the study...... 146 Table 4.14: Horizontal motion for GT8 over all three years of the study...... 149 Table 4.15: Elevation differences at GT9 over all three measurement years...... 150 Table 4.16: Horizontal motion for GT9 over all three years of the study...... 152 Table 4.17: Comparison of average elevation changes over year two and three...... 159 Table 5.1: Specifications of ERS-1...... 204 Table 5.2: Specifications of RADARSAT-2...... 206 Table 5.3: Specifications of TerraSAR-X...... 207 Table 5.4: ERS-1 scenes provided...... 216 Table 5.5: TerraSAR-X scenes provided...... 216 Table 5.6: RADARSAT-2 scenes provided...... 219 Table 5.7: TerraSAR-X 11 day interferograms used for analysis ...... 225 Table 5.8: RADARSAT-2 24 day interferograms used in analysis...... 229

xv Table 6.1: Comparison of interferometric and GPS displacements ...... 267 Table 6.2: Comparison of displacements from GPS and manual feature tracking ...... 268 Table 6.3: Comparison between GPS observations and DEM differences ...... 272

xvi List of Acronyms used

ALOS: Advanced Land Operation Satellite AO: Absolute Orientation ASAR: Advanced Synthetic Aperture Radar ASL: Above Sea Level ASTER: Advanced Spaceborne Thermal Emission and Reflection Radiometer COSMO-SkyMed: Constellation of small Satellites for the Mediterranean basin Observation DEM: Digital Elevation Model ELA: Equilibrium Line Altitude ENU: East, North, Up ENVISAT: Environmental Satellite EO: Exterior Orientation EOP: Exterior Orientation Parameters ERS-1/2: European Remote Sensing satellite - 1/2 ERTS-1: Earth Resources Technology Satellite ESA: European Space Agency ETM: Enhanced Thematic Mapper GCP: Ground Control Point GPR: Ground Penetrating Radar GPS: Global Positioning System InSAR: Synthetic Aperture Radar Interferometry IOP: Interior Orientation Parameters JERS-1: Japanese Earth Resources Satellite-1 LiDAR: Light Detection and Ranging LOS: Line of Sight MAMM: Modified Antarctic Mapping Mission

xvii MSS: Multispectral Scanner System NAPL: National Air Photo Library NSIDC: National Snow and Ice Data Centre NTS: National Topographic Series RADAR: Radio Detection And Ranging RAMP: RADARSAT Antarctic Mapping Project RMS: Root Mean Square RO: Relative Orientation RTK: Real time Kinematic SAR: Synthetic Aperture Radar SPOT: Système Pour l’Observation de la Terre SRTM: Shuttle Radar Topography Mission UAV: Unmanned Aerial Vehicle UTM: Universal Transverse Mercator

xviii Chapter 1: Introduction

1.1 Synopsis

This thesis describes the application of a number of complementary techniques

using data from both remotely-sensed and in-situ sources. The overall emphasis is on developing an integrated approach to the analysis of a small arctic glacier, which will allow long-term and short-term patterns of change to be identified and surface dynamics

to be characterised in three dimensions, as well as through time. While local conditions

obviously will have an effect on wider applicability, it is hoped that the approach outlined

here provides a logical framework which can be used to develop effective analysis

strategies in other glaciated areas throughout the arctic.

1.2 Background

The study of glaciology has seen major changes over the last few decades. Prior

to the 1970s, knowledge was derived largely from fieldwork, but technical limitations to

equipment meant that detailed surveys over large areas were generally impractical.

Surface features could also be mapped from aerial photography, but photographic

coverage of most glaciers was limited, and if available was separated by long time intervals. The launch of ERTS-1 in 1972, later renamed Landsat-1, heralded a new era in

which satellite remote sensing allowed the Earth's surface to be seen as never before.

1 While the Multi-Spectral Scanner (MSS) carried by the first four Landsat satellites had limited spatial and spectral resolutions by today's standards, it nonetheless started a

revolution in the study of glaciology. For the first time the extents of glaciated areas

could be mapped in detail, over large areas. The repeatability of satellite coverage also

made it possible to measure changing glacial extents over time, allowing large-scale

patterns of change to be discerned, and providing a global record which now dates back over 40 years.

The science of remote sensing has evolved considerably since the launch of

ERTS-1. Optical satellites now carry sensors which can image the ground at resolutions as small as half a metre, while one-metre resolution radar satellite imagery is routinely available from satellites such as TerraSAR-X. Techniques such as SAR interferometry and feature tracking now make it possible to measure glacier flow rates to a high degree of accuracy, while the measurement of surface elevations from space is now possible on a routine basis. Taken as a whole, these new forms of imagery and analysis techniques are powerful tools which allow us to observe and measure changing glacial environments at an unprecedented level of detail.

Complementing the development of remote-sensing technologies has been an evolution in field data collection procedures and instrumentation. The Global Positioning

System (GPS) has revolutionised data gathering. High-density point surveys may now be

made of glacial and periglacial environments in the time it takes to walk the study area,

and high-accuracy survey-level measurements may be made with comparatively little

2 extra effort. Automated weather stations can now provide detailed records of temperature

and precipitation throughout the year. Techniques such as the use of ground-penetrating

radar make it possible to obtain detailed measurements of ice thickness and condition,

while an increasing number of sensors are available to measure such varied parameters as

sediment loads and basal water pressure.

The availability of large quantities of remotely-sensed and in-situ data make it possible to model future changes in ice cover and climate with ever more sensitivity, at both regional and global scales. Measurements of past glacial extents and dynamic patterns allow predictions of future behaviour to be made, while estimates of ice loss from all sources worldwide can be used to improve estimates of future sea level rise.

Satellite remote sensing has proven to be very useful in measuring changes to the mass balance and dynamics of the major continental ice sheets of Greenland (e.g. Zwally et al. 2005; Rignot and Kanagaratnam 2006) and Antarctica (e.g. Zwally et al. 2005;

Rignot 2006). SAR interferometry and feature-tracking techniques work well for measuring surface dynamics for the comparatively featureless interiors of the major continental ice sheets, where ground-reference points are few and far between. Remote sensing measurements have also been used to measure speed changes and thinning of major outlet glaciers from the Greenland ice sheet (e.g. Joughin et al. 2004; Thomas et al.

2009). From a combination of different measurements, an understanding is gradually emerging of many of the processes which will determine the future response of the major ice sheets to changing environmental conditions.

3 At the other end of the scale are temperate valley glaciers. While these glaciers do

not usually cover large spatial extents, their locations at comparatively low latitudes and

in areas with high temperature fluctuations render them particularly vulnerable to the

effects of climate change. Due to the fact that many temperate glaciers are accessible year

round, long-term historical records often exist, particularly for glaciers in the European

Alps. Consequently mass-balance estimates are strongly biased towards the European

Alps and the mountains of western North America (Zemp et al. 2009). Although there is

considerable variation between temperate glaciers in different parts of the world,

predictive models can often provide good regional estimates of potential changes in mass

balance under a variety of future climatic scenarios.

The polar glaciers and small icecaps found in arctic environments have historically attracted less attention than either the major continental ice sheets or the more accessible temperate valley glaciers. This is now changing however, as a number of studies have shown that these glaciers are reacting rapidly to changing climatic conditions (e.g. Burgess et al. 2005; Bahr et al. 2009) and that they are currently contributing disproportionately to increasing sea levels (Oerlemans et al. 2005; Gardner et al. 2011; Gardner et al. 2012). The icecaps and glaciers of the Canadian Arctic

Archipelago are now believed to be contributing more to increasing sea levels than any other region outside of Greenland and Antarctica (Gardner et al. 2011). There is a clearly a need to understand the linkage between ice loss and climate in arctic and sub-arctic regions, since this trend is likely to continue through the next century.

4 While polar glaciers show considerable variation in their form and dynamics, they

share a number of common characteristics. They tend to be polythermal in nature, and

typically comprise a layer of cold ice overlying a warmer core of temperate ice. Marginal

regions usually consist of cold ice, with the glacier terminus often being frozen to its bed.

In many cases this results in a thermal dam, which can act to trap water at the base of the

glacier at certain times of year (Irvine-Fynn et al. 2006). Polar glaciers tend to be slow flowing, with typical flow rates being considerably less than those observed for temperate glaciers. While there are a number of recent studies which have been carried out on specific glaciers (e.g. Bingham et al. 2003; Copeland et al. 2003; Burgess et al. 2005), polar glaciers are generally under-represented when compared with studies of the major continental ice sheets, or of temperate valley glaciers. In view of their role as a bellwether for potential future changes to the major ice sheets there is an obvious need to obtain detailed measurements of mass balance, surface melt rates, and surface dynamics for a representative sample of polar glaciers.

Measurements of changing glacier extents and surface flow rates may be obtained using optical and radar remote sensing techniques. If suitable Digital Elevation Models

(DEMs) are available from different dates, then these may be used to compute changes to mass balance, using the photogrammetric method (Patterson 1994). This technique presupposes that the average firn depth at any given point on the glacier surface is known, and that density conversions have been applied to account for the firn distribution. There is however no remote-sensing technique currently available which will allow changes in ice thickness to be accurately determined for small glaciers, on a

5 daily or weekly basis. Average surface differences can be computed for multi-year periods by subtracting DEMs. However this gives no information about the processes involved, whether the changes were similar for each year, and what the overall trends are.

This thesis describes the development of a system which makes use of both remotely-sensed and in-situ data in an attempt to characterise the surface dynamics, as well as the seasonal and longer-term patterns of ice gain and loss for a small arctic glacier. While the specific measurements are too localised to be applied generally, it is hoped that many of the techniques used can be adapted to have wider application in glaciated areas, leading to increased understanding of changes which are likely to occur in the future. While the system was optimised for use on slow-flowing arctic glaciers there is no reason why specific components could not be adapted for use in other glaciated environments.

The research described in this thesis is innovative in that a number of the techniques used have not been applied to glacier research before. It is believed that the survey carried out by an Unmanned Aerial Vehicle (UAV) over Fountain Glacier in July of 2010 is the first time that a UAV has been used to provide overlapping aerial photographic coverage for a glaciated area, and that the resulting DEM and orthophoto mosaic represent the first usage of UAV-based photogrammetry over a glaciated area.

Also the use of intersecting photographs to measure the daily XYZ positions of targets on the glacier surface represents a novel application for the established technique of ground-

6 based photogrammetry, making it possible to measure short and medium-term changes to

the glacier surface.

Measurement of the full 3D motion field of Fountain Glacier was made possible because an interferogram was produced from two left-looking RADARSAT-2 scenes.

Though this has been done regularly in the Antarctic, left-looking scenes are very rare for the Arctic, due to satellite tasking constraints. Consequently most InSAR-derived motion estimates still rely on the assumption of surface-parallel flow, which can potentially introduce large errors in cases where there is a significant vertical component to the surface motion.

The significance of this work is that it provides a logical framework for monitoring the health of polar glaciers, both spatially and temporally. Because of the remote location of many such glaciers, and the extremely harsh environmental conditions which are present through much of the year, field work is necessarily limited to the short arctic summer. There is very little direct knowledge of glacial behaviour through the rest of the year. By making regular photogrammetric measurements of targets on the glacier surface it is possible to obtain information about temporal patterns of surface change throughout the year, which cannot be obtained through any other means. Combining this information with spatial information derived through various remote-sensing techniques makes it possible to analyse patterns of change in four dimensions, giving a comprehensive overview of the response of the glacier to changing environmental conditions.

7 The importance of this work is that it provides a way of monitoring the changes affecting polar glaciers in a consistent manner. Applying a similar monitoring strategy across a representative number of glaciers in the Canadian Arctic would provide a comprehensive information resource, from which patterns of change could be inferred.

By providing comprehensive monitoring, improved rates of surface melt and estimates of associated sea level rise could be obtained, as well as changes to ice flow patterns associated with changing environmental conditions. This would provide valuable information linking the response of glaciers with environmental variables and help to improve future climate modeling. Overall, increased knowledge about future changes to the glaciers and icecaps of the Canadian Arctic Archipelago will help to fill in a missing piece of the puzzle, and help to refine our knowledge of what is likely to happen to glaciated areas worldwide.

1.3 Overall objectives

The overall objective of this work is to describe the development of a system which uses both remotely-sensed and in-situ data to characterise surface dynamics, as well as seasonal and longer-term patterns of change for a small polythermal arctic glacier.

Specific objectives include the following:

• Establish long-term patterns of surface change for Fountain Glacier using DEMs

derived from all available sources of aerial photography.

• Establish recent patterns of surface change for the terminus region.

8 • Use ground-based photogrammetry to monitor the seasonal decay of Fountain

Glacier’s proglacial icing.

• Use ground-based photogrammetry and GPS measurements to measure changes

in the thickness of the glacier close to the terminus, and to measure seasonal

patterns of surface elevation change.

• Use ground-based photogrammetry and GPS to measure the horizontal motion of

targets located in the terminus region of the glacier.

• Determine the full 3D winter displacement field for the glacier using a

combination of SAR interferometry and feature tracking.

• Estimate annual displacements for the glacier using feature tracking.

• Determine areas where the glacier surface is undergoing uplift or subsidence

using SAR interferometry.

Data sources used include the following:

• Historical aerial photographs from 1958 and 1982.

• DEMs derived from aerial photography from 1958, 1982, 2010, and 2011.

• Orthophotos of the terminus region derived from a 2010 overflight using a UAV,

and from a 2011 helicopter survey.

• SPOT satellite images from 2008 and 2009.

• ERS-1 radar images from 1992.

• TerraSAR-X radar images covering the period from 2008 - 2011.

9 • RADARSAT-2 radar images covering the winter of 2009 - 2010.

• Daily time-lapse photographs from two cameras covering the period from August

2008 - July 2011.

• GPS measurements for all point source data.

• Records from a network of four automated weather stations within the area of

interest.

1.4 Structure of thesis

This thesis is primarily methodological in structure, with chapters being grouped around the application of a common set of techniques. For this reason, similar measurements may be reported in different chapters, when derived by different methods.

• Chapter 1 is the introduction and provides the background to the project, the

overall objectives and a description of the study area.

• Chapter 2 describes the use of photogrammetric measurements derived from 1958

and 1982 aerial photography to derive DEMs and orthophotos covering the

majority of the glacier. DEMs and orthophotos are also generated for the terminus

region from a 2010 UAV overflight and a 2011 helicopter survey. A comparison

between orthophotos from different years is used to establish the retreat of the

terminus since 1958. DEMs from all years are used to establish long term and

recent patterns of ice loss at the glacier terminus, with ice thickness being

calculated using a basal DEM. Manual feature tracking between features on the

10 2010 and 2011 orthophotos is also used to establish annual flow rates at the

terminus.

• Chapter 3 introduces the ideas behind ground-based photogrammetry and applies

them to the study of the seasonal decay of the proglacial icing situated adjacent to

the terminus of Fountain Glacier. A time series of photographs obtained from two

cameras overlooking the icing is used to generate a series of orthophotos from

which changes in the extents of the icing can be measured.

• Chapter 4 takes the idea of ground-based photogrammetry further. Two cameras

are used to take intersecting time-lapse photos of the glacier terminus region, over

a three year period. Photogrammetric measurements are made to a series of

targets set up on the glacier surface, from which their daily or weekly positions

and elevations can be calculated. These measurements are verified by annual GPS

measurements of target positions and elevations. The results of this analysis

provide a detailed record of the seasonal and multi-year dynamics of the terminus

region, as well as allowing seasonal ice-melt patterns to be observed.

• Chapter 5 describes the use of both SAR interferometry and feature tracking to

derive estimates for down-glacier flow. Both TerraSAR-X and RADARSAT-2

scenes are used to derive winter flow rates using interferometry. Feature tracking

using TerraSAR-X amplitude images is used to verify the estimates obtained from

SAR interferometry. Feature tracking of SPOT scenes is also used to estimate

annual flow rates, from which the differences between summer and winter flow

rates are estimated. Vertical displacements are also calculated using SAR

11 interferometry. These are used to identify areas of the glacier surface which are

undergoing thickening or thinning, and which show a high level of variability.

• Chapter 6 brings all the information from the previous chapters together to

establish the overall picture. Measurements from different chapters, derived using

different techniques, are compared. These results are then used to provide

evidence for the seasonality of the glacier, and to show the effects of subglacial

hydrological processes. The results are then used to provide a comprehensive

description of the surface dynamics of the glacier and of the long and short-term

patterns of seasonal surface variation.

1.5 Description of study area

The study focuses on Fountain Glacier, which is a small arctic glacier situated on southern Bylot Island, in Canada's Nunavut Territory. Fountain Glacier is officially designated as B26 by the Glacier Atlas of Canada (Inland Waters Branch 1969). The terminus of the glacier is located at latitude 72° 57' 45" N, longitude 78° 24' 15" W. The location of the study area is shown in Figure 1.1.

The Bylot Island Icefield forms part of a series of small icecaps and icefields which occupy the Canadian Arctic Archipelago, and which cover a distance of over 1,600 km from southern Baffin Island to the northernmost point of the Ellesmere Island Icecap.

The icefields and icecaps of the Canadian Arctic Archipelago have been identified as being particularly vulnerable to the effects of changing climatic conditions, with

12 dramatically increased melt rates being observed in response to a series of warm summers which have occurred in the last few years (Oerlemans et al. 2005; Gardner et al.

2011; Gardner et al. 2012).

Figure 1.1: Location of the study area; (a): General location; (b): Landsat 7 image of

Fountain Glacier study area, supplied by Geobase ®.

Bylot Island is approximately 180 km in length, running from northwest to

southeast, and is approximately 120 km wide at its widest point. The centre of the island

is dominated by the rugged Byam Martin Mountain Range, which forms the nucleus

around which the Bylot Island Icefield has developed. The icefield occupies 43% of the

island, and has been measured as being 4,783 km2 in extent (Dowdeswell et al. 2007).

The central icefield is pierced by a number of nunataks, which reach to a height of 1905

m asl at Angilaaq, the highest point on the island. From the central portion of the icefield,

a number of outlet glaciers flow out to the coastal lowlands in a radial pattern.

13 Fountain Glacier is approximately 16 km long, with the lower half of the glacier

being roughly 1.2 km wide. Its surface elevation varies from 245 m asl adjacent to the

proglacial icing at the glacier terminus, to over 1,750 m asl at the top of the accumulation

zone, giving it an average surface slope of 5.4°. A number of previous studies have

suggested that both Fountain Glacier and the neighbouring Stagnation Glacier are

polythermal in nature (e.g. Moorman 2005; Irvine-Fynn et al. 2006; Wainstein et al.

2008). Fountain Glacier is unusual in terms of its shape. For the top two-thirds of the glacier the flow direction is from north to south, but the glacier then turns through 90°, with the lower section flowing west to east (see Figure 1.1b).

The former Equilibrium Line Altitude (ELA) of Fountain Glacier was determined as being approximately 920 m asl. This figure was determined from the position of the snow line on a Landsat ETM scene, obtained on the 9th of August, 2001. Technically the

ELA for polar glaciers should correspond to the lower limit of the zone of superimposed

ice (Benn and Evans 1998). However this could not be identified from the available

satellite imagery. SPOT images from the 4th of August 2008, and the 25th of August 2009

showed the snow line to be at 1,100 m and 950 m asl respectively, suggesting that there

has been little net accumulation in recent years. This suggests that Fountain Glacier has a

strongly negative mass-balance, although there is no recent elevation data for the upper

glacier which would allow this to be verified. Other than measurements obtained from

historical photography from 1958 and 1982, and ERS-1 radar imagery from 1991, all

observations described in this thesis can therefore be considered as applying primarily to

the ablation zone.

14 Observations from nearby automated weather stations, as well as longer-term observations from the weather stations in Pond Inlet show that the region has an average temperature of -15°C (Irvine-Fynn et al. 2006). The area has a dry arctic climate, with an average annual precipitation of less than 200 mm, which includes a maximum of 80 cm of snow falling in the winter near the terminus of Fountain glacier (Moorman 2005).

Recent temperature measurements suggest a warming trend (Wainstein et al. 2010), and the last few years have seen a succession of warmer than average summers, with higher than average temperatures being recorded by the network of automated weather stations in the area.

Fountain Glacier has a large perennial proglacial icing, which occupies the portion of the glacial outwash plain immediately below the terminus. In the past this icing was observed to have extended over 11 km down-valley from the terminus of the glacier

(Moorman and Michel 2000). The current extents of this feature are approximately 1.2 km in length by 350 m in width, with a valley constriction forming its eastern or lower boundary. While parts of this feature are perennial, the majority of the icing is melted by summer runoff and regenerates each winter. It is believed that water is supplied to the icing via a subglacial talik, ensuring a supply of liquid water throughout the winter

(Moorman 2003; Wainstein et al. 2008).

Prior to the mid 1990s, Fountain Glacier’s extents appeared to be stable, having changed little since the neoglacial maximum, approximately 120 years ago (Dowdeswell et al. 2007; Wainstein et al. 2008). However recent retreat rates of the terminus over the

15 period from 1995 to 2001 were measured at 10 ma-1 by Wainstein et al. (2008), who also

noted that the surface of the glacier close to the terminus showed average thinning rates

of approximately 1 ma-1 over the 25 year period from 1982 to 2007. This amount of

retreat is small compared with that of neighbouring Stagnation Glacier, which was observed by Moorman (2003) to have retreated by more than 1.8 km since 1948.

The terminus of Fountain Glacier has seen major changes over the last two decades. In the early and mid 1990s it was possible to walk straight on to the front of the glacier, as it terminated in a slope. Starting in the early 1980s and continuing though the

1990s, two collapse features developed on the southern and northern sides of the terminus

(Wainstein et al. 2010). These were believed to be caused by the collapse of subglacial caverns, which were formerly supported by stored water. Over time these two features have developed into two major calving fronts, with the glacier now terminating in a 20 -

30 m high cliff face (Wainstein et al. 2010). Dry-calving is now believed to be a significant contributor to the overall loss of mass from Fountain Glacier, and during fieldwork carried out in August 2008, the main southern calving face was observed to be extremely active, as can be seen from Figure 1.2.

Figure 1.2: Active calving from the main southern calving face in August 2008.

17 Chapter 2: Determination of Surface Thinning and Surface Dynamics Using

Aerial Photogrammetry

2.1 Introduction

Aerial photogrammetry is a well-established technique that has been used for topographic mapping since the advent of vertical aerial photography in the early years of the 20th century. It is commonly used in glaciological studies as a means of determining

glacier-surface topography. The photogrammetric method is also often used in glacier mass-balance studies (Patterson 1994), whereby photogrammetrically-derived surface

elevations from different years are compared. If the measurements cover the entire

glacier, then it is possible to compute changes in net balance over time. In recent years, measurements have been made digitally, by comparing DEMs from different years.

These may either be produced directly from source photography, satellite imagery, or by

airborne laser scanning (LiDAR). DEMs from older source photography are usually

produced from digitised map contours.

Numerous studies have used such techniques to analyse glacier surface change.

Examples include studies by Conway et al. (1999), who described measurements of mass

change for Blue Glacier in Washington State. Elevations were derived from photography

obtained in 1939, 1952, 1957, and 1987, and from LiDAR data acquired in 1996. Rippin

et al. (2003) used DEMs from 1977 and 1995, along with a basal DEM obtained from

Ground-Penetrating Radar (GPR), to model changes in subglacial drainage for Midre

Lovénbreen on Svalbard. Fox and Nuttall (1997) compared DEMs derived from 1974 and

18 1990 photography for Finsterwalderbreen and Hessbreen glaciers on Svalbard, and

described the application of aerial photogrammetry to the study of surging glaciers.

Glacier surges on Svalbard were also investigated by Sund et al. (2009), who used a

combination of photography from 1936, 1961, and 1990, along with 2003 ASTER data

and 2006 LiDAR data to investigate surges for a number of different glaciers. They concluded that surge behaviour on Svalbard was considerably more common than previously reported.

While aerial photogrammetry can provide highly detailed information on glacier

surface change, it has traditionally had a number of disadvantages. Firstly the cost of

acquisition has generally ruled out the possibility of custom photo surveys. This means

that researchers often have to rely on photography gathered for other purposes, such as

government map updates. While such photography can be useful, it is usually small scale,

and is normally gathered at less than optimal times. For example, mass-balance studies

usually require imagery to be obtained at the end of the balance year, which for most

glaciers in the northern hemisphere occurs between the months of September and

October. However in the arctic, most surveys are flown in the summer months. Also

photo surveys of remote arctic areas are generally infrequent, making such photography

less than ideal for investigating applications such as climate change.

2.1.1 Feature tracking

Because of the limited availability of suitable photography and the expense of

custom surveys, the application of aerial photogrammetry has largely been limited to

19 topographic mapping of glacier surfaces. However if medium to large-scale photography

is available, separated by a time period of several months to one or two years, then it is

often possible to use feature tracking to make estimates of surface motion, and to thereby

determine short or medium-term dynamic patterns. Automated feature tracking using

both optical and radar satellite imagery is commonly used to measure down-glacier

velocities of fast-moving temperate and arctic outlet glaciers. A number of programs are

available which use the cross-correlation between different images to compute surface

displacements. Examples of automated feature tracking include studies by Berthier et al.

(2005), who carried out feature tracking from SPOT-5 images to determine glacier velocities for the Mer de Glace in the French Alps, and Copland et al. (2009), who used

ASTER data to measure the speeds of temperate valley glaciers in the Karakorum

Mountains.

Manual feature tracking differs from automated approaches in that prominent

features are identified on both images visually. While this is more time consuming, it

may give better results in cases where the images differ significantly. An application of

manual feature tracking was described by Brecher (1986) for the rapidly moving Byrd

Glacier in West Antarctica. Using photography from flights 56 days apart, researchers

were able to map velocities and strain rates to an estimated 5% accuracy.

The small size and slow rates of motion observed on many polythermal arctic

glaciers may rule out the use of optical feature tracking from satellite imagery for

dynamic studies. A different approach was used by Rees and Arnold (2007), who

20 compared high resolution LiDAR generated DEMs of Midre Lovénbreen on Svalbard.

This was partially successful, but was reliant on sufficient surface roughness being

present to enable image matching. On Bylot Island, many glaciers have smooth surfaces,

so this approach could only be used over small sections of the glacier surface. Ideally the

preferred solution would be the use of high-resolution photography, which would allow

for the identification and tracking of small-scale surface features, such as boulders.

2.1.2 On-demand photogrammetric surveys

Two comparatively recent developments may make low-cost, on-demand

photogrammetric surveys a practical option for glaciological applications. The first is the

development of digital photogrammetric software packages which are able to create

stereo models and orthophotos, using photography acquired from low-cost digital cameras. Since a high-end aerial camera is no longer required, photography can be obtained from small fixed-wing aircraft or helicopters, vastly reducing the cost of acquisition. Modern software packages can now accommodate orientation angles significantly greater than those encountered in traditional aerial photography. The necessity to have the camera pointing downwards is therefore reduced, and it may be possible to obtain acceptable stereo photography for small areas simply by holding the camera out a window. It is still necessary for the camera to be properly calibrated, and for accurate ground control to be established for the survey, but if these requirements are met, good results can often be obtained.

21 The second development, which has the potential to revolutionise glacial dynamic

studies, is the advent of lightweight, low-cost UAV platforms. These resemble radio control hobby aircraft, but fly a pre-programmed flight path. Flight planning software is used to work out the optimal photo coverage in advance, so that the area of interest is fully covered by stereo photography. The aircraft then flies the predetermined course, using an onboard autopilot, with the photos being acquired at intervals determined by the flight planning software. On completion of the flight, a log file is downloaded from the aircraft. This file gives provisional orientation parameters for each photograph acquired, and can be used as an input to a photogrammetric block adjustment process. The use of such a platform means that surveys can be carried out effectively on demand, subject to weather constraints.

2.2 Outline

This chapter describes the use of airborne photogrammetry for measuring long and short-term changes in topography and for establishing recent ice flow patterns across

the terminus region of Fountain Glacier. The primary objective was to establish baseline

measures of surface change and flow. This involved the production of a series of DEMs

and orthophotos using imagery from various dates and sources. The photography used in

this analysis was obtained from past aerial surveys, a UAV overflight, and a helicopter

survey. A basal DEM of the terminus region was also used to provide estimates of ice

thickness. This combination of data provides a valuable record of long and short-term

22 changes in ice thickness, as well as information on contemporary ice flow patterns.

Baseline values obtained using airborne photogrammetry were also compared with

observed short-term seasonal variations in surface elevation and flow rates, derived from

a variety of in-situ and remotely-sensed measurements. This chapter describes how these

baseline measurements were obtained. More detailed measurements of short-term

seasonal patterns are described in the following chapters.

2.3 Methodology

Stereo aerial photography from 1958 and 1982 covering Fountain Glacier was

provided by the Canadian National Air Photo Library (NAPL). High-resolution 1200 dpi

scans were obtained for 1:70,000 scale photos A26078 48, 49, and 50, which were taken

on the 6th of July 1982, and for 1:60,000 scale photos A16047 4, 5, and 6, which were taken on the 16th of June 1958. National Topographic Series (NTS) 1:50,000 scale map

sheets 038C03 and 038B14, which cover Fountain Glacier, are based on the 1982

photography. At the time this study was undertaken no detailed DEMs were available for

the study area. Digitised contours and spot heights were however available from Natural

Resources Canada’s Geogratis web site. A 10 m resolution DEM of the area surrounding

Fountain Glacier was generated from these layers, using PCI Geomatica software.

2.3.1 1982 photography

The three scanned 1982 photos were processed using Inpho photogrammetric software. Using a camera calibration supplied by the NAPL, and the spot heights

23 obtained from Geogratis as ground control points, a strip adjustment was carried out to obtain the full orientation parameters for each photo. Because the spot heights were originally measured from the 1982 photography, these points could generally be identified easily. Two stereo models were created, covering the lower two-thirds of

Fountain Glacier. The scanned photography covering much of the lower glacier was saturated however, so accurate elevations could not be obtained for these regions from the stereo models alone.

The DEM produced from the digitised contours was then loaded into the Inpho surface model editor. Measurements made in 3D confirmed the fact that the DEM fitted the oriented stereo models, with contours produced from this DEM defining the surface of the glacier well. For steeply-sloping marginal regions of the glacier, the fit was generally not so good, as the 20 m contours from which the DEM had been derived tended to smooth out the topography. These areas were edited in Inpho, with form lines and break lines being added to better represent the terrain. The DEM points were then re- interpolated to provide a more detailed representation for these marginal regions. The final edited DEM was then used as the reference surface, against which other DEMs could be compared. It was used to generate two orthophotos, enabling the 1982 glacier extents to be accurately determined. An orthophoto generated from 1982 photography is shown in Figure 2.1.

Figure 2.1: Orthophoto generated from 1982 photography.

25 2.3.2 1958 photography

This process was then repeated for the 1958 photography, using a camera

calibration supplied by NAPL. In this case the spot heights were considered to be less

reliable, as many of them were situated on snow-covered mountain tops, where elevations

could potentially have changed by several metres. Additional spot heights were measured from the 1982 DEM for locally-flat areas which were snow-free in both images. Using the Inpho photogrammetric package, a strip adjustment was carried out on the three 1958 photos in order to determine the orientation parameters, and two stereo models were generated. Although the ground control was generally easy to identify, and horizontal and vertical residuals were of the order of two to three metres, the two models did not match up well. The model formed from photos A16047 4 and 5 in particular did not agree well with the 1982 reference surface. In the end only the model generated from photos

A16047 5 and 6 was used, as it covered most of the glacier. However height variations of up to 40 m from the 1982 DEM were observed in bare areas adjacent to the glacier, where elevations would not be expected to have changed significantly.

To enable comparison between the 1982 and 1958 elevations, a series of points were measured in 3D on both the 1982 and the 1958 photography. These points were situated all around the edges of the glacier in locally-flat, ice-free areas. In total 57 points were used, spaced as evenly as possible around the glacier. The elevation differences between the 1958 and the 1982 photography were calculated for each point, and these were used to produce a low-resolution correction surface by linear interpolation, using

PCI Geomatica software. A 5*5 median filter was applied to this initial correction surface

26 to remove extreme values. After filtering, the surface was resampled to 10 m resolution

using cubic convolution resampling, in order to provide a generalised, smooth correction surface. A preliminary DEM was then generated from the 1958 photography, using Inpho software. The correction surface was added to this 1958 DEM to produce a corrected

DEM. Comparison between the 1982 DEM and the corrected 1958 DEM showed good agreement between points on bare ground surrounding the edge of the glacier, with height differences typically in the two to five metre range. This corrected DEM was therefore accepted as being representative of surface elevations in 1958. Orthophotos were then generated from photos A16047 5 and 6 using the corrected DEM, in order to facilitate comparison of glacier extents with the 1982 photography. It is believed that the errors present in the 1958 photography prior to correction may have occurred because of film instability, which is commonly observed in older photography. The 1958 orthophoto is shown in Figure 2.2.

Figure 2.2: Orthophoto generated from 1958 photography.

28 2.3.3 UAV survey

A full UAV survey of Fountain Glacier’s terminus region was carried out on the

1st of July 2010. The survey covered a region which extended 1.5 km up-glacier from the terminus. The aircraft used was an Outlander UAV, developed by Manitoba-based

Cropcam. The UAV was provided by Accuas, a BC-based company which specialises in

UAV surveys. The camera used for the survey was a Panasonic Lumix LX3, which is a

lightweight compact camera with a retractable lens assembly. While it would have been

preferable to use a camera with a fixed focal length, the payload weight was limited to

approximately 0.5 kg, effectively limiting the choice of camera. The retractable lens was

an obvious possible source of calibration error, and prior to the survey it was not possible

to assess the stability of calibration. To ensure that the calibration remained as consistent

as possible, the camera was used with the zoom set to the widest possible coverage,

giving an effective focal length of approximately 5 mm. Although the camera had already

been calibrated in previous UAV surveys, this calibration was considered to be provisional and the calibration was refined during the subsequent block-adjustment process.

Flight planning was carried out using Mission Planner; a software package developed by Accuas. A total of 148 photos were collected, with 16 north / south oriented flight lines being required to fully cover the terminus region of the glacier. The overlap was set to 65% between adjacent photos, and 65% between adjacent strips. This high level of redundancy was chosen to ensure there were no gaps in stereo coverage. Flying height was set to 300 m above the glacier surface, which ensured a pixel resolution of

29 better than 10 cm. To avoid problems of varying scale as the aircraft and the terrain

height changed, as well as the possible loss of stereo coverage higher up the glacier, the

aircraft was programmed to drop 12 m between flight lines, thus staying approximately

300 m above the glacier surface throughout the survey. Upon completion of the survey,

the log file was downloaded from the aircraft for use in subsequent processing.

Prior to the aerial survey, Ground Control Points (GCPs) were surveyed on the

glacier surface and in the adjacent moraine areas. In total, 16 targets were surveyed using

a Trimble Real Time Kinematic (RTK) GPS system. The assumed accuracy of these

points was 5 cm in X and Y, and 5 cm in Z. Typically such a system can deliver relative

accuracies of better than a centimetre in X and Y, and slightly less in Z. However the

estimate of 5 cm reflects uncertainty associated with identification of the centres of the

targets. Targets on the glacier were 30 cm diameter red circles, with larger 60 cm targets

being used in the darker moraine areas, where the contrast with the background was

lower. The GCPs were surveyed the day before the aerial survey, so it was assumed that

no significant change to the glacier surface would have occurred over the intervening

period.

Aerial triangulation and block adjustment were carried out using Inpho software.

Photos from every second strip were used to cover the whole area, with fill-in photos

from the remaining strips being used to ensure stereo coverage of the steeply-sloping valley sides. Two or three manual tie points per photo were also added, to help initialise the adjustment process. Triangulation and block adjustment were carried out twice. The

30 first time, all the GCPs were used to give the best overall adjustment. A calibration

refinement was then carried out in Inpho to minimise the residuals. After the camera

calibration had been refined, the triangulation was re-initialised, and the process was then

repeated, with half the targets being used as check points to provide a check of the accuracy of the adjustment. Following triangulation and block adjustment, a one-metre resolution surface model was generated for the entire area of the survey. This surface model generally represented the glacier surface well. Measurements made from the

oriented photos using Inpho showed that elevation differences were less than 0.5 m over

most of the glacier. However in steeply-sloping marginal areas, and in the vicinity of the

main supraglacial stream, some of the elevations were observed to be incorrect. These

areas were manually edited in 3D, by adding a series of break lines and form lines. The

elevation points were then re-interpolated to better reflect the surface. This edited surface

model was then used to generate a 10 cm resolution orthophoto mosaic, covering the

entire survey area, which is shown in Figure 2.3a.

2.3.4 Helicopter survey

In 2011 it was hoped to repeat the UAV survey carried out the previous year.

However no UAV was available at the time required. A survey was therefore carried out

by helicopter on the 2nd of July. For this survey a Panasonic Lumix GF1 camera was

used. The camera was fixed to the landing gear of the Bell 206L helicopter, facing downward. This camera had a fixed 14 mm lens, giving a similar field of view to the

Lumix LX3 used the previous year. Flight lines were flown across the glacier in a north / south pattern, at a height of approximately 400 m above the glacier surface. The camera

31 was triggered remotely, approximately every four seconds. In total 190 photos were

acquired, giving full stereo coverage of the area flown the previous year.

No log file was available from the helicopter survey, so photo centre positions

were estimated using the photo mosaic produced from 2010, and assuming a nominal

flying height. Due to time constraints, it was not possible to survey in targets prior to the

survey. Instead 20 GCPs were gathered after the photo survey was completed, using

natural features on the glacier surface, which could be easily identified on the photos.

These points were surveyed using a Trimble RTK GPS. Although the survey accuracy would be expected to be similar to that of the previous year, the uncertainty associated

with these points was higher, since exact identification of them on each photo was more

difficult.

The photos were processed the same way as for the previous year. In this case, the

calibration of the camera did not need to be refined, since a good calibration already

existed. Eight of the GCPs were converted to independent check points to provide an

estimate of overall survey accuracy, with the remaining points being used for the

triangulation and block-adjustment process. On completion of the adjustment, a one-

metre resolution surface elevation model was produced. This was edited manually to

improve the fit in marginal areas, and in the vicinity of the supraglacial stream. The

height model was then used to generate a 10 cm orthophoto mosaic, which could be

directly compared with the mosaic produced the previous year. This mosaic is shown in

Figure 2.3b.

Figure 2.3: Orthophoto mosaics generated from 2010 and 2011 photo surveys; (a): Orthophoto from 2010 UAV survey, (b): Orthophoto from 2011 helicopter survey. Both images show 10 m contours derived from the respective DEMs.

33 2.3.5 Data comparisons

The four available DEMs were compared, in order to measure long and short-term changes to the ice thickness. The difference between the 1958 and 1982 DEMs gave a measure of change over this period for the lower two-thirds of the glacier, whereas the difference between the 1982 and 2010 DEMs, and between the 2010 and 2011 DEMs could only be calculated for the common area, close to the terminus. There was also a basal DEM available for the terminus region. This DEM was compiled from Ground-

Penetrating Radar (GPR) measurements made by Pablo Wainstein in the summer of 2007 and 2008 (Wainstein 2011). This DEM is incomplete on the southern side of the glacier, where it was not possible to gain access. Elevations in this region were therefore interpolated.

2.3.6 Ice flow analysis using feature tracking

Feature tracking was used to determine surface motion between 2010 and 2011,

using the respective orthophoto mosaics. Both automated and manual methods were

tested. Automated feature tracking was attempted using Cosi-Corr software, which was

developed by Stanford University. Although this gave acceptable results over parts of the

lower glacier, there were large areas which had relatively poor correlation. After testing,

this method was therefore abandoned. The second method used a direct visual

comparison between prominent surface features on the two images. In this case care had

to be taken in the selection of features. Rocks often slide over the glacier surface, so

clusters of rocks which maintained the same relative geometry on both images were used

in preference to single rocks. It was found that horizontal banding tended to move up-

34 glacier as the surface melted, so these features were avoided, although vertical-cracks in the ice generally provided a reliable estimate of surface motion. In total some 400 points were identified and 10 m resolution rasters of magnitude and direction were produced from these points using PCI software. These rasters were then filtered using a 5*5 median filter to remove extreme values. The points used for feature tracking are shown in Figure

2.4.

Figure 2.4: Points used for feature tracking.

2.3.7 Accuracy estimates

All elevations were compared to the surface derived from the 1982 contours. This

elevation surface was chosen as a reference because it was created using the same

contours as the NTS 1:50,000 scale map sheets of the area. It is not easy to measure

accuracy, since this will normally vary randomly or systematically between the surfaces

35 being compared, and will usually be lower in some areas than in others. It is however

possible to get an idea of the overall agreement between the surface elevations from the

standard deviation of height differences determined at a number of check points

distributed across the common area.

For the 1982 photography, the heights from the reference surface were compared

with those measured directly from the source photography. Measurements were made in

3D at a number of points across the glacier surface and the surrounding terrain. The

check points around the edge of the glacier were spaced approximately every 2,000 m,

and where possible were positioned on locally-flat, snow-free terrain. Points on the glacier surface were positioned to maintain similar spacing, giving a total of 18 check points. The standard deviation for all points measured was 4.9 m, with the largest variation being 10.2 m, on a steeply-sloping hillside.

The corrected 1958 DEM was also compared with the 1982 reference DEM. In this case 15 check points were identified where possible in locally-flat, snow-free areas adjacent to the glacier, where no change in surface height would be expected. Again the points were spaced at approximately 2,000 m intervals, although in this case points could not be placed on the glacier surface, since it was expected that this would have changed between 1958 and 1982. The points were also selected to be different to the 57 points previously used to produce the correction surface described in section 2.3.2. The standard deviation for all measured height differences was 7.0 m, with the largest difference being

-14.4 m, on a steeply-sloping hillside. It would have been preferable to use some form of

36 stratified random sampling to provide suitable sample points. However the requirement

of finding locally-flat snow-free areas on both sets of photographs had a major influence

on the check point locations for both years, especially for the middle and upper regions of

the glacier.

For the DEMs and orthophotos produced from the 2010 and 2011 surveys, the

accuracy was assessed using a series of check points, as described in the previous section.

In each case, approximately half of the GCPs were converted to check points. These points were distributed as widely as possible over the surface of the glacier. For 2010, eight check points were used. These gave RMS errors of 0.18 m, 0.21 m, and 0.42 m in

X, Y, and Z respectively, compared to the target positions measured using RTK GPS.

For 2011, eight check points were also used. These gave RMS errors of 0.63 m, 0.52

m, and 0.19 m in X, Y, and Z. The higher errors in X and Y for the 2011 data were likely

due to the fact that natural features were used as GCPs, and these could not be measured

as precisely on the photos as the targets used in 2010. All heights were referred to the

same GPS base station in both years. To test the influence of the selected points, the

triangulations for both years were repeated using different sets of GCPs and accuracy

checks were carried out using the remaining points. For both years, the RMS errors were

similar to those from the original triangulations, suggesting that individual points were

not unduly influencing the results of the triangulation and block adjustment process.

37 2.4 Results

Comparisons between imagery and DEMs from the different dates showed that

Fountain Glacier lost a considerable volume of ice over the period from 1958 up to the present day. This is illustrated clearly in Figure 2.5, which shows 3D perspective views of the glacier, generated from 1958 photography, and 2008 SPOT imagery.

Figure 2.5: 3D perspective views of Fountain Glacier; (a): from 1958 photography (b): from

2008 SPOT imagery, supplied by Geobase ®.

Because no recent DEM existed for most of Fountain Glacier, direct comparisons

of ice thickness for regions outside the terminus were only possible between the 1958 and

1982 DEMs. These measurements suggested that ice loss was significant over this period.

Surface elevations were measured along a centre-line profile to facilitate comparison

(profile AA’ on Figure 2.6). It can be seen from looking at Figure 2.6 and Figure 2.7 that

ice loss did not occur evenly, with three zones showing levels of ice loss of between 10 m

38 and 20 m. These occurred at the terminus, approximately 4,000 m up-glacier from the

terminus, and approximately 8,000 m from the terminus. Areas between these zones showed lower ice loss, with some parts of the glacier even showing small amounts of thickening.

Figure 2.6: Ice loss between 1958 and 1982. Surface elevations for both dates, measured along

profile AA’, are shown in Figure 2.7 below.

Figure 2.7: Change in surface elevation along profile AA’. Note the relatively high levels of ice

loss at 1,000 m, from 4,000 m – 5,000 m, and at 8,000 m, compared with low levels of ice loss at

2,500 m, and 7,000 m.

2.4.1 Terminus region

It was possible to carry out a full multi-date comparison over the terminus region,

using DEMs generated from 1958 and 1982 photography, as well as from the photo

surveys carried out in 2010 and 2011. Ice loss has been considerably greater from this

region than from the glacier as a whole, due to the recession of the glacier margins.

Figure 2.8 shows the terminus position in 1958, 1982, and 2010. Parts of the terminus have retreated by as much as 250 m since 1958, with the average retreat being around half of that. Most of this retreat has occurred since 1982. This is supported by previous

research by Moorman (2003) who suggested that the terminus position was relatively

stable prior to 1996.

Figure 2.8: Position of Fountain Glacier Terminus in 1958, 1982, and 2010. The backdrop is a

2008 SPOT image supplied by Geobase ®.

Figure 2.9 shows measured changes in ice thickness in metres per annum over

three periods; 1958 to 1982 (a), 1982 to 2010 (b), and 2010 to 2011 (c). These diagrams do not account for differences in the onset and relative intensity of the summer melt seasons, which could significantly affect the 2010 / 2011 measurements. However the

first two estimates of ice loss are averaged over 24 years, and 28 years respectively, so

the effects resulting from any differences in the timing of the photo acquisition are likely

to be small. Seasonal differences between the 2010 and 2011 melt seasons will be discussed in more detail in Chapter 4.

41 Using the basal DEM gathered in 2007 and 2008, ice thicknesses were calculated

along an E / W profile, representing the centre-line of the glacier. Ice thicknesses were

also calculated along two cross-profiles running from north to south at distances of 300 m and 1000 m from the glacier terminus. These profiles are shown in Figure 2.10.

Figure 2.9: Average annual ice loss for the terminus region; (a): Annual Ice loss between

1958 and 1982, (b): Annual ice loss between 1982 and 2010, and (c): Annual Ice loss between

2010 and 2011.

Figure 2.10: Surface elevations for profiles AA', BB', and CC'; (a): E / W centre-line profile AA’, (b): N / S cross-profile BB’, (C): N / S cross-profile CC’. The location of the three profiles is shown in (d).

43 Cross-sectional areas were calculated for the two north / south profiles, in order to estimate the percentage of ice loss across each section. It can be seen from looking at the profiles that the eastern profile (BB’) lost a considerably greater proportion of ice than the western profile (CC’) over the period of comparison. However in absolute terms, it can be seen from the centre line profile (AA’) that ice loss was relatively even over most of the terminus region, excluding the margins. The ice thickness measured at the deepest point of each north / south profile is shown in Table 2.1 and Table 2.2. Also shown are the amount of ice loss from the surface at that point, cross-sectional ice areas for each profile, and the percentage of ice remaining, relative to the 1958 cross-sectional area.

Table 2.1: Maximum ice thickness, ice loss, and cross-sectional areas for profile BB’.

Ice thickness at Percentage of Ice loss since Cross-sectional deepest point 1958 ice 1958 (m) area (m2) (m) remaining

1958 143 - 100,846.8 -

1982 131 12 82,720.7 82.0

2010 100 43 48,957.1 48.5

44 Table 2.2: Maximum ice thickness, ice loss, and cross-sectional areas for profile CC’.

Ice thickness at Percentage of Ice loss since Cross-sectional deepest point 1958 ice 1958 (m) area (m2) (m) remaining

1958 171 - 159,217 -

1982 157 14 139,081 87.4

2010 133 38 103,506 65.0

From Figure 2.9, Figure 2.10, and Table 2.1 and Table 2.2, it can be seen that the

terminus region lost an average of between 35 m and 45 m of ice over the period from

1958 to 2010, with between two-thirds and three-quarters of this loss occurring since

1982. This is supported by observation by Moorman (2003), who identified an increase in

the retreat of the terminus starting in 1996. It is likely that such a change would also have

been associated with increased thinning rates from this time on.

2.4.2 Ice flow

The results of the analysis of ice flow between 2010 and 2011 are shown in

Figure 2.11. From this diagram, it can be seen that ice flow rates ranged from near zero

for marginal regions on the northern and southern sides of the glacier, up to eight metres

per annum in the centre of the glacier, at a distance of about 1,300 m from the terminus.

The velocities shown are horizontal (XY), rather than surface-parallel (XYZ) velocities.

For slow-flowing glaciers, surface melting may be of the same order of magnitude as the flow speed and could potentially introduce a significant error into any surface-parallel

45 measurement of down-glacier velocity. The direction of ice flow is also shown in Figure

2.11. It can be seen that this is generally down the glacier, although there a deflection of ice flow towards the margins close to the terminus. The ice flow shown in Figure 2.11 represents averaged annual flow, since it was measured over a period of almost exactly one year.

Figure 2.11: Average ice flow measured between 1 July 2010 and 2 July 2011. Flow direction is indicated by arrows.

46 2.5 Discussion

Any analysis of ice loss using DEMs requires that they accurately reflect the elevation of the glacier surface. In the case of the modified 1982 DEM used for this

analysis, the fact that the original DEM derived from the 20 m contours agreed well with

3D measurements made from the source photography suggests that this modified DEM

can be considered to be reliable, with the relative accuracy of points on the gently-sloping glacier surface likely better than the measured vertical accuracy of 5 m, which was determined from a combination of points on and off the glacier.

Of more concern is the 1958 DEM. The stereo model used to generate the original uncorrected DEM did not agree well with measured elevation points from the 1982 photography. The 57 points used to produce the correction surface were densely spaced and located in snow-free areas surrounding the glacier. However there was no way to ensure that all the points were observed to the same standard of accuracy. The subsequent linear interpolation and filtering of the correction surface were designed to reduce the effect that individual points would have on the derived surface.

Another concern is that if the errors observed in the 1958 DEM are due to film instability, they are unlikely to be linear in nature. The derived correction surface therefore represents an approximation, which will almost certainly contain residual errors. That being said, the subsequent comparison between points around the edge of the glacier did suggest that the 1958 DEM was substantially correct, with an estimated elevation accuracy of 7 m for areas off the glacier. The profiles shown in Figure 2.10 also

47 show that the 1958 surface matches the 1982 surface fairly well, differing only in

absolute elevation, which suggests that the influence of any residual errors is small in the

terminus region. It is believed that while there may still be localised errors present in the

corrected DEM, it is sufficiently reliable to form a reasonable base for comparison with

the 1982 DEM.

A comparison between the 1958 and 1982 DEMs suggests that significant ice loss

occurred between these two dates. This ice loss appears to be uneven, with areas of high

ice loss, in the 10 m to 20 m range, interspersed with sections of the glacier which appear

to have suffered negligible ice loss (see Figure 2.6 and Figure 2.7). While it is possible

that this may simply reflect the residual errors in the corrected 1958 DEM as mentioned

above, it could also be caused by surface uplift affecting either the 1958 or 1982 DEMs.

This could possibly have occurred as a consequence of changing ice flow patterns, or

because of high basal water pressure at the time when one or other set of source photos

was acquired.

It is also important to take into account the timing of image acquisition, especially

when making short-term comparisons. According to ground-based photogrammetric measurements made over the summers of 2009 and 2010, ice loss in the terminus region averaged between 2 m and 3 m over the melt season. These measurements will be described in Chapter 4. The evidence presented above suggests the average ice loss during the melt season was considerably lower than this between 1958 and 1982.

Therefore, when comparing the 1958 and 1982 DEMs, and the 1982 and 2010 DEMs,

48 seasonal differences in the time the photos were acquired may be effectively ignored,

since any effects will be small, relative to the total change in surface elevation.

It is however misleading to make direct comparisons between measurements

made in 2010 and 2011, without first accounting for differences in the timing of the melt

season. The 2010 measurements of melt rates which will be described in Chapter 4

suggest that the average rate of ice loss in late June / early July of 2010 was around 3 cm

per day. Although the timing of the 2010 and 2011 surveys differed by only one calendar

day, time-lapse photography of the glacier revealed that surface melting in 2010 began

around the end of the first week of June, shortly after the nearby Bylot-1 weather station

started recording predominately positive mean air temperatures. In 2011 melting began

two weeks later, suggesting that melt season was two weeks more advanced in 2010.

However these same measurements also show that the melt season started more slowly in

2010 than in 2011.

A comparison of Figure 2.9(a), (b), and (c) suggests that surface melt has increased considerably since 1958. Ice loss per year between 1982 and 2010 was approximately 35% greater than that measured between 1958 and 1982. While the differences in surface elevation between 2010 and 2011 need to be treated with caution, it still appears that ice loss over this period from parts of the northern terminus was close to double the average ice loss between 1982 and 2010. It is also interesting to note the pattern of melting. Figure 2.9 shows that comparatively little change in the melt rate has occurred in the central parts of the terminus region. However the melt rate in marginal

49 regions has doubled since 1958, particularly on the northern side of the glacier and at the terminus itself.

A period of a single year is insufficient to determine whether the rate of ice loss between 2010 and 2011 is representative of current conditions, or whether this year represents a statistical anomaly. However observations for Pond Inlet over the summer months of June, July, and August show that mean-monthly temperatures increased by between two and three degrees Celsius over the period between 1976 and 2011, so an increased amount of ice melting would be expected to occur under current conditions.

The evidence presented above suggests that, on average, the terminus region of the glacier has lost between 35 m and 45 m of ice thickness over the last 50 years, and that the rate of ice loss has been increasing over time. This figure is in line with that given by Gardner et al. (2012) who estimated that the terminus regions of most glaciers on Bylot Island had lost between one and two metres of ice per year between 1979 and

2010. In order to remain stable, ice flow into this region would need to match ice loss from all sources, including melting and dry-calving. Clearly this has not been the case over the last 50 years, with a net loss of ice occurring even between 1958 and 1982.

Assuming that flow speeds over the lower glacier have not changed significantly over the last 50 years, ice loss from all sources is now significantly greater than inflow of ice from higher up the glacier, especially in the slow-moving marginal regions.

The behaviour of Fountain Glacier has been contrasted with that of neighbouring

Stagnation Glacier. Over the last 50 years or so, this glacier has retreated by over 1.8 km,

50 showing an average retreat of around 35 ma-1 (Moorman and Michel 2000). Fountain

Glacier, on the other hand, has retreated by only around 250 m over the same period (see

Figure 2.8). However analysis of the above results suggests that Fountain Glacier has lost a considerably greater portion of its volume than was previously thought. The difference in response between the two glaciers is therefore likely due to the fact that Fountain

Glacier was considerably larger and thicker than Stagnation Glacier to start with. The shape of the centre-line profile shown in Figure 2.10a also suggests that the Fountain

Glacier is unlikely to show a rapid retreat over the next few years. Instead it is likely that the majority of ice loss will occur gradually as a result of surface melting, with the northern portion of the terminus showing the greatest change.

The second part of this analysis looked at deriving surface velocities by feature tracking. The Cosi-Corr automated feature tracking gave reasonable results in the slower moving marginal areas, but correlations were poor in the faster moving centre of the terminus region. Had the time interval between the two image mosaics been shorter, it is likely that this approach would have been more successful. Manual feature-tracking using clusters of rocks, as well as vertical cracks in the ice proved to be more successful. By using this approach, it was possible to reliably determine glacier speed and direction over the course of a full year. In the next few chapters, other methods will be described for measuring glacier speed at different times of year. By comparing these different measurements, it is possible to determine the relative summer and winter speeds of the glacier; giving clues to how much basal sliding contributes to overall motion.

51 The values shown in Figure 2.11 show the speed of ice flow in the terminus

region over a one year period. One feature of interest is the rapid transition from the

relatively fast motion at the centre of the upper-terminus region to the slower speeds closer to the terminus. This could be related to the transition between basal sliding, close to the centre-line of the glacier, and motion resulting purely from ice deformation, closer to the margins. Alternatively it may represent a slowing in response to changing bed topography. This transition zone will be investigated in more detail in the chapters to follow.

2.6 Conclusions

The analysis carried out in this chapter was designed to establish baseline values for ice loss and to determine ice flow patterns over the terminus region of Fountain

Glacier. The results show how airborne photogrammetry, using photography from a variety of sources, may be used to obtain accurate repeat measurements of surface topography and dynamics. The versatility of the photogrammetric approach made it possible to compare historical photography from 1958 and 1982 with high resolution photo mosaics and DEMs produced from contemporary UAV and helicopter surveys.

While there were variations in the accuracy of the DEMs from different years, these were generally smaller than the magnitude of the changes measured.

It is apparent from looking at the data that the terminus region of Fountain Glacier is currently losing a great deal of ice. Although the comparison between the 2010 and

52 2011 DEMs is too short a time period to have any statistical validity, it is nonetheless

revealing to observe that ice loss over one year is significantly greater than the average

rate of loss between 1958 and 1982. Inspection of the profiles shown in Figure 2.10

suggests that the terminus will not retreat significantly over the next few years, but that

ice loss from the surface will continue, with the northern terminus region likely to show

the greatest amount of melting.

This chapter also demonstrates how repeat photogrammetric surveys can be used to determine surface dynamics through feature tracking. Although the use of automated feature tracking was unsuccessful in this case, it is likely that this approach would work well for high resolution image mosaics separated by a shorter time period. This is an approach for which repeat UAV surveys would be ideally suited, as they could be carried

out at regular intervals for comparatively little cost. The manual feature-tracking

approach adopted was successful because it did not depend on image correlation, but

rather on the positions of prominent features on the glacier surface. This approach is

therefore more appropriate when images are separated by longer time periods.

With the development of digital-photogrammetric packages capable of using photography from off-the-shelf cameras, and the advent of lightweight UAVs which can be flown virtually on demand, it is likely that aerial photogrammetry will enjoy a resurgence for glaciological applications. The orthophotos produced from such surveys are much more detailed than any form of satellite imagery currently available, and the

DEMs produced are similar in accuracy to those obtained from a LiDAR survey. The use

53 of UAVs may well help to make regular low-cost high-resolution surveys a realistic option for monitoring ongoing glacial processes.

54 Chapter 3: Using Oblique Photogrammetry to Monitor the Seasonal Decay of a

Proglacial Icing

3.1 Introduction

Oblique or ground-based photogrammetry has been used for many studies of glaciological processes. At its simplest, historical photography, often dating back to the early 1900s has been used as a basis for comparison with current day glacial conditions.

Comparisons of this nature can highlight the often significant changes in ice cover which occur over the medium term and may play an important part in creating public awareness of changing climatic conditions.

More rigorous studies have been carried out for a number of glacial environments, often using calibrated metric cameras. Typically in such studies the same camera station is reoccupied, and photographs are taken every few years e.g. (Brecher and Thompson

1993; Kaufmann and Landstäedter 2004). Quantitative information about changes in the glacier surface and patterns of glacier advance and retreat can then be obtained through photogrammetric measurement of common points. This process is inexpensive and more flexible than traditional aerial photogrammetry, since photos can be obtained during field

visits to the glacier, rather than requiring an expensive aerial survey to be carried out each

time. Another advantage is that the photos can always be acquired from the same fixed

positions, greatly improving the measurement accuracies obtainable from the

photogrammetric process.

55 Ground-based photogrammetric surveys often use convergent photography to measure discrete points. This is different to aerial photogrammetry, which generally uses vertical or near-vertical photography to provide stereo coverage of the area of interest. In many cases the large depth variation associated with oblique photography can make it unsuitable for continuous mapping of features, since accuracies decline rapidly with increasing distance away from the camera. However the stronger geometry provided by a suitably-spaced convergent camera configuration allows for high measurement accuracies to be maintained over greater distances.

Convergent photography was used by Brecher and Thompson (1993) in their multi-year study documenting the retreat of the Qori Kalis glacier in the Peruvian Andes between 1963 and 1991. A baseline DEM was produced using 1963 aerial photography.

Ground-based photography was then obtained in 1978, 1983, and 1991, from two surveyed camera positions 380 m apart. Three permanent ground control points were surveyed and used to orient the photos for each year. Measurements were then made to a set of points on the surface of the glacier. Comparison of measurements showed that the glacier was thinning rapidly, with the rate of thinning increasing over time.

Kaufmann and Landstäedter (2004), studied the retreat of the Goessnitzkees

Glacier in the Austrian Alps. Photography was obtained in 1988, 1996, 1997, and 2003, using three different cameras. In this case the photos were analysed stereoscopically, with

DEMs being produced for the central part of the glacier for each year. An analysis was carried out to determine the accuracy of a longitudinal profile, when compared with

56 measured survey points. This comparison suggested that RMS accuracies for the

photogrammetric survey ranged from 12 cm to 23 cm, showing that well-controlled

oblique photogrammetry has considerable potential for undertaking accurate glacier

surface mapping.

In another study carried out by Landstäedter and Kaufmann (2004), ground-based

photogrammetry was used to study the motion of the Outer Hochebenkar Rock Glacier in

the Austrian Alps. Photo pairs were acquired in 1986, 1999, and 2003. Cameras were

located on the slope opposite, with photos being acquired from six known positions. A

total of 70 GCPs were identified from 2003 aerial photography and used to produce a series of orthophotos, which allowed average flow vectors to be derived for the glacier.

Pitkänena and Kajuuttib (2004) investigated the utility of panoramic stereo

photography for forming detailed DEMs of small areas on the snouts of Engabreen

Glacier in Norway and Hintereisferner Glacier in Austria. In each case, the area covered

by the DEM was small (10m by 10m). Photography was obtained once a year for three

successive years. The two glaciers were quite different in character. Engabreen was steep

and heavily crevassed, so the camera and control points had all to be sited in front of the

glacier. This had the advantage that the same camera positions and control points could

be reoccupied each year. A highly detailed 20 cm resolution DEM was formed for the test

area of this glacier for each year of photography. Hintereisferner was flatter, but was

covered in debris. It was necessary to set up both cameras and control points on the

57 glacier itself, meaning that the same positions could not be occupied in successive years.

A 50 cm resolution DEM was produced for the test area on this glacier in each year.

Though not strictly ground-based photogrammetry, Sanjosé and Lerma (2004) described a system which used a combination of geodetic survey and helicopter-based convergent photogrammetry to monitor changes in the flow of the Argualas Rock Glacier in the Spanish Pyrenees. Photography was taken in 1991, 1993, 1994, 1995, 1998, and

2000, using a Rollei 6008 semi-metric camera, with targets being used to identify the position of a number of surveyed control points. This study concluded by discussing the sensitivity of rock glaciers to changing temperatures, and thus the importance of developing a system for regular monitoring of rock glacier flow.

A number of photogrammetric studies have been carried out using photographs acquired from a single camera station. Where camera orientation parameters can be recovered for a single photo using GCPs, the process is known as a single-photo resection. Accurate measurements may be made of surface change, providing that the photo is correctly oriented and additional positional information is available, e.g. a reliable DEM covers the area of interest. This technique is often used in cases when a time series of photographs is automatically acquired by the camera.

Ashenwald et al. (2001) used time-lapse photography from a single 35 mm camera to investigate snow cover for the Passeier Valley in the Italian Tyrol over the period between November 1996 and September 1997. The time series of photographs were projected onto an Italian National DEM in order to produce a series of orthophotos.

58 These allowed measurements to be made of snow extents throughout the duration of the

study.

In another study using individual cameras, Harrison et al (1992) used time-lapse photography to monitor glacier speed during a surge of the West Fork Glacier in the

Central Alaska Range. Two 35 mm cameras were set up overlooking different sections of

the glacier. Both cameras were programmed to take one exposure per day for nearly a year. The speed of visible features on the glacier surface was calculated, relative to reference points on the valley side. Feature positions were mapped using aerial photography prior to and after the surge, and also by field surveying. These positions were used to determine scale factors for the photography.

Triglav et al (2000) developed a methodology to make use of historical archive

photography of the Triglav Glacier, which had been acquired monthly since 1976. This

archive was considered to be of great value in studying the retreat of the glacier in recent years. The photographs were taken from two camera stations with a Russian made

Horizont panoramic camera. This camera was not calibrated and the first step was to develop a calibration model for it. A multi-disciplinary survey was carried out in 1999, and current photos were obtained using a Rolliflex 6006 metric camera. Using a specially produced 10 m resolution DEM, a series of pseudo-orthophotos were generated from the original panoramic photography. From these it was possible to document the changing glacial extents over the period from 1976 to 1999.

59 In recent years, the advent of easily programmable digital cameras means that it is

now a fairly simple matter to collect regular time-lapse photographs in the field. These

photos can be used to quantify displacements arising from glacial dynamic processes.

Recent work using digital time-lapse photography has been carried out on the Argentière

Glacier in the French Alps by Fallourd et al. (2010). Time-lapse photography was used to estimate relative glacier motion in terms of pixels per day. However lack of knowledge of the distance between the camera and the glacier surface prevented the determination of true glacier surface velocity.

Maas et al. (2008) used a combination of a terrestrial laser scanner and high resolution terrestrial photography to estimate velocity fields close to the terminus of three

Greenland outlet glaciers. In 2004 photography was acquired using a 14 MP camera, whereas in 2007 a high-resolution 39 MP camera was used, allowing the tracking of

4,500 points on the glacier surface. The cameras took photos every 15 minutes over periods varying between one and three days. In addition to determining surface velocities, the measurements had a sufficient temporal frequency to enable the determination of the

vertical signal associated with tidal effects on the floating ice shelf at the terminus of

Jacobshaven Isbrae.

Ahn and Box (2010) and Ahn and Howat (2010) describe the use of single camera

time-lapse photography for determining velocity fields on a number of Greenland outlet

glaciers. Automated image-matching techniques were used to ensure that all photographs

were coregistered, and orientation parameters were obtained using the ASTER Global

60 DEM. The cameras were programmed to acquire hourly photographs throughout the course of an entire year. Using this technique, detailed estimates were obtained of surface velocities for sections of these glaciers. The long distances between the camera stations and the glacier surface meant that spatial resolutions were low, typically between 10 and

20 m. However this was compensated for by the high speed of the glacier, allowing estimates of glacier speed to be determined to within an estimated one metre per day.

These studies show some of the advantages that oblique photogrammetry offers for glaciological studies. It has been found to be particularly useful for monitoring changes to glacier margins and surface elevations over time. Time-lapse photography has also been successfully combined with photogrammetry for use in determining the velocity field on fast-moving glaciers, where surface velocity significantly exceeds the measurement uncertainty present at each point. To date however, little attention has been given to the use of oblique photogrammetry for the study of slow-moving polar glaciers.

Such a task poses a number of challenges, since the surface movements of such glaciers are typically in the order of millimetres to centimetres per day, which is usually lower than the accuracy associated with individual photogrammetric measurements.

This chapter and the following chapter describe how ground-based photogrammetry was used to monitor a number of glacial and periglacial processes associated with Fountain Glacier. In this chapter, a theoretical background is given to the photogrammetric process, and issues relating to camera calibration and the stability of the camera stations are discussed in the context of a trial project set up to monitor the

61 seasonal decay of the proglacial icing. The following chapter will focus on the

glaciological applications of oblique photogrammetry and describe how it was used to

estimate surface dynamics, determine seasonal melt rates and to provide estimates of the

emergence component of velocity of Fountain Glacier.

Improved understanding of the changing state of the icing is important, as its

formation depends on the availability of a steady supply of liquid water from beneath the glacier itself. Similarly, the summer decay of the icing is due to a combination of surface melt and hydrothermal erosion from streams fed by glacial surface meltwater. The formation and decay of the icing are therefore closely linked to the processes affecting the glacier at different times of year, and can thus provide insight into the condition of the glacier itself. Quantitative measurements of the state of decay of the icing may therefore directly relate to the timing and intensity of the summer melt season.

3.2 Objectives

The study described in the current chapter had three main objectives.

• The first objective was to capture a series of time-lapse photographs, showing the

summer melting and decay of the proglacial icing associated with Fountain

Glacier, over the period between mid June and mid August, 2008.

• The second objective was to carry out a photogrammetric analysis of the time-

lapse photographs, in order to provide quantitative measurements of the changing

62 extents of the icing and to produce a time-series of orthophotos showing the

transition from full ice cover to minimal ice cover, over the course of the summer

melt season.

• The third objective was to test the cameras and time-lapse units, prior to their

longer-term installation in less accessible locations overlooking Fountain Glacier.

3.3 Photogrammetric theory

For a single photograph, the perspective-projection equations can be used to define the relationship between photo positions and ground positions. The situation can be simplified by assuming that both the real-world (object space) and photo coordinate

(image space) systems share an origin at the centre of the camera lens, and a common axis defined by the line between the principal point of the image plane and the lens centre. This situation is illustrated in Figure 3.1. The perspective projection equations can then be expressed as:

X Y x = − f y = − f [3.1] Z Z

Where f is the focal length of the camera.

Figure 3.1: The Geometry of perspective projection.

These equations map 3D ground positions to 2D photo positions. If the distance from the real-world point to the centre of the camera lens is known, and if the size of each detector element and the focal length of the camera are also known, it is possible to calculate the X and Y dimensions of a feature in object space. However in practice the simple form of the perspective projection equations cannot be used for more than one photograph, since each photo has its own unique coordinate system. Figure 3.2 illustrates the relationship between the object-space and image-space coordinate systems.

Figure 3.2: The relationship between object and image coordinates. The photo

coordinates of point a are (xa,ya). The coordinates (XL,YL,ZL) and (XA,YA,ZA) describe

the object-space coordinates of the perspective centre of the camera lens O, and the real-

world point A respectively.

The general case is described by the collinearity equations. It is assumed that a

point in object space, the perspective centre of the camera lens, and the representation of

the point on the camera image plane are all collinear. The collinearity equations can be formulated as shown in equation 3.2 (Clarke and Wang 1998). It should be noted that this

is a theoretical formulation, and in practice additional terms are usually added to each

equation to account for errors introduced by radial and decentring lens distortions as well

as in and out of plane distortions.

65 m (X − X ) + m (Y − Y ) + m (Z − Z ) x = −c 11 A L 12 A L 13 A L a m (X − X ) + m (Y − Y ) + m (Z − Z ) 31 A L 32 A L 33 A L

m21 (X A − X L ) + m22 (YA − YL ) + m23 (Z A − Z L ) ya = −c [3.2] m31 (X A − X L ) + m32 (YA − YL ) + m33 (Z A − Z L )

Referring to Figure 3.2, xa and ya represent the photographic coordinates of point

a in the image-space coordinate system, xy. The coordinates of point A(XA,YA,ZA) and the perspective centre of the camera O(XL,YL,ZL) are expressed in the object-space

coordinate system, XYZ. The terms m11 - m33 are elements of the 3x3 rotation matrix M,

which describes the angular relationship between the image and the object-space

coordinate systems. Although this matrix contains nine elements, the only independent

parameters are the three rotation elements ω, φ, and κ, which represent sequential

rotations about the camera X, Y, and Z axes respectively. The focal distance of the

camera is represented by c.

3.3.1 Single-photo resection

A camera has six degrees of freedom. These are defined by the three possible

translations in X, Y, and Z, and by the three possible rotations ω, φ, and κ. Together these

six parameters are known as the Exterior Orientation Parameters (EOP). If these

parameters are known, the orientation of a photo in space can be uniquely defined. Two

collinearity equations can be formed for each control point. Thus having three known

points will permit the formation of six equations, which is sufficient to solve for the six

66 unknowns. The determination of orientation parameters in this manner is known as a

single-photo resection. In practice the solution is normally over-determined, with optimal

values for each parameter being calculated using a least squares adjustment. If the camera

position is known through independent measurement, then only the rotation elements

need to be determined. In such cases, a minimum of two GCPs are required to determine

the remaining three unknowns.

3.3.2 Inner orientation

An inner orientation is carried out in order to establish the position of the principal point in the image plane of the camera, and also to establish the relationship between the perspective-centre of the camera lens and the image plane. This procedure is carried out as part of a camera calibration. During calibration, lens distortions are also mapped for a particular camera / lens combination. The primary Interior Orientation

Parameters (IOP) are xp, yp, the image-plane coordinates of the principal point, and c, the

principal distance or focal length, which is the distance between the perspective centre of

the lens and the principal point on the camera image plane. In practice IOP may also

include terms to correct for radial lens distortion (K1, K2, K3), for decentring lens

distortion (P1, P2, P3), as well as for affine and out-of-plane distortions. In general a calibration should remain stable for a particular camera / lens combination if the conditions under which it was carried out remain unchanged. However, if the camera settings are changed, or if the camera is dropped, it may be necessary to recalibrate it.

External factors, such as extreme temperatures can also have an effect on camera stability, which is a concern when using non-metric cameras in arctic environments.

67 Conventional camera calibration of metric cameras is a complex procedure involving the use of an autocollimator, or a precision calibration field to determine the

IOP. These procedures are summarised by Clarke and Fryer (1998). The use of digital consumer cameras for photogrammetric measurement has provided impetus for the development of simplified calibration methods. The use of straight lines has been suggested by a number of authors as a simple way to derive calibration parameters, e.g.

(Prescott and McLean 1997; Habib and Morgan 2003). Alternatively, flat-panel calibration targets are used by a number of commercial applications such as

PhotoModeler and Image Master, and can provide reasonable results for many applications, in cases where it is not practical to use a calibration field.

Another option is to carry out a self calibration procedure, which is described by

Fraser (1997). In a self-calibrating bundle adjustment, IOP are extracted at the same time as EOP, through the use of multiple GCPs. These are determined during a single-photo resection process. In a self calibration, EOP and IOP are determined separately for each photograph. While this technique has many advantages, it depends on the availability of multiple, well-distributed GCPs for every image.

For the projects described in this chapter and in the following chapter, none of the calibration techniques described above were suitable, as there were limited numbers of

GCPs available, the available GCPs were not well distributed, and the camera IOP could not be assumed to remain constant over time. However the problem can be simplified considerably since the camera X, Y, and Z positions were fixed, and changes to the

68 camera rotations were expected to be small, meaning that the effect of lens distortions could be effectively discounted.

3.3.3 Determination of 2D-photo and 3D-ground positions for a single photo

Once the camera orientation parameters have been determined, the collinearity equations can be used to calculate the photographic coordinates of any known ground point within the field of view of the camera. This process can be reversed if there is a

DEM of the area covered by the photo. A theoretical ray of light can be projected from the measured point on the image plane of the camera through the perspective centre of the camera lens. The object-space coordinates of the point are defined as the point where this ray intersects the ground surface defined by the DEM. If this process is repeated for every point on the photograph then it is possible to create an orthophoto from the original photo. Another way of generating an orthophoto is to use the collinearity equations to reproject the DEM into the image space coordinate system. Since each DEM pixel has a set of known 3D coordinates associated with it, the photos can then easily be reprojected into the object-space system. If multiple photos share the same orientation parameters this second approach is more computationally efficient, since the transformation only needs to be applied once. This approach is described by Ashenwald et al. (2001) for a sequence of time-lapse photographs obtained from a single camera.

69 3.4 Methodology

3.4.1 Camera set up

Two camera stations were set up in June of 2008 overlooking different sections of

Fountain Glacier Icing. Camera 1 was positioned close to the terminus of the glacier

looking south over the upper icing (see Figure 3.3), and Camera 2 was positioned on a low ridge, close to the valley constriction marking the lower end of the main section of the icing (see Figure 3.3). Camera 2 was oriented facing northwest, looking up the icing

towards the glacier. Though most of the icing was visible from this camera, it was located

only 22 m above the surface of the icing, limiting the effective range to within a few

hundred metres of the camera. Light rays from further-away parts of the icing were

virtually parallel to the ground surface, so contained little useful information.

Both camera stations used identical 10 Mp Canon XTi cameras, which were fitted

with 50 mm fixed lenses. The cameras were both secured inside weatherproof enclosures

lapse systems. The units consisted of the enclosure itself, a solar panel, battery, backup

battery, and a time-lapse controller. The time-lapse controller ensured that long-term

power usage was minimised by sending the camera into a state of hibernation between

exposures. Power was consumed only when photos were taken.

Figure 3.3: Location of Camera Station 1 and Camera Station 2. The dotted white lines

show the field of view for each camera. The six targets on the icing are indicated by white

triangles, with the two check points used for verification shown as white crosses. The

image backdrop is a SPOT image provided by Geobase ®., acquired on the 3rd of August

2008, showing the icing at close to its minimum extents.

Both camera installations were surrounded by rocks to ensure maximum stability

over time. Camera 1 acquired its first photo at 1:20 am on June the 11th 2008, whereas

Camera 2 acquired its first photo at 2:27 pm on June the 9th 2008. Both cameras were set to take a single photo every three hours throughout the summer. The timing of the photos

71 was chosen to study the seasonal melting of the icing throughout the summer of 2008.

Camera Station 2 is shown in Figure 3.4.

Figure 3.4: Camera Station 2.

3.4.2 Photo retrieval and control survey

Photographs were retrieved from both cameras on the 10th of August 2008. At the time of photo retrieval, GPS measurements were made of the camera station positions using a Trimble RTK GPS, with an estimated horizontal and vertical accuracy of 5 cm.

One day prior to image retrieval, six targets were placed on the icing. These targets comprised a 60 cm diameter red circle on a white background, and were mounted vertically in positions visible from both cameras. The targets were also surveyed using

GPS, and were left set up for 24 hours, to ensure that they would be included in the last

72 few photographs acquired by each camera. The locations of these targets are shown in

Figure 3.3 and Figure 3.5.

In addition to the control survey, GPS surveys of the icing were carried out in both June and August. These surveys were carried out in conjunction with the gathering of GPR profiles, and as such did not provide high density point coverage. However the measurements were sufficiently detailed to allow the formation of representative DEMs covering the icing, at times approximately corresponding the start and end of the study.

3.4.3 Camera calibration

Prior to the cameras being taken to Bylot Island, a preliminary flat-panel calibration was carried out for Camera 1, using PhotoModeler software. A single-photo resection carried out later, using well distributed targets spread over the terminus of

Fountain Glacier, showed the focal length derived from the initial calibration to be in error by approximately 1 mm for both cameras. Since no other calibration information was available, it was decided to use the focal length derived in the field, and make the assumptions that the principal point was located in the centre of the image plane for each camera, and that image distortion was negligible. While this is a simplification, image distortion for a 50 mm lens can usually be expected to be small, and it is unlikely that it would exceed the uncertainty in measurement for any given terrain point. Also, since the features being measured were expected to always lie in roughly the same region of the photographs, it was thought that any residual errors due to lens distortion would be unlikely to significantly affect the overall result. Subsequent analysis described in this

73 chapter assumes a focal length of 51.336 mm for both cameras. This value was derived from the initial single-photo resection described above.

3.4.4 Processing

3.4.4.1 Orientation of the reference photographs

The final photographs collected from each camera were used as reference photos, since they included the targets placed on the icing. All six targets were identified, and their positions measured on the photographs. The targets were not optimally distributed for either camera, since they occupied narrow strips across the centre of each of the photographs (see Figure 3.5). This effect was particularly pronounced for Camera 2, since the reference targets were over 800 m away and were at a similar height to the camera, with the result that all targets had similar y values. Nominal values for the ω, φ, and κ rotation parameters were used as initial estimates to approximately orient each camera.

To calculate the initial orientation for Camera 1, targets 2 and 6 were selected, while for Camera 2, targets 1 and 5 were chosen. These targets were chosen in order to maximise the distance between measurements on each photo, and to ensure that both selected targets for each camera were approximately equidistant from the photo centres.

Using the Noobeed photogrammetry software package, the measured GPS positions of the selected targets and camera stations were used, along with the initial estimates for ω,

φ, and κ, in order to calculate preliminary photo coordinates for the two targets on each of the reference photographs.

Figure 3.5: Targets and reference points as seen from Camera 1 (a), and Camera 2 (b).

Targets are shown as black circles, with reference points being shown by white triangles.

75 The preliminary calculated photo coordinates were then compared with the measured photo coordinates. The difference in x and y was then computed, and sequential corrections were applied to the values of ω, and φ in order to minimise the differences. After applying these corrections, the estimated coordinates were recalculated and again compared with the measured coordinates. This time a correction was applied to the κ value to minimise the discrepancy. This procedure was run over several iterations, allowing the final camera orientation parameters to be determined from a set of poorly conditioned GCPs, while keeping the camera X, Y, and Z fixed.

Table 3.1 shows the measured error in pixels for each GCP after the orientation parameters were calculated.

Table 3.1: Error measured at each target.

Camera 1 Camera 2

Error (pixels) x error y error x error y error

Target 1 0 5 1 0

Target 2 0 -1 2 0

Target 3 2.5 11 -0.5 -1

Target 4 2 2 0 -0.5

Target 5 0 -8 -0.5 0.5

Target 6 0 0.5 1 -1

RMSE 1.3 6.0 1.0 0.6

76 It can be seen that the errors in measurement from Camera 1 were significantly

higher than those from Camera 2, especially in the y direction. This is likely due to the

fact that most the targets were less than 400 m away from Camera 1, whereas they were

more than double this distance from Camera 2. Small errors in identifying the target

centres would therefore be expected have a greater effect on the x and y coordinates

measured from Camera 1 than on those measured from Camera 2. Also the targets

appeared more spread out in the y direction from Camera 1, which could also help to

explain the greater errors in y observed from this camera.

3.4.4.2 Determination of orientation parameters for the remaining photographs

Although the camera positions were known and assumed to be invariant, it was not possible to orient the remaining photographs from each series, as there were no GCPs

available, from which values of ω, φ, and κ could be derived. Analysis of the photos

showed that both cameras underwent significant rotations over the duration of the study,

so these parameters could not be assumed to be invariant.

Two reference points were identified for each camera. The points chosen were

easily identifiable rocks, which were clearly visible on all the photographs in each series.

The positions of these reference points are shown in Figure 3.5. Photo coordinates for the

each of the selected points were then measured on the oriented reference photographs.

Approximate elevations for each of the four points were estimated using NTS 1:50,000

topographic map 038B14. Using these heights and measured photo positions, 3D ground

coordinates were calculated for each reference point, using the back-projection technique.

The coordinates obtained in this manner could not be assumed to be accurate in absolute

77 terms, since the exact height remained unknown, thereby introducing errors into the

length of the projected ray between the camera and the point. However, since the

positions of both cameras were fixed, the correct angular relationship was maintained,

meaning that the points could be used to derive the rotation parameters, relative to those

of the reference photograph. To reduce the size of the data set, only one image from late

morning of each day was used from each camera. The appropriate reference points were

measured on each image and orientation was then carried out using the same technique as

was used for the reference images. In this way a full set of orientation parameters were

derived for each image.

3.4.4.3 Orthophoto generation

After orientation was completed, an orthophoto was produced from each photograph, using Noobeed software. A comparison of the two DEMs from early June and early August showed that there was an average 70 cm difference in ice thickness between the start and the end of the study. A compromise height model was produced by subtracting 35 cm from the June DEM, and this was used to generate all orthophotos from both cameras. Ground coordinates were calculated by intersecting the theoretical light rays from each image pixel with this DEM. The image was then cropped so that it only covered the area of the icing. The final orthophotos generated from Camera 1 had a ground resolution of 0.3 m (see Figure 3.6 and Figure 3.7). Since Camera 2 covered a larger area, the orthophotos generated from this camera were given a ground resolution of

0.5 m (see Figure 3.8 and Figure 3.9).

Figure 3.6: Source photographs and orthophotos obtained from Camera 1.

Figure 3.7: Reference photo (a), and associated orthophoto (b), for Camera 1. The position of the check point used for verification is shown in b. Note how the elevated area to the left is elongated and appears to cut off the stream. This is a consequence of this area not being correctly represented by the DEM used.

Figure 3.8: Source photographs and orthophotos obtained from Camera 2. Note the significant shift in y which occurs between the middle two images.

Figure 3.9: Reference photo (a), and associated orthophoto (b), for Camera 2. The position of the check point used for verification is shown in b. Note how far away detail is distorted. This is a consequence of the low viewing angle.

82 3.5 Verification

Measurements were made of the position of check points on the icing in order to provide a check on the derivation of the EOP and to ensure that the orthophotos were consistent. Because the surface of the icing was constantly changing over the period of the study, it was only possible to identify a single check point visible from each camera station. Both points were rocks which were exposed by the melting ice. The check point for Camera 1 was visible on photos covering the last 43 days of the study, whereas the check point for Camera 2 was only visible for the final 38 days prior to image retrieval.

3.6 Results

Over the 43 days for which it was tracked, the measured position of the Camera 1 check point showed a shift to the north. This started after day 35 and continued until the end of the study (see Figure 3.10). There was a maximum measured eastward shift of 1.5 m and a northward shift of 7.8 m. The standard deviations of these measurements over the measurement period were 1.5 m and 3.5 m respectively. However the standard deviation masks the fact that motion occurred consistently in the same direction and was therefore unlikely to be a result of random measurement errors.

The check point for Camera 2 was tracked for 38 days. Over this period it had a maximum variation in easting of 4 m, with a standard deviation of 1 m, and a maximum variation in northing of 2 m, with a standard deviation of 0.8 m (see Figure 3.11). It can be seen that the measured point positions were more variable than for the Camera 1 point.

83 While there was a slight trend apparent in the eastward direction, there appears to be no significant trend for the northward position of this point. This suggests that the variability in measurement for this point is due largely to measurement errors, with the point itself appearing to remain consistent.

Figure 3.10: Movement of Camera 1 check point; (a): Change in eastward position, and

(b): Change in northward position of Camera 1 check point, relative to its position on the last day of the study. Note the trend in the northward direction which occurs from day 35 onward.

Figure 3.11: Movement of Camera 2 check point; (a): Change in eastward position, and

(b): Change in northward position of Camera 2 check point relative to its position on the last day of the study.

3.6.1 Assessment of the rotational instabilities for each camera station

In order to assess the variation of camera rotational parameters throughout the

summer, the daily ω, φ, and κ parameters were compared for each camera station. The

results for Camera 1 are shown in Figure 3.12 and for Camera 2 in Figure 3.13. It can be

seen that Camera 1 was generally more stable than Camera 2 over the duration of the

study. The total rotation for Camera 1 was around 0.6 degrees in the ω direction, 0.3

degrees in the φ direction, and 0.4 degrees in the κ direction. While the ω rotation did

85 show some irregularities, changes in φ and κ tended to be smooth and to show consistent

trends.

Camera 2 showed considerably more instability over the same period. Between day 38 and day 40, the camera underwent a rotation of around 8 degrees in the ω

direction, 0.6 degrees in the φ direction, and 6 degrees in the κ direction. This was a one

off shift which caused the photos from this camera to shift by around 600 pixels in the y

direction (see Figure 3.8). Although the other rotations were overshadowed by this shift,

it can be seen that the average daily variation of the rotation parameters was larger than

for Camera 1. It is believed that the sudden shift which occurred at this camera station

resulted from settling of the rocks beneath, due to thawing of the active layer. However,

while this shift significantly affected the rotation parameters of Camera 2, it is unlikely

that it would have had a significant effect on its XYZ position.

3.6.2 Variations in focal length over time

It was also apparent that there was some variation in the photo scale which

occurred over the duration of the study. The separation between the reference targets

observed for both sets of images was compared over time. This comparison showed that

for Camera 1, the scale had increased by approximately 0.3% over the two months of the

study. This is equivalent to the separation between the reference targets increasing by 12

pixels. Camera 2 showed a change of approximately 0.1% over the same period.

Figure 3.12: Variation in rotational parameters for Camera 1.

Figure 3.13: Variation in rotational parameters for Camera 2.

88 The observed scale variations were likely due to variations in the focal length of

the cameras over time, possibly as a result of changing temperatures. It is also likely that

the position of the principle point on the image plane would have drifted over time for

both cameras. While both of these effects would affect the derivation of the camera EOP,

and would also cause some changes to the orthophotos, these changes would likely be

small relative to the five metre accuracy required for measurement of the icing extents over time. For this reason, the focal length for each camera was considered to be fixed throughout this part of the study. However this assumption cannot be made for the higher accuracy measurements required to measure target positions on the glacier surface. The next chapter investigates the effect of varying IOP more thoroughly, and describes how these variations were accounted for when measuring surface changes on the glacier.

3.7 Discussion and conclusions

Over the duration of the study, the rotational EOP were continuously changing at both camera stations. However, even when the images acquired by Camera 2 shifted through 600 pixels in two days the final orthophotos appeared unaffected, with the position of the check point remaining unchanged. This suggests that the method for calculating the EOP was sufficiently robust to account for the considerable variations affecting images acquired from Camera 2. The measurements from Camera 1 suggested that there was an apparent movement of the check point towards the camera. While this could potentially mean that the EOP for Camera 1 were incorrectly determined, the

89 consistent nature of this motion suggests that the check point itself may have been

unstable. The apparent shift towards the camera was likely due to a drop in surface height, as a result of ice melting out beneath the point.

The two sections of the icing covered by the different cameras were significantly different in character, and each presented a unique set of challenges. While the area covered by Camera 1 was smaller, it was more topographically varied, and contained a number of glacio-morphic features, some of which were several metres higher than the general level of the icing. The DEM used for orthophoto generation was only gathered

over the ice-covered sections, so many of these elevated features were incorrectly

represented on the final orthophotos. The effects of this can be seen clearly in Figure

3.7b, where an elevated section to the left hand side of the image appears elongated on

the orthophoto and appears to cut off the proglacial stream flowing through the centre of

the image. Had the DEM correctly represented the elevated section, the resulting

orthophoto would have shown the proglacial stream flowing around this elevated section.

The section of the icing visible from Camera 2 was relatively flat, but the main

problem with location of this camera was the low elevation difference between the

surface of the icing and the camera. This meant that further-away sections of the icing

could not be clearly discerned. Under such conditions, the effects of even minor

variations in relief were exaggerated in the output orthophotos. This was apparent when

the orthophotos were examined in sequence. As the ice level dropped over the summer,

the ice surface appeared to be displaced towards the camera.

90 The results of this study could have been improved by locating the cameras in

more elevated positions. This would have reduced the effect of relief displacement, and

would also have allowed more of the icing surface to be included. The ideal location for

the cameras would have been on the elevated ridge which lies to the north of the icing.

Locating the cameras on this ridge would have allowed most of the icing to be viewed from both cameras simultaneously. The elevation difference would have been around 200 m, which would have allowed for better resolution of more distant features. However this location was not practical, as considerable time needed to be spent on initial camera setup and on checking the operation of the cameras and time-lapse units.

Further improvements could have been made by having permanently installed

reference targets. While there are few stable areas on the icing itself, targets could have

been placed in adjacent areas, within the field of view of the cameras. If several targets

had been permanently installed, a number of them could also have been used as

independent check points, which would have provided a considerably better check on the

accuracy of the EOP and of the final orthophotos than was possible in the current study.

The use of permanent targets and reference points was subsequently adopted for the study

of Fountain Glacier described in the next chapter.

This chapter shows how oblique photogrammetry can be used successfully for

low-accuracy monitoring applications. In this case the final objective was to produce a set

of daily orthophotos, showing the condition of the icing throughout the summer. The

resulting orthophotos were used by Pablo Wainstein to obtain measurements of the icing

91 extents throughout the summer of 2008 (Wainstein 2011). For such applications

measurement errors of up to five metres in XY could be tolerated. While this study

looked at the changing extents of the icing, the techniques described here could easily be

applied to variety of different monitoring applications, such as the study of stream

migration, or beach erosion. One of the most revealing ways that this information can be

presented is to produce a time lapse movie from the orthophotos. Movies were created

from both sets of daily orthophotos. These clearly showed the patterns relating to the

seasonal melting for the upper and lower icing. Presenting the information in this way

can help to provide new insight into many landscape processes.

While this chapter described a low-accuracy application and used two

independent cameras, the next chapter will look at how oblique photogrammetry can be

used to make more precise measurements, using convergent and stereo-camera configurations. These measurements can be used to provide valuable information on a variety of dynamic processes, and the availability of regular time-lapse imagery can provide information on processes which occur outside of the summer field season.

92 Chapter 4: Using Oblique Photogrammetry to Characterise Glacier Surface

Dynamics and Elevation Changes

4.1 Introduction

One of the advantages of using oblique photogrammetry for glaciological studies is that repeat photography with consistent image geometry can be obtained from the same viewpoint. Cameras may be programmed to acquire a time-sequence of images over a specified period, and these images can then be used to analyse how discrete points on the glacier surface move over time. If the camera-orientation parameters are known then measurements can be made of the relative or absolute positions of specific points, allowing detailed information to be gathered on the motion of the glacier surface.

Obtaining quantitative values describing the motion of a point on the glacier surface over time requires that the full X, Y, and Z coordinates of the point be calculated from each available set of photographs. In order to do this it is necessary to have photographs acquired from at least two different camera positions. For time-lapse photography this can be achieved by having at least two permanent camera stations, with each camera programmed to acquire photographs at the same time of day.

4.1.1 Stereo photogrammetry

Traditional aerial photogrammetry normally makes use of stereo photographs.

Stereo viewing is usually possible when the photos have a significant amount of overlap and share similar rotation parameters. However the large depth variation usually

93 associated with ground-based oblique imagery means that measurement accuracy for

stereo photography declines rapidly with increasing distance. Typically a convergent

camera configuration is adopted, in which the camera axes are not parallel, but rather oriented to provide the optimal intersection for the area of interest. This provides the

strongest possible imaging geometry, and will improve the accuracy of measurement for

further away points. Convergent photogrammetry normally has the disadvantage that

photographs cannot be viewed in stereo, which may make it unsuitable for mapping of

continuous features. However if target positions are accurately measured on two or more

photos, point positioning accuracy can be very high.

In traditional non-digital photogrammetry, pairs of photographs are oriented to

recreate the conditions under which they were acquired. This is usually done in two

stages. Firstly a Relative Orientation (RO) is carried out. This procedure recreates the

orientations of the photographs relative to each other, with the two oriented photos

combining to form a 3D model. Measurements may then be made of X, Y, and Z model

coordinates. These are correct, relative to the coordinates of other points within the

model, but they have no absolute value in terms of any real world coordinate system. The

second stage is known as an Absolute Orientation (AO). The 3D model is oriented and

scaled as a whole, in order to fit with known ground coordinates. Once this process is

complete, and relative and absolute orientations have been carried out, 3D measurements

can then be made of real world coordinates.

94 With digital photogrammetry, relative and absolute orientations are normally carried out as part of a single Exterior Orientation (EO) process. In order to carry out an

EO, the X, Y, and Z positions of at least three well distributed GCPs are usually required.

Additional horizontal and vertical GCPs and tie points can be added in order to improve the accuracy of this procedure, with the final model orientation parameters being derived through a least squares adjustment. In the case of oblique photogrammetry, the positions of the cameras may be already known from ground survey. If this is the case these positions can be included in the adjustment to strengthen the orientation. Where the camera positions and rotations of each photo have already been determined, by single- photo resection, or through a process such as that described in Chapter 3 these parameters can be used to directly form an oriented 3D model. This process is not as rigorous as carrying out a full EO, but it can allow the formation of a 3D model in circumstances where there would otherwise be insufficient control, or when GCPs and tie points cannot be easily identified. This situation is frequently encountered with convergent photography, since the same feature can look completely different on each photograph.

Once a model has been oriented, measurements can then be made of 3D point positions. Point positions are calculated by the intersection of theoretical rays which are projected from the measured point on each photograph, through the perspective centre of the respective camera lenses, and into object space. This process is illustrated in Figure

4.1, and is similar to the process described in Chapter 3 for the formation of orthophotos.

The main difference is that in this case two rays are intersected from different cameras, rather than a single ray and a surface. Since both photographs are usually acquired within

95 a short time period, measurements made from a 3D model will reflect the position of the

unknown point at the time of acquisition.

Figure 4.1: Point measurement from two cameras using intersecting rays. P(Xp,Yp,Zp),

O1(X1,Y1,Z1), and O2(X2,Y2,Z2) represent the object-space coordinates of the point of

interest and the perspective centres of the two camera lenses respectively, while p1(x1,y1) and p2(x2,y2) represent the measured photo coordinates for each camera.

4.1.2 The effect of baseline length and convergence on measurement accuracy

For stereo aerial photography the relationship between image parallax and height

resolution was described by Petrie (1970) as:

96 fB dp = dh [4.1] H 2

Where dp represents the difference in parallax of the point as measured on the two images, f is the focal length of the camera lens, B is the baseline distance between the two camera positions, H represents the height above ground level, and dh represents the height difference associated with change in parallax dp. For oblique photogrammetry depth can be substituted for flying height. This can be defined as the perpendicular distance between the baseline and the point being measured. For stereo photography therefore, assuming that the focal length of the camera remains constant, it can be seen that the accuracy of a measurement depends on the ratio of the photographic base length to the square of the distance to the point being measured. Since this concept was developed from aerial photogrammetry, it is referred to as the base / height ratio.

A longer baseline will therefore allow the point position to be defined more accurately, although the overlap between the photos will decrease correspondingly.

However using a convergent camera configuration allows the use of longer baselines, which will in turn strengthen the angular fix. This effect is shown in Figure 4.2. It can be seen that a convergent camera configuration over baseline AC will give a stronger fix for point P than baseline AB with a parallel camera configuration.

Figure 4.2: The effect of baseline length and convergence on the accuracy of point

positioning.

4.1.3 Elevation measurement from a single photograph

In cases where a series of photographs is available from only one camera, it is still

possible to make measurements of target elevations, as long as good estimates of the

target X and Y positions are available. Assuming that target positions are surveyed by

GPS each year, estimated daily XY positions can be interpolated. The elevation of a

target can then be computed, since the horizontal distance from the camera to the target is assumed to be known. The elevation is calculated from the length and the angle of the projected ray. This technique can provide valuable information on surface elevation change in cases where only one set of photographs is available

4.1.4 Focal length and principal point drift

In the previous chapter, some scale variations were noted over the duration of the icing study. These were believed to be related to changes in the camera focal length over

98 time, most likely as a result of temperature variations. On Bylot Island, temperatures recorded by the network of automated weather stations show an annual temperature range

of between 50° C and 60° C, so the effect of temperature on the camera focal length

cannot be discounted. These scale variations could effectively be ignored for the icing

study since the accuracy requirements were low, with an allowable error of five metres.

However to measure glacial motion on a slow-moving arctic glacier, relative horizontal

and vertical accuracies of between 10 cm and 20 cm need to be maintained over long

periods. Any variations in focal length therefore have to be properly accounted for.

Additionally it is likely that any variation in the focal length would also be accompanied

by a shift in the position of the principal point for the camera.

The stability of consumer-grade digital cameras has been investigated by a

number of authors (e.g. Labe and Forstner 2004; Habib and Morgan 2005; Habib et al.

2006). While many of these studies have investigated the stability of the lens and camera

sensor array under laboratory conditions, there has been little work published to date

investigating camera stability in the field, particularly over prolonged time periods. The

location of the cameras overlooking the glacier precluded the use of any repeatable in- situ calibration, so continuous recalibration of the cameras throughout the study was not considered to be a practical option. It was therefore necessary to develop an analysis strategy which would allow for variations in focal length, but which would not require a full recalibration of the camera for each photograph.

99 4.1.5 Analysis strategy for determining accurate relative target positions

It can be assumed that targets on the glacier surface will move by only a few metres each year. If it is further assumed that any changes in the camera rotations are small, the corresponding photo positions for each target can therefore be expected to change by only a few pixels over the course of the year. To determine surface motion, accurate measurements are required for the position of the targets relative to their initial positions. However since there is no requirement for high absolute accuracy in positioning, the initial focal length needs only to be approximate. A calculated scale factor can then be used to refine the specific focal length for each photo, relative to the first photo. The assumption that changes in target positions are small also has the benefit that the influence of lens distortion can be effectively discounted, since each target remains in the same general location on all the photographs.

By keeping the camera positions fixed throughout the duration of the study, only the ω, φ, and κ rotation parameters need to be derived for each photograph. The use of permanently-installed reference targets allows these rotations to be determined, and their separation can be used as a means of determining the scale factor for each photograph, relative to that of the first photo in the series. As long as it is small, any change to the principal-point position will also be compensated for by the ω, φ, and κ rotation parameters, since the camera positions are held fixed and their orientations are derived relative to the known positions of the reference targets. The process of obtaining camera

EOP and IOP is thus simplified, since only the ω, φ, and κ rotations, and relative focal distance are required for each photograph.

100 The strategy outlined above makes a number of simplifying assumptions which would not normally be appropriate for photogrammetric analysis. It is possible to do this because it is only the relative positions of the targets which are of interest. This method offers a practical empirical solution to the challenges of acquiring useful measurements under adverse physical conditions, where good camera calibration information is unavailable. To ensure that such a strategy provides useful results, it is necessary to provide independent data which can be used to verify any measurements. This can be done using annual GPS measurements of target elevations and positions.

4.2 Objectives

This chapter describes the use of ground-based photogrammetry for the

measurement of a number of parameters associated with changes to the surface and to the

surface dynamics of Fountain Glacier. The objectives of this study are summarised

below:

• Develop 3D measurement techniques using convergent ground-based

photogrammetry to track discrete points on the glacier terminus.

• Determine summer and winter ice flow patterns for the terminus region of

Fountain Glacier.

• Measure summer melt rates and the vertical component of surface motion in the

winter, for the terminus region of Fountain Glacier.

101 • Identify anomalous ice flow patterns and surface-elevation changes for the

terminus region.

• Use ground-based stereo photogrammetry to generate a series of DEMs, in order

to investigate the broader spatial pattern of surface elevation change throughout

the summer melt season and over the winter.

• Provide estimates of the horizontal and vertical accuracy for each measurement.

A number of the studies discussed at the start of Chapter 3 used ground-based photogrammetry to measure glacial surface dynamics (e.g. Harrison et al. 1992; Maas et al. 2008; Ahn and Box 2010). However no studies published to date have described the use of ground-based photogrammetry for carrying out measurements of slow-moving arctic glaciers. The slow flow rates pose a number of measurement challenges, since the daily movement of the glacier surface can be expected to be less than the accuracy associated with individual measurements.

4.3 Methodology

4.3.1 Fieldwork

4.3.1.1 August 2008

In August 2008, two camera stations were established high on the valley sides

overlooking the terminus region of Fountain Glacier, such that the northern part of the

glacier terminus was visible from each camera. The cameras were set up in a highly

102 convergent configuration in order to enable the strongest possible intersection over the

area of interest, as shown in Figure 4.3. The same cameras and camera enclosures

described in Chapter 3 were used for the glacier study. Each camera station was mounted

on a large rock, and rock cairns were built up around the enclosure in order to keep the camera as steady as possible over the duration of the study.

Figure 4.3: Camera station and target positions for measurement years one and two.

Four orientation reference targets were set up on the outwash plain in front of the glacier on large stable rocks, such that two reference targets were visible from each camera. The targets comprised 60 cm diameter circles, which were located at a distance of approximately 500 m from the respective camera stations. The positions of the camera stations and the reference targets were surveyed using an RTK GPS system, with an estimated horizontal and vertical accuracy of five centimetres.

103 Ten targets, named from GT1 to GT10, were set up on the glacier surface, in the overlap region between the two cameras. The targets were mounted on metal road sign stands, and oriented so that they faced mid way between the two camera stations, in order to ensure optimal visibility from both cameras. The distances between Camera Station 1 and the targets varied from 500 m to 850 m, while the distances between Camera Station

2 and the targets varied from 600 m to 1,150 m. The targets on the glacier were surveyed by GPS, to an estimated five centimetre horizontal and vertical accuracy. The locations of the camera stations, reference targets, and glacier targets are shown in Figure 4.3. Figure

4.4 shows photographs taken from Camera Stations 1 and 2, along with target locations.

Figure 4.4: (a): View from Camera Station 1, (b): View from Camera Station 2. Both views show the target configuration for 2008 – 2009 (measurement year one), and for

2009 – 2010 (measurement year two).

4.3.1.2 June / July 2009

On returning to the site in June 2009, it was found that most targets were still intact. However analysis of the photographs showed that GT1 could not be seen from

104 either camera station, and targets GT2 and GT7 were not visible from Camera Station 2.

These targets were therefore repositioned so that they could be seen from both camera

stations and renamed GT1new, GT2new, and GT7new, respectively. GT6 was also

replaced by GT6new, since it was situated close to a supraglacial stream and would likely

have been lost. The original and replaced positions of all targets on the glacier were

surveyed by GPS. Both camera stations were also raised in order to reduce the chances of

snow obscuring the camera view, since snow accumulation in front of the cameras

prevented useable photographs being acquired by either camera during the first four

months of 2009. The new positions of both camera stations were then surveyed.

4.3.1.3 June / July 2010

In June 2010 all the targets were found to be in various stages of collapse, with

only five targets remaining standing. GPS positions were measured for all targets, with estimated positions being obtained for collapsed targets, based on where the target centre would have been had the target been upright. All targets were then repositioned close to

their original positions and were resurveyed. To differentiate the repositioned targets

from the original positions, they were renamed GT101 to GT110. The new target

positions are shown in Figure 4.5.

In order to investigate the use of stereo photography, Camera 2 was moved to a

new position, 84 m from Camera Station 1. This new location was named Camera Station

3. The two cameras were arranged so that they provided full stereo coverage of the

northern terminus region. The two reference targets which had been visible from Camera

105 Station 2 (Ref3 and Ref4) were also moved, so that all four reference targets were visible from both Camera Station 1 and Camera Station 3. These targets were named Ref103 and

Ref104. The positions of the four reference targets and the two camera stations were then surveyed by GPS. The new arrangement of cameras and targets established at this time is shown in Figure 4.5, with annotated photographs showing the targets as seen from

Camera Station 1 and Camera Station 3 shown in Figure 4.6.

Figure 4.5: Camera station and target positions for measurement year three.

106

Figure 4.6: (a): View from Camera Station 1 (b): View from Camera Station 3. Both

views show the target configuration for the 2010 – 2011 (year three) measurement

period.

4.3.1.4 June 2011

In June 2011, all targets were again found to be in various stages of collapse. Six

of the targets were still standing, but none was completely upright. Target positions were

once again surveyed, with estimated positions being measured for targets which had

fallen over. The positions of the reference targets were also resurveyed during this visit.

4.3.2 Data retrieved

Photographic datasets were retrieved for each of the three measurement years of the study. Due to technical problems with the cameras, most of the photographs acquired over the first two measurement years came from Camera 1 alone, with full convergent photography only being obtained for the first 59 days of the first measurement year. Over the three-year duration of the study, the following datasets were obtained:

107 • Measurement year one: An 81 day record from Camera 1, acquired between

August the 20th and November the 10th 2008. Imagery was acquired from Camera

2 for the first 59 days of this period. A 22 day record was also acquired from

Camera 2 for the period between the 27th of May and the 17th of June 2009.

• Measurement year two: A full year’s record acquired from Camera 1, starting

on June the 24th 2009 and continuing through to June the 29th 2010. This record

had some breaks during the winter, when snow obscured the view of the reference

targets. Though both cameras worked over this whole period, the photographs

from Camera 2 were out of focus and could therefore not be used.

• Measurement year three: A 353 day record of stereo photographs, acquired

from both Camera 1 and Camera 3, for the period between the 10th of July 2010

and the 29th of June 2011.

The main reason for the large gap in the photo series for the first measurement

year was that snow obscured both camera lenses and also limited the view of the

reference targets, preventing correct orientation of some of the photographs. During this

period, the battery of Camera 1 experienced a short circuit, preventing this camera from

restarting after the snow melted in the spring.

4.3.3 Data Processing

4.3.3.1 Measurement year one: 20 August 2008 - 20 June 2009

Measurements were made of the row and column positions for each glacier target and for the two reference targets visible on each photograph. In order to compare

108 measurements obtained for different dates it was necessary to derive the ω, φ, and κ

rotation parameters for each photograph, since analysis showed them to be constantly

changing. The assumption was made that camera and reference target X, Y, and Z

positions did not change prior to data collection in June 2009. Using the measured row

and column positions for the two reference targets, and the known X, Y, and Z position

of each camera station, values for the three rotation elements of each photograph were

calculated iteratively using the technique described in Chapter 3, section 3.4.4.1.

The process was modified to incorporate varying focal lengths, which were

computed using a scale factor. The initial estimate for the focal length of both cameras of

51.336 mm was obtained from a single-photo resection carried out from Camera Station 1

on the 20th of August 2008, which used all ten glacier targets along with two reference

targets, and which took place just after the glacier targets had been surveyed by GPS. For

each photograph, the distance between the reference targets was measured and compared

with the distance measured on the initial photographs, taken on the 20th of August. The

calculated scale factor was then used to correct the focal lengths for each photograph.

Both cameras showed some rotational instability, with Camera 2 being

particularly affected. It is believed that freezing and thawing of the active layer was

primarily responsible for this instability. In both the autumn and the spring, this camera

underwent relatively rapid rotational changes, with changes in ω and κ of several degrees.

By contrast, the changes for Camera 1 were much smaller and more gradual. The variation of the rotational parameters for both cameras over the period between August

109 and November 2008 is shown in Figure 4.7. The variation for Camera 2 in May and June

2009 is shown in Figure 4.8.

Figure 4.7: Autumn 2008 Rotational parameters for Camera 1 and Camera 2.

110

Figure 4.8: Rotational parameters for Camera 2 for May and June 2009.

A series of daily photogrammetric models were produced for the initial 59 day

period, over which photographs were available from both camera stations. Because only

two reference points were available for each photograph, and because of software

limitations, these models were formed by using the exterior orientation parameters

calculated for the individual photos, rather than using the more rigorous exterior orientation procedure described in section 4.1.1. Daily X, Y, and Z positions of the targets on the glacier surface were then calculated by space intersection, as described in section 4.1.1.

Because targets GT1, GT2, and GT7 could not be seen from Camera Station 2, and because no observations were available from Camera 2 after the 59th day, it was not

possible to obtain a full set of X, Y, and Z coordinates for all targets. However GPS

measurements made of the target positions on the 20th of August 2008 and on the 20th

June 2009 allowed estimated daily horizontal positions to be interpolated for all targets,

111 with an averaged value for down-glacier velocity being assumed for the whole time

period. To provide a comparison with the intersected measurements, target elevations

were calculated independently for photos from both Camera 1 and Camera 2, using the

method described in section 4.1.3.

Between the 27th of May and the 20th of June 2009, a daily series of photographs

were collected from Camera 2 only. These photos were processed in the same way as

described above. This set of target elevations was particularly useful, as it covered the

onset of the 2009 summer melt season.

4.3.3.2 Measurement year two: 24 June 2009 – 29 June 2010

Over the second measurement year of the study, both cameras collected a full set of photographs. However all photos acquired from Camera 2 were found to be out of focus, and therefore only photos acquired from Camera 1 could be used in the analysis.

The processing methodology employed was similar to that used for the previous measurement year and described in section 4.1.3, with target X and Y positions being interpolated from GPS observations made on the 20th of June 2009 and the 3rd of July

2010. However since the camera stations had been rebuilt, new X, Y, and Z values were

used for Camera Station 1. Rotations for this camera generally showed similar variations

to those of the previous measurement year. They are shown in Figure 4.9.

Photographs were acquired through the summer of 2009. Since it was considered

likely that the glacier speed would increase under summer conditions, it was necessary to

account for this effect when estimating target positions. By using a combination of GPS

112 positions obtained on the 20th of August 2008, the 20th of June 2009, and on the 3rd of

July 2010, estimated summer and winter velocities were calculated for each target. To

remain consistent with the dates of GPS data acquisition, summer velocities were

assumed to apply only to the two month period between 20th June and 20th August, with

winter velocities applying over the remainder of the measurement year. Though this

represents a simplification, typical velocities at each target were of the order of 1 cm per

day, so any errors introduced by this assumption were considered to be small. For the purposes of interpolation, the direction of flow was assumed to be constant, with no change occurring between summer and winter. Because there were no 2008 GPS

measurements available for the repositioned targets GT1new, and GT2new, summer

velocities were assumed to be 50% greater than winter velocities, a factor which

approximately matched the average differences observed at the other targets.

113

Figure 4.9: Camera rotations for measurement year two of the study.

Analysis of the photographic record showed that a number of the targets collapsed

during the summer of 2009. Because of this, it was only possible to obtain a full set of

elevation measurements for GT1new, GT2new, GT4, GT5, GT8, and GT9. Two rocks

were also tracked, but these were later omitted from the study, since analysis of the time- lapse photography suggested that both rocks had moved several metres across the glacier surface over the summer. Elevations for the remaining targets were obtained through the measurement year, although there were large gaps in the series between mid December

114 and the start of February, during February and March, and between mid April and the start of June. These gaps were caused by snow obscuring the targets, with targets intermittently becoming visible for several days as the wind blew the snow clear.

4.3.3.3 Measurement year three: 10 July 2010 - 29 June 2011

In the third measurement year of the study an additional goal was to produce three

DEMs of the terminus area. These were to be generated for middle of July 2010, the end of the melt period in September 2010, and for the start of the following summer in June

2011. In order to achieve this, Camera 1 and Camera 3 were set up in a stereo configuration with a baseline separation of 84 m. Determination of target positions and elevations was carried out using two different methods. The first method used interpolated X and Y positions derived from GPS measurements made on July the 3rd

2010 and July the 2nd 2011. The estimated target positions were calculated in the same way as for measurement year two. A scale factor was calculated from the separation of the reference targets, and this was used to correct the focal length for each photograph.

Weekly elevations were calculated from photos obtained from Camera 1, using the same techniques described for the previous two measurement years.

Because the two cameras were set up in a stereo configuration, it was also possible to apply stereo processing techniques to the analysis. Using Inpho photogrammetric software, a series of 3D models were set up using photos from Camera

1 and Camera 3. Reference targets Ref 1, Ref 2, and Ref 103, were used as GCPs, with the glacier targets being used as tie points. The camera positions were held fixed by

115 giving them very low standard deviations. Focal lengths of the cameras were once again adjusted according to a scale factor calculated from the separation of the reference targets. The models were then triangulated in order to calculate the full X, Y, and Z coordinates for each target. Coordinates were calculated in this way weekly through the summer of 2010, and daily between June the 15th and June the 29th 2011.

By the end of the study period in July 2011, all targets had either collapsed, or had

developed substantial leans, with the result that it was only possible to track targets

GT102, GT105, GT106, GT107, GT108, and GT109 through the entire measurement year. A comparison between the changes in surface elevations calculated using each method showed good agreement, with the 3D coordinates derived by stereo photogrammetry providing a useful check on the accuracy of elevations derived from

Camera 1 alone. Analysis of rotations for both cameras showed that there was comparatively little movement of either camera over this period. A partial record of rotations at both Camera Station 1 and Camera Station 3 is shown in Figure 4.10. This only shows rotations derived from the stereo photogrammetric analysis, since these were the only rotations calculated for Camera 3.

116

Figure 4.10: Camera rotations for measurement year three.

117 Using Inpho software, one metre resolution DEMs were then produced for three different periods, in order to investigate ice melt though the summer and vertical ice motion through the winter. For July 2010, DEMs were generated for each day between the 10th and the 15th of July 2010. A final DEM was then produced by averaging the

individual daily DEMs. A similar process was used to generate DEMs in September

2010, at the end of the summer melt season. DEMs were produced for each day between

the 10th of September and the 14th of September, and these were then averaged to produce a DEM representing surface conditions at the end of the melt season. In 2011 DEMs were produced for each day between the 15th and the 19th of June, and these were averaged to

produce a DEM showing surface elevations at the beginning of the 2011 melt season. The

height models were generated using Inpho’s digital terrain model option, which

introduces a level of filtering into the final result. This was found to give a much better

quality result than using a straight unfiltered surface model, especially for areas with poor

correlation.

4.3.4 Calculating three year surface elevation changes

To interpret the pattern of elevation change at each target, it was necessary to

combine the various measurements to produce a series of multi-year profiles. In order to

do this, the GPS-derived yearly elevation differences for each target were used as

reference points. The elevation differences for each of the three years of the study were

added sequentially to arrive at the total elevation change for the target. Using the sum of

yearly differences meant that the true change in surface elevation was measured, even in

cases where the targets had been re-established and hence had moved slightly.

118 Photogrammetric elevation change was measured relative to the first observation

in any given measurement year, with values for each measurement year being processed

separately. Because photos were available from two cameras in measurement years one

and three, elevations were calculated both by intersection and using modelled

displacements. Where multiple elevation values were available for a specific target, the

mean value was taken in order to ensure consistency.

4.3.4.1 Estimation of surface melt rates

For each of the three measurement years of the study, the photogrammetric series was shorter than the interval between GPS measurements. In measurement year one, the photogrammetric series was three days shorter than the time between GPS observations; for measurement year two the difference was eight days, while for measurement year three the difference was ten days. In every case, these gaps in the photogrammetric series occurred in June or July, during the summer melt season. This missing data meant that photogrammetric and GPS elevation changes could not be directly compared. Estimated melt rates for the missing data from each year were calculated as follows:

• Measurement year one: For the last three days of measurement year one,

estimated melt rates were calculated using the average slope derived from the

photogrammetric elevation differences at each target from the preceding few

days. The values were averaged for all targets, giving an estimated ice loss of 3.3

cm per day, with a total estimated ice loss of 10 cm over the three days.

119 • Measurement year two: For the first four days of measurement year two,

estimated melt rates were calculated using the average slope derived from the

photogrammetric elevation differences at each target over the following few

days. This gave an average ice loss of 3 cm per day, or 12 cm in total over the

four days. To determine the average melting for the last four days of

measurement year two, targets surveyed on June the 30th 2010 for the UAV

survey described in Chapter 2 were used. These targets were resurveyed seven

days later on July the 6th, providing detailed measurements of surface melt over

this period. From these measurements, the average melting over the last four days

of measurement year two was estimated to be 5.5 cm per day, giving an

estimated ice loss of 22 cm over four days.

• Measurement year three: Estimated melting for the first seven days of

measurement year three also used the same value of 5.5 cm per day, giving a total

of 37.5 cm. For the last 3 days of measurement year three, the ice loss was

estimated using the slope derived from the preceding photogrammetric

measurements, with values at each target being averaged. This gave an estimated

melt of 4 cm per day, for a total estimated loss of 12 cm.

4.3.4.2 Compensation for the vertical component of down-glacier motion

By adjusting the data in this way it was possible to produce detailed profiles

showing how the elevation of each target changed over time. However in order to correctly derive the elevation change for a point on the glacier surface it was necessary to compensate for the vertical component of down-glacier motion, which would cause the

120 surface elevation of each target to drop over time as it moved down glacier, even if no

melting occurred. The difference in surface height relative to the starting point for each

target was measured from the one-metre DEM produced in the 2010 UAV survey. This

DEM was resampled to 10 cm resolution using bilinear interpolation resampling in order to provide a smooth correction surface. The derived correction was then added to the

calculated elevation change, in order to estimate the change in elevation which would

have occurred had the target remained stationary.

4.3.5 Measuring horizontal motion

Because it was only possible to directly measure horizontal motion when imagery

was available from both cameras, changes in X, Y position could only be calculated for

the first 59 days of measurement year one, and for measurement year three. In year one all motion was assumed to have occurred under winter flow conditions, since the data series began on the 20th of August, whereas it was assumed that measurement year three

included components of both summer and winter flow. As with the vertical motion, all

horizontal motion was considered to be relative to the first point in the measurement year.

This avoided the need for high absolute accuracies and meant that the camera IOP did not

need to be precisely determined for each photograph.

Horizontal motion estimates were derived for both measurement years one and

three. However because of the short baseline in year three the values showed a large

spread at all targets. The derived values for horizontal motion and their associated

accuracies will be discussed in more detail in the next section.

121 4.4 Results

This section describes the changes in target positions and elevations for each

target. For the sake of consistency, results are presented for each target sequentially.

Many of the targets could only be tracked for one or two years out of the three

measurement years, and where interpolated coordinates were used as input to the photogrammetric process it was only possible to derive horizontal motion estimates from

GPS measurements.

It was found that generally the photogrammetric and GPS elevation observations showed good agreement when the average melt rates calculated in section 4.3.4.1 were taken into account. However for measurement year two, GPS elevation changes were consistently 20 cm less than those estimated using photogrammetry with averaged melt rates. In measurement year three GPS elevation changes were consistently 20 cm greater than those derived photogrammetrically with averaged melt rates. Since the agreement between the 2008, 2009, and 2011 GPS elevation changes, and the photogrammetric observations was consistent, it was determined that the likely cause was a GPS antenna height error for the 2010 observations. The 2010 GPS elevations were therefore lowered by 20 cm to account for this discrepancy.

4.4.1 GT1

Measurements were only obtained for GT1 over the second measurement year of

the study. Since the estimated elevation changes were based on interpolated XY

coordinates, no measurement of horizontal motion was possible for this target, other than

122 from the GPS observations. The change in target elevation over measurement year two is

shown in Figure 4.11 and in Table 4.1 below. It can be seen from Table 4.1 that the

difference between the GPS and the photogrammetric elevations changes agrees well

with the predicted melt. Slope-corrected elevation differences are also shown in Figure

4.11 and Table 4.1. These give an estimate of the actual change in elevation for the glacier surface, over the measurement period.

The horizontal distance and direction travelled by GT1 is shown in Table 4.2. It

should be noted that all GPS-derived distances and elevation changes for measurement

year two refer to the 378 day period between GPS measurements, rather than an exact

year. This will likely result in a small overestimate in total displacement and average

speed, since there will be an over-representation of summer days, in which the glacier

surface would be expected to show a greater displacement.

Figure 4.11: Elevation change at GT1 over measurement year two.

123 Table 4.1: Elevation change at GT1 over measurement year two.

GPS elevation difference for target -3.59 m

Photogrammetric elevation difference -3.26 m for target

Difference between GPS and -0.33 m photogrammetric estimates

Predicted difference, based on -0.34 m interpolated melt rates

GPS elevation difference corrected for -2.71 m down-glacier motion

Photogrammetric elevation difference -2.72 m corrected for down-glacier motion and interpolated ice melt

Table 4.2: Horizontal motion for GT1 over measurement year two.

GPS-measured horizontal distance 3.45 m

Average daily distance (378 days) 9.12 mm

GPS-derived direction 90°

4.4.2 GT2

Measurements were available for GT2 for both measurement years two and three.

Although the targets for each year were named GT2new and GT102 respectively, they were close enough in position to effectively be considered to be the same target. For measurement year two, target X and Y positions were interpolated from GPS

124 measurements. GT2 was snow covered from mid December 2009 until mid June 2010, so no elevation data could be obtained over this period. For measurement year three, target elevations were calculated using interpolated X and Y positions and also by intersection from Camera 1 and Camera 3. This meant that it was possible to obtain photogrammetric estimates of both horizontal speed and direction, although the short base between the cameras ensured that there was a large spread in the XY values.

While the GPS and photogrammetric elevation changes showed good agreement over measurement year three, the GPS elevation change over measurement year two was

44 cm greater than the photogrammetric elevation change, even when ice melt was taken into account. It is believed that an incorrect GPS antenna height may have been entered for GT2new in 2009, although there is no direct evidence to support this. Although considered unlikely, it is also possible that there could have been an actual change in surface elevation at the start or end of measurement year two, during the period when no photogrammetric measurements were made. This target was located in the centre of a surface depression, which was linked by Wainstein (2011) to the presence of an over- deepening at the base of the glacier. Under such circumstances it is possible that the fluctuating basal water pressures could have caused rapid changes in surface elevation to occur over a short time period. The elevation differences for both years are shown in

Figure 4.12 and Table 4.3. Note that the values shown in Table 4.3 cannot be directly compared on an annual basis, since there were 378 days between GPS measurements for measurement year two and 365 days for measurement year three.

125

Figure 4.12: Surface elevation change for measurement years two and three at GT2.

Table 4.3: Elevation change at GT2 over measurement years two and three.

Year 2 Year 3

GPS elevation difference for target -2.86 m -2.21 m

Photogrammetric elevation difference for target -2.08 m -1.70 m

Difference between GPS and photogrammetric -0.78 m -0.51 m estimates

Predicted difference, based on interpolated melt rates -0.34 m -0.50 m

GPS elevation difference corrected for down-glacier -2.61 m -1.93 m motion

Photogrammetric elevation difference corrected for -2.17 m -1.92 m down- glacier motion and interpolated melt rates

126 The horizontal motion of GT2 was interpolated for measurement years two and three from the GPS measurements. Photogrammetric measurements of X and Y positions

were also calculated by intersection for measurement year three from Camera 1 and

Camera 3. The photogrammetrically-derived changes in eastings, northings, and total distance travelled over measurement year three are shown in Figure 4.13. Linear regression lines were fitted to the each of the three data series, with the slopes of the lines being used calculate the total distance travelled down glacier, as well as the overall change in easting, change in northing, and direction of travel. These results are summarised in Table 4.4. The changes in easting value, and the total distance travelled down glacier had R2 values of 0.8995 and 0.9013 respectively, indicating a strongly

linear trend. The change in northing however had an R2 value of close to zero, which was

likely due to the fact that the glacier was moving from west to east, so any movement in

the north / south direction would have been smaller than the error associated with the

individual measurements.

127

Figure 4.13: Change in horizontal position for GT2 over measurement year three.

128 Table 4.4: Horizontal motion for GT2 over measurement years two and three.

Year 2 Year 3

GPS-derived horizontal distance travelled 3.45 m 3.36 m

GPS average daily distance 9.13 mm 9.21 mm

GPS-derived direction of travel 90° 92.4°

Photogrammetrically-derived horizontal distance 2.59 m (estimated from regression line)

Average daily distance from photogrammetry 7.30 mm

RMS error E / W 0.33 m

RMS error N / S 0.35 m

Photogrammetrically-derived direction of travel 89.8°

To estimate the accuracy associated with the calculated year three XY positions, the individual observations were compared to the theoretical coordinates calculated from the regression line fit for eastings and northings. These gave RMS errors of 0.33 m and

0.35 m respectively, suggesting that the accuracy associated with individual horizontal observations in measurement year three was comparatively low. This does not take account of any speed variation which may have occurred throughout the year. Figure 4.13 does appear to show more rapid flow rates through the summer as would be expected.

However the number of observations and the spread of the data is insufficient to quantify this.

129 4.4.3 GT3

No useful data was obtained for this target over the duration of the study.

4.4.4 GT4

Target GT4 was also located in the surface depression, approximately 30 m south

of GT2. Elevation data was retrieved for this target for measurement years one and two of

the study, but a premature collapse of the target in the summer of 2010 prevented useful

data being acquired for year three. In measurement year one, elevation differences were

calculated independently from Camera Stations 1 and 2 using interpolated XY coordinates. Elevation differences were also calculated by intersection for the first 59 days, when both cameras successfully acquired photographs. The elevation changes derived from interpolated and intersected elevations showed good agreement, typically being no more than 10 cm different for any given day. A further 22 day record of photos was acquired from Camera 2, with the last image collected on the 17th of June. Elevations for this series were calculated from interpolated XY coordinates.

For measurement year two, elevation differences were calculated from Camera

Station 1 alone, using interpolated XY coordinates derived from GPS measurements made on the 20th of June 2009 and the 3rd of July 2010. Using predicted melt rates, the photogrammetric elevation changes were adjusted to account for the difference in time between the GPS data collection dates and the length of the photogrammetric data series.

Elevation differences derived for GT4 for measurement years one and two are shown in

Figure 4.14 and in Table 4.5. For measurement year one, the difference between the

130 corrected GPS and photogrammetric elevation changes was 14 cm, whereas for measurement year two the corrected GPS and photogrammetric height differences were almost identical.

Figure 4.14: Surface elevation change for measurement years one and two at GT4.

131 Table 4.5: Vertical motion for GT4 over measurement years one and two.

Year 1 Year 2

GPS elevation difference for target -0.28 m -2.69 m

Photogrammetric elevation difference for target -0.32 m -2.34 m

Difference between GPS and photogrammetric +0.04 m -0.35 m estimates

Predicted difference, based on interpolated melt rates -0.10 m -0.34 m

GPS elevation difference corrected for down-glacier -0.10 m -2.34 m motion

Photogrammetric elevation difference corrected for -0.24 m -2.33 m down-glacier motion and interpolated melt rates

Photogrammetrically-derived changes in eastings, northings, and total distance

travelled were calculated for the first 59 days of measurement year one. These are shown in Figure 4.15. Total distance travelled, change in easting, and change in northing were

determined by linear regression from the photogrammetric data series. These results are

summarised in Table 4.6. The changes in easting, and the total distance travelled down glacier had R2 values of 0.9726 and 0.9818 respectively, indicating a strongly linear

trend. However the change in northing had an R2 value of 0.2303, likely due to the fact that the N / S component of motion was relatively small. Table 4.6 also shows that there

was a difference of almost six degrees in the GPS-measured direction of surface flow

between year one and year two, which is equivalent to a difference of around 35 cm in

the north / south distance travelled between the two years. This difference is likely to be

132 the result of measurement error introduced as a result of target lean when the target position was measured in 2010.

Figure 4.15: Change in horizontal position for GT4 over measurement year one.

133 Table 4.6: Horizontal motion for GT4 over measurement years one and two.

Year 1 Year 2

GPS-derived horizontal distance travelled over 2.98 m 4.00 m measurement year

GPS average daily distance 9.8 mm 10.0 mm

GPS-derived direction of travel 97.6° 91.7°

Photogrammetrically-derived horizontal distance over 3.36 m measurement year (estimated from regression line)

Average daily distance from photogrammetry 11.0 mm

RMS error E / W 0.03 m

RMS error N / S 0.05 m

Photogrammetrically-derived direction of travel 98.1°

To estimate the accuracy associated with the calculated XY positions, the individual observations were compared to the theoretical coordinates calculated from the regression line fit for eastings and northings. These gave RMS errors of 0.03 m and 0.05 m respectively, suggesting that the accuracy associated with individual observations in measurement year one was relatively good. Since little speed variation was expected to occur over the winter period, down-glacier surface speed and direction could therefore be predicted from the photogrammetric observations with a high level of confidence.

4.4.5 GT5

For GT5, it was possible to obtain a full three year record, although there were some gaps in the data series over the winter of 2011 when the target was obscured by

134 drifting snow. Although this target was replaced by GT105 in the third year, the new target was located sufficiently close to the previous one that it could be considered to represent the same point. The elevation differences for GT5 for all three measurement years are shown in Figure 4.16, and in Table 4.7 below.

For measurement year one, the difference between the photogrammetric and GPS elevation changes closely matched the predicted value for surface melt. In measurement year two, the difference was 16 cm, which was less than the predicted 34 cm of surface melt. For measurement year three, the photogrammetrically derived elevation change was

3 cm greater than the elevation change derived from GPS measurements, whereas the predicted difference due to melting was 50 cm. When its GPS position was measured in the summer of 2011, GT5 was found to have collapsed. The GPS elevation was therefore taken to the estimated height of the target had it remained upright, providing a possible explanation for the large difference in measurement year three elevation changes.

Elevation changes for GT5 derived from both photogrammetry and GPS are therefore assumed to have a low degree of accuracy for measurement year three.

135

Figure 4.16: Three year surface elevation change at GT5.

Table 4.7: Three year surface elevation change for GT5.

Year 1 Year 2 Year 3

GPS elevation difference for target -0.51 m -2.58 m -1.96 m

Photogrammetric elevation difference for target -0.39 m -2.42 m -1.99 m

Difference between GPS and photogrammetric -0.12 m -0.16 m +0.03 m estimates

Predicted difference, based on interpolated melt -0.10 m -0.34 m -0.50 m rates

GPS elevation difference corrected for down- -0.26 m -2.20 m -1.69 m glacier motion

Photogrammetric elevation difference corrected -0.24 m -2.38 m -2.22 m for down-glacier motion and interpolated melt rates

136 Since X and Y positions for GT5 were computed by intersection for measurement

years one and three, it was possible to compare the accuracy of horizontal motion

estimation in both years, using linear regression to estimate the displacements from the

photogrammetric measurements. The results can be seen in Figure 4.17 and they are

summarised in Table 4.8. For measurement year one, the change in easting, and the total

distance travelled down glacier had R2 values of 0.9788 and 0.9838 respectively, indicating a strongly linear trend. The change in northing had an R2 value of 0.2627,

likely due to the fact that movement occurred primarily in the E / W direction. For

measurement year three, the corresponding values were 0.9454, 0.956, and 0.0255.

For measurement year one the estimated RMS errors of the photogrammetric

measurements were 0.03 m and 0.05 m respectively, suggesting that the accuracy

associated with individual observations was relatively good. For measurement year three,

the corresponding RMS errors were 0.28 m and 0.36 m. The considerably lower accuracy

of XY positions in measurement year three is a result of the shorter baseline used for

intersection. This will be discussed in more detail in section 4.5. Figure 4.17 also

provides evidence that seasonal changes in motion occurred in measurement year three. It

can be seen that the summer velocity is greater than the winter velocity. However the

number of observations is insufficient, and their spread too great to quantify this trend.

137

Figure 4.17: Change in horizontal position of GT5 for years one and three.

138 Table 4.8: Horizontal motion for GT5 over all three years of the study.

Year 1 Year 2 Year 3

GPS-derived horizontal distance travelled over 3.02 m 4.26 m 3.15 m measurement year

GPS average daily distance 9.90 mm 11.27 mm 8.63 mm

GPS-derived direction of travel 96.0° 96.5° 94.9°

Photogrammetrically-derived horizontal 3.54 m 3.10 m distance over measurement year (estimated by regression)

Average daily distance from photogrammetry 11.60 mm 8.49 mm

RMS error E-W 0.03 m 0.28 m

RMS error N-S 0.05 m 0.36 m

Photogrammetrically-derived direction of 98.8° 92.7° travel

4.4.6 GT6

For GT6, measurements were only available for measurement year three of the

study. The elevation differences are shown in Figure 4.18, and in Table 4.9. In this case, the difference between the GPS elevations was 54 cm greater than the photogrammetrically-derived elevation difference. This agrees well with the predicted surface melt of 50 cm over the period during which no photogrammetric observations were made.

139

Figure 4.18: Elevation change at GT6 for measurement year three.

Table 4.9: Elevation differences at GT6 for measurement year three.

GPS elevation difference for target -2.41 m

Photogrammetric elevation difference -1.87 m for target

Difference between GPS and -0.54 m photogrammetric estimates

Predicted difference, based on -0.50 m interpolated melt rates

GPS elevation difference corrected for -1.94 m down-glacier motion

Photogrammetric elevation difference -1.90 m corrected for down-glacier motion and interpolated melt rate

140 The changes in the horizontal position of GT6, derived from photogrammetric

measurements over year three, are shown in Figure 4.19. The total distance moved, as

well as the change in easting and change in northing, were determined by linear

regression. These results are summarised in Table 4.10. The change in easting, and the total distance travelled down glacier had R2 values of 0.932 and 0.9453 respectively,

while the change in northing had an R2 value of 0.1373, again most likely because

surface motion was predominantly from west to east. The RMS errors were 0.35 m in

easting and 0.56 m in northing, suggesting that the measurement accuracy for GT6 was

relatively low.

Figure 4.19: Change in horizontal position at GT6 over measurement year three.

141 Table 4.10: Horizontal motion at GT6 for measurement year three.

GPS-derived horizontal distance travelled over 4.15 m measurement year

GPS average daily distance 11.6 mm

GPS-derived direction of travel 101.3°

Photogrammetrically-derived horizontal 3.58 m distance over measurement year (estimated by regression)

Average daily distance from photogrammetry 9.8 mm

RMS error E / W 0.35 m

RMS error N / S 0.56 m

Photogrammetrically-derived direction of 98.4° travel

4.4.7 GT7

For GT7, measurements were only available from year three of the study. The elevation differences are shown in Figure 4.20, and in Table 4.11. In this case, the difference between the GPS elevations was 40 cm greater than the photogrammetrically- derived elevation difference. Once again this figure shows reasonable agreement with the predicted difference of 50 cm.

142

Figure 4.20: Measurement year three elevation changes measured at GT7.

Table 4.11: Elevation differences at GT7 for measurement year three.

GPS elevation difference for target -2.46 m

Photogrammetric elevation difference -2.06 m for target

Difference between GPS and -0.40 m photogrammetric estimates

Predicted difference, based on -0.50 m interpolated melt rates

GPS elevation difference corrected for -1.92 m down-glacier motion

Photogrammetric elevation difference -2.02 m corrected for down-glacier motion and interpolated melt rate

143 Changes in the horizontal position of GT7 over measurement year three are

shown in Figure 4.21. The total movement, change in easting, and change in northing

were determined by linear regression. These results are summarised in Table 4.12. The

changes in easting value, and the total distance travelled down glacier had R2 values of

0.9455 and 0.9605 respectively, whereas the change in northing had a very low R2 value

of 0.0252, again most likely because the motion of the glacier was overwhelmingly from

west to east. The associated RMS errors were 0.33 m in easting and 0.42 m in northing,

again showing the horizontal observations to be of comparatively poor quality.

Figure 4.21: Change in horizontal position at GT7 over measurement year three.

144 Table 4.12: Horizontal motion at GT7 for measurement year three.

GPS-derived horizontal distance travelled over 4.55 m measurement year

GPS average daily distance 12.4 mm

GPS-derived direction of travel 93.0°

Photogrammetrically-derived horizontal 3.50 m distance over measurement year (estimated)

Average daily distance from photogrammetry 9.6 mm

RMS error E-W 0.33 m

RMS error N-S 0.42 m

Photogrammetrically-derived direction of 92.7° travel

4.4.8 GT8

A full three year record was obtained for GT8. Although this target was replaced

by GT108 in measurement year three, the new target was sufficiently close to the

previous one that it effectively represented the same point. The elevation differences for

GT8 for measurement years one, two, and three are shown in Figure 4.22, and in Table

4.13. For all three years, the differences between the photogrammetric and GPS elevation

changes closely matched the predicted amount of ice melt.

145

Figure 4.22: Elevation changes at GT8 over all three years.

Table 4.13: Elevation differences at GT8 over all three years of the study.

Year 1 Year 2 Year 3

GPS elevation difference for target -0.40 m -3.09 m -2.52 m

Photogrammetric elevation difference for target -0.24 m -2.76 m -1.98 m

Difference between GPS and photogrammetric -0.16 m -0.33 m -0.54 m estimates

Predicted difference, based on interpolated melt -0.10 m -0.34 m -0.50 m rates

GPS elevation difference corrected for down- -0.05 m -2.56 m -2.20 m glacier motion

Photogrammetric elevation difference corrected +0.01 m -2.57 m -2.16 m for down-glacier motion and interpolated ice melt

Changes in the horizontal position of GT8 for measurement years one and three are shown in Figure 4.23. The total movement, change in easting, and change in northing

146 were determined by linear regression from the photogrammetric observations for both

years and are summarised in Table 4.14. For measurement year one, the changes in easting value, and the total distance travelled down glacier had associated R2 values of

0.882 and 0.902 respectively, while the change in northing had an R2 value of 0.706. This

is considerably higher than at most of the other targets and likely reflects the fact that

there was a significant N / S component to the glacier flow at this target. For

measurement year three, the corresponding values were 0.9017, 0.8798, and 0.7446

respectively. For measurement year one, RMS errors were 0.03 m in easting and 0.02 m

in northing, whereas for measurement year three, the corresponding RMS errors were

0.17 m and 0.16 m. The improved RMS errors for measurement year three are most likely because GT8 was nearer both cameras than the other targets, resulting in an improved base / height ratio, and a correspondingly stronger angular intersection.

147

Figure 4.23: Change in horizontal position of GT8 for years one and three.

148 Table 4.14: Horizontal motion for GT8 over all three years of the study.

Year 1 Year 2 Year 3

GPS-derived horizontal distance travelled over 1.58 m 2.21 m 1.82 m measurement year

GPS average daily distance 5.18 mm 5.85 mm 4.99 mm

GPS-derived direction of travel 69.3° 68.0° 66.7°

Photogrammetrically-derived horizontal 1.80 m 1.60 m distance over measurement year (estimated by regression)

Average daily distance from photogrammetry 5.90 mm 4.40 mm

RMS error E-W 0.03 m 0.17 m

RMS error N-S 0.02 m 0.16 m

Photogrammetrically-derived direction of 68.2° 61.7° travel

4.4.9 GT9

A full three year record was obtained for GT9. Although this target was replaced by GT109 in the third year, the new target was sufficiently close to the previous one that it could be considered to represent the same point. The elevation differences for GT9 for measurement years one, two, and three are shown in Figure 4.24, and in Table 4.15.

While the agreement was not as good as at GT8, the differences between the photogrammetric and GPS elevation changes still agreed well with predicted melt rates for each of the three years.

149

Figure 4.24: Elevation changes at GT9 over all three measurement years.

Table 4.15: Elevation differences at GT9 over all three measurement years of the study.

Year 1 Year 2 Year 3

GPS elevation difference for target -0.45 m -3.24 m -2.48 m

Photogrammetric elevation difference for target -0.47 m -2.84 m -2.17 m

Difference between GPS and photogrammetric +0.02 m -0.40 m -0.31 m estimates

Predicted difference, based on interpolated melt -0.10 m -0.34 m -0.50 m rates

GPS elevation difference corrected for down- -0.04 m -2.88 m -1.96 m glacier motion

Photogrammetric elevation difference corrected -0.14 m -2.82 m -2.15 m for down-glacier motion and interpolated ice melt

Photogrammetrically-derived changes in easting, northing, and total distance travelled were obtained by linear regression for the first 59 days of measurement year

150 one, and for the whole of measurement year three. These are shown in Figure 4.25, with

the results summarised in Table 4.16. For measurement year one, the changes in easting,

and the total distance travelled had R2 values of 0.9598 and 0.9337 respectively, while the change in northing had an R2 value of 0.6143. This is similar to the values for GT8

and likely reflects the fact that there was also a northern component to the glacier flow at

GT9. For measurement year three, the corresponding values were 0.8928, 0.8744, and

0.6274 respectively. The associated RMS errors for measurement year one were 0.02 m

and 0.03 m in easting and northing respectively, while for measurement year three, the corresponding RMS errors were 0.24 m and 0.18 m. The lower year three RMS errors

again are likely because GT9 was relatively close to the cameras.

Figure 4.25: Change in horizontal position at GT9 for years one and three.

151 Table 4.16: Horizontal motion for GT9 over all three years of the study.

Year 1 Year 2 Year 3

GPS-derived horizontal distance travelled over 1.85 m 2.45 m 2.48 m measurement year

GPS average daily distance 6.10 mm 6.48 mm 6.81 mm

GPS-derived direction of travel 69.5° 63.3° 75.1°

Photogrammetrically-derived horizontal 1.86 m 2.04 m distance over measurement year (estimated by regression)

Average daily distance from photogrammetry 6.10 mm 5.60 mm

RMS error E / W 0.02 m 0.24 m

RMS error N / S 0.03 m 0.18 m

Photogrammetrically-derived direction of 70.5° 71.6° travel

4.4.10 GT10

No useful data was obtained from this target over the duration of the study.

4.4.11 Comparing measurement year two and three elevation changes for each target

In order to compare the amount of elevation change at different points on the

glacier, slope-corrected photogrammetrically-derived target elevation changes were

compared at all available targets for measurement years two and three. The results for

year two are shown in Figure 4.26. Elevations were normalised relative to the 24th of

June, which was the first day of photogrammetric data collection for measurement year

152 two. For this year, data was available for targets GT1, GT2new, GT4, GT5, GT8, and

GT9. In order to represent the entire 2009 / 2010 balance year, relative elevations were also included over the period from May the 27th to June the 17th 2009, although technically these observations were made in the previous measurement year.

Figure 4.26: Slope-corrected photogrammetric elevation changes for all targets over year two.

It can be seen that during the winter period, elevations at all targets followed a similar pattern, with target elevations rising by around 15 cm from early-October through to mid-December, dropping by a similar amount between mid-December and early

153 February, then rising steadily by between 30 cm and 60 cm from early February onward.

The main distinction between the targets appeared to be the amount of elevation loss which occurred in the summer of 2009. Targets GT2new, GT4, and GT5 were located in or around the surface depression, and these tended to show less of a drop in elevation over the summer than targets GT8 and GT9, which were located closer to the terminus of the glacier. Target GT1 showed the greatest drop of all. This target was located on the relatively steep slope up-glacier of the depression (see Figure 4.3).

For measurement year three, data was available for targets GT102, GT105,

GT106, GT107, GT108, and GT109. Slope-corrected elevation changes are shown in

Figure 4.27. In this case target elevations were normalised relative to the 10th of July

2010, which was the first day of photogrammetric data collection for measurement year three. To cover the full balance year, elevations were also included for the period between the 1st and the 29th of June 2010, although these originated from measurement

year two. Because of the elevation discrepancy for target GT2 over measurement year

two, no information was included for this target prior to the 10th of July.

154

Figure 4.27: Slope-corrected elevation changes for all targets over year three.

In year three the overall drop in elevation over the summer was smaller than for year two, and it can also be seen that the uplift of the ice surface measured over the winter was less than during the previous year, averaging around 30 cm. The profiles for measurement year three were all fairly similar, with targets higher up the glacier once again showing a smaller drop in elevation than GT108 and GT109, which were closer to the terminus of the glacier.

To illustrate the differences in surface change over each of the two measurement years, profiles were compared for GT2 (including GT2new and GT102), GT5 (including

GT105), GT8 (including GT108), and GT9 (including GT109). These four targets were

155 the only ones for which data from both measurement years two and three were available.

The results of this comparison are shown in Figure 4.28. To facilitate comparison, the year two and year three profiles were normalised, so that all profiles shown in Figure

4.28 were given a zero elevation value at the end of the summer melt season between

September and October, which is the time when the surface elevation typically reaches a minimum. Change in surface elevations are shown as positive on Figure 4.28, rather than negative as has been the case with the preceding diagrams, because the profiles were normalised to the lowest surface elevation.

It can be seen from Figure 4.28 that the summer melt rate for GT5 appears to be much more rapid during measurement year two than in measurement year three. The melt rates shown in the other three graphs also showed year two melt rates to be more rapid, though the difference did not appear to be so great. This suggests that either the year three data for GT5 is unreliable, or there was a greater difference between the surface melt rates in measurement years two and three at this target than at any other target.

156

Figure 4.28: Comparison of slope-corrected elevations for year two and year three. Note that elevation changes are shown as positive and are relative to elevations at the end of the ablation season.

To get an overall perspective of how the glacier surface elevation was changing over the terminus region, and to reduce the effect of individual errors, the profiles from measurement years two and three were averaged. These averaged profiles are shown in

Figure 4.29. While this simplifies the situation by ignoring local differences, it nonetheless provides a useful basis for comparing surface response in each of the two years. It can be seen that for year two, surface melting commenced roughly nine days

157 earlier than in year three, with the overall balance year, measured from the start of one melt season to the start of the next, being around two weeks longer. Figure 4.29 also shows that the total drop in surface elevation over the summer melt season was around

0.3 m greater in measurement year two than in measurement year three, which is likely to have been at least partly due to the longer melt season. Changes in surface elevation shown in Figure 4.29 are summarised in Table 4.17.

Figure 4.29: Averaged year two and year three profiles. ABC and A’B’C’ refer to the maximum surface elevation at the start of the melt season, the minimum surface elevation at the end of the melt season, and the peak at the start of the following melt season for measurement years two and three respectively.

158 Table 4.17: Comparison of average elevation changes over year two and three.

Year 2 Year 3

Change in elevation over summer melt period -2.66 m -2.39 m

Change in elevation over winter +0.21 m +0.36 m

Total elevation change over balance year -2.45 m -2.03 m

Length of balance year 374 days 359 days

The points A, B, C, and A’, B’, C’ shown in Figure 4.29 define the maximum surface elevation at the start of the melt season, the minimum surface elevation reached at the end of the melt season, and the maximum surface elevation at the start of the following melt season for measurement years two and three respectively. To see how well these points predicted the start and end of the melt season in both years they were plotted against the respective daily minimum and maximum temperature records from the nearby Bylot-1 weather station. This comparison is shown in Figure 4.30. It can be seen that there is a large variation in the measured temperatures over comparatively short periods, especially in the first half of the winters of both measurement years, with temperatures becoming more stable in the latter half of the winter, from February onward. To reduce the effects of short-term temperature spikes, five day running means of the daily maximum and minimum temperatures were used. It can be seen that there is a close correspondence between the maxima and minima identified on Figure 4.29 and the average daily minimum temperature in both years.

159

Figure 4.30: Plots of 5 day running means of minimum and maximum temperatures recorded at the Bylot-1 weather station for (a): measurement year two and (b): measurement year three. Notice the strong correspondence of the maxima and minima shown in Figure 4.29 with the minimum daily temperature.

160 4.4.12 DEM generation and comparison

For measurement year three, Camera 2 was moved to a new position 84 m away

from Camera Station 1 and was renamed Camera 3. While the comparatively short

baseline significantly reduced the accuracy of positioning for specific points, the near-

parallel configuration allowed for the production of a series of DEMs, through a process

of spatial autocorrelation. Using Inpho Match-T software, one-metre resolution DEMs

were generated from five oriented stereo pairs acquired between the 10th and 15th of July

2010, as well as five oriented stereo pairs acquired between the 10th and the 14th of

September 2010, and five oriented stereo pairs acquired between the 15th and the 19th of

June 2011. The five DEMs from each time period were then averaged to minimise the

effects of any orientation errors. This gave three averaged DEMs, representing the glacier

surface approximately 3.5 weeks after the start of the 2010 melt season, at the end of the

2010 melt season, and roughly one week after the start of the 2011 melt season.

To determine spatial patterns of elevation change over the summer and winter of

measurement year three, the July 2010 DEM was subtracted from the September 2010

DEM, and the September 2010 DEM was subtracted from the June 2011 DEM. The

results of this comparison are shown in Figure 4.31. It can be seen that over the summer

of 2010, the greatest ice loss occurred closest to the terminus of the glacier, in the region

where targets GT108 and GT109 were located, as well as along the course of some of the supraglacial streams which developed over the course of the summer melt season. In

contrast, the lowest amount of surface melting occurred south of the line BB’, shown on

Figure 4.31 in the region where targets GT105, GT106, and GT107 were located.

161 Over the winter the changes in surface elevation showed a different pattern. Much of the glacier surface showed a small increase in surface elevation, which was likely due to an inflow of ice into the terminus region from higher up the glacier. It can be seen that the greatest elevation gain occurred on the steep slope immediately up-glacier of the surface depression, in which target GT102 was located. There was also a significant rise in the elevation of some supraglacial stream beds, which may have been because they were still filled with snow when the June DEMs were created, or possibly because of the smoothing effects of glacier surface flow.

Figure 4.31: Differences between computed DEMs; (a): DEM difference between mid-

July and mid-September 2010, and (b): Difference between mid-September 2010 and mid-June 2011. Note that thinning is shown as positive and thickening is negative.

162 Profiles were measured from each of the three DEMs for line AA’, which crossed the surface depression, and line BB’, which passed through the centre of the depression in the approximate direction of down-glacier flow. These profiles are shown in Figure 4.32.

The development of surficial features over the summer melt season can be clearly seen in

Figure 4.32. It can also be seen that over the following winter there was a small recovery in surface height across profile AA’, along with a smoothing out of many of the features which developed over the previous summer. Profile BB’ shows little variation in surface melt over the summer. However it can be seen that the steep slope up-glacier of the surface depression shows a significant increase in surface elevation over the winter period, recovering much of the ice lost in the previous summer.

163

Figure 4.32: Profiles across photogrammetrically-generated DEMs; (a): Profiles across line AA’ from July 2010, September 2010, and June 2011, and (b): Profiles across line

BB’ from July 2010, September 2010, and June 2011.

164 4.5 Accuracy Assessment and Sources of Error

The methodology described above has a number of potential sources of error

which are likely to have had an effect on the overall accuracy of the results. In this

section possible sources of error will be examined, along with their potential contribution,

with a view to determining estimates of the accuracy of all measurements made using

ground-based photogrammetry. It is important to stress that all measurements made

during this study were of surface change, and accuracy estimates therefore apply to

relative, rather than absolute, positions and elevations.

4.5.1 Photo measurement errors

Two possible sources of error arise directly from the photo measurement stage.

Firstly inaccurate measurement of the glacier targets would result in errors in the

estimated elevation and XY position of an individual target. Secondly inaccurate

measurement of the reference targets would result in incorrect determination of the

camera rotation parameters, which would affect all the target elevations and XY positions. From repeated measurements of multiple targets, it was determined that the target centres could be consistently estimated to within half a pixel, for photos in which

the target was well defined. Each target was 60 cm in diameter, which at a distance of

500 m represented approximately 10 pixels. The centre of the reference targets could thus

be identified to an accuracy of around 3 cm. For the targets located on the glacier surface, the accuracy of determination varied with distance, from 3 cm for GT8 and GT9, to a maximum of 7 cm for targets GT6 and GT7, which were over 1,000 m distant from

Camera Station 2.

165 The effects of errors in measuring individual targets on the glacier surface were easy to estimate. However, the method used to establish the photographic orientation parameters when using a single camera was particularly sensitive to errors in measuring the reference targets, since the orientation was determined from only two observations to reference points. To test the effect of errors in the measurement of the reference targets, row and column coordinates for these targets were varied, and the positions of the targets on the glacier surface were recalculated for each permutation. These tests showed that a one-pixel measurement error for either of the reference targets could potentially introduce an error of between 4 cm and 8 cm in target elevation, depending on the radial distance of the target from the centre of the image, and on its distance from the camera station.

Combining errors from both sources suggests that the typical measurement accuracy associated with each target was in the range of 8 cm to 15 cm, depending on how far the target was located from the centre of the photo, and on the distance between the target and the camera station. It should be noted that these estimates are applicable to observations made under good conditions. Many of the measurements were made of targets which were partially obscured by snow, or under foggy conditions. In such cases measurement accuracies are likely to be correspondingly lower.

4.5.2 The effect of baseline length on the accuracy of intersected positions

The estimated accuracy for target measurement on each photo can be used to

calculate the potential positional error associated with intersected XY positions. If it is

assumed that there is a potential half pixel error associated with each target measurement,

166 there is therefore a potential measurement error of one pixel associated with each photo

pair. Though the parallax equation (equation 4.1) was developed primarily for stereo

photography, it is still applicable to the more general case of convergent

photogrammetry. Equation 4.1 can be rewritten as:

dpD 2 error = [4.2] fB

Where dp is the error in the photographic measurement, which is expressed in

image plane coordinates, with one pixel being equal to 5.86 μm for the Canon XTi. D

represents the depth, defined as the 3D perpendicular distance between the baseline and

the target, f is the camera focal length, and B is the baseline.

For observations made by intersection from Camera Station 1 and Camera Station

2, the baseline was 940 m, the perpendicular distance to the targets varied between 500 m

and 800 m, and the height difference was approximately 100 m. Equation 4.2 gives a

range of possible errors between three and eight centimetres in the estimated distance to

the targets. This projected level of accuracy shows reasonable agreement with the RMS

errors calculated for the XY position of each target over the first 59 days of measurement

year one. In measurement year three, the separation between Camera Station 1 and

Camera Station 3 was 84 m, giving a range of projected horizontal errors of between 34 cm and 87 cm in the estimated distance to the target. Once again, this level of accuracy is

167 comparable with the actual RMS error calculated for each XY target position in

measurement year three.

4.5.3 The effect of errors in XY position on elevation

Vertical accuracy is calculated differently, since it is a function of the vertical

angle and distance from the camera to the target. Errors in the target XY position affect the apparent distance to the target, and so affect the final elevation. Using intersected XY positions, and using XY positions interpolated from GPS measurements could both potentially introduce a significant level of uncertainty into the target location, which would have a corresponding effect on the accuracy of elevation estimation. For

interpolated coordinates, this uncertainty is likely to be systematic, being at a minimum

close to the timing of the GPS measurements and reaching a maximum half way through the measurement period. Because of the relatively small distances moved by the targets, and because the movement generally occurred in a consistent direction, this uncertainty

in XY position was considered unlikely to have exceeded 50 cm at any time. In contrast,

errors in intersected positions are random, as could be seen from the year three estimates

of XY position in the previous section, which showed a number of individual

observations with variations of over one metre.

To assess the effect that positional errors in interpolated target positions would

have, the vertical errors which would result from a 50 cm error in horizontal position

were calculated for each target. They varied between 5.7 cm at GT4 to 8.8 cm at GT9.

For targets fixed by intersection, it was estimated that the vertical error resulting from

168 positional uncertainty ranged between 0.5 cm and 1 cm over measurement year one. In

measurement year three, the much greater uncertainty in XY position could potentially have introduced vertical errors of between 5 cm and 15 cm. However, since these errors are random, the use of multiple observations can improve overall accuracies significantly.

4.5.4 The effect of focal length variations

As discussed in sections 4.1.4 and 4.1.5, significant variations were measured in

focal length over time for both cameras. The variation in focal lengths for Camera 1 and

Camera 3 over year three are shown in Figure 4.33. It can be seen that the focal length for

both cameras changed by around 0.3 mm over the course of the measurement year. This

is equivalent to a scale change of around 14 pixels, or roughly 40 cm over the measured

distance between the reference targets. It can also be seen that the change in focal length

at both cameras appears to be correlated, suggesting that the variation is likely related to

changing temperatures. While measurement year three is shown as an example, similar

scale variations were also apparent in measurement years one and two.

169

Figure 4.33: Variation of camera focal length over year three.

Compensation for changing focal length was applied, using the separation of the reference targets to determine a scale factor which was then used to compute a new focal length. While this method does compensate for most of the scale variation, it depends on accurate measurement of the reference targets. On some winter days these were difficult to identify, particularly target Ref 2, which was partially obscured by snow on a number of occasions. It is therefore possible that some residual scale error could apply to some of the winter observations. In general this effect is anticipated to be small, and probably contributed no more than 10 cm at maximum to the derived target positions and elevations.

4.5.5 Stability of camera stations

Figure 4.7 through to Figure 4.10 illustrate the rotation parameters at both camera stations over all three years of the study. It can be seen from Figure 4.7 that in 2008

170 Camera Station 2 was considerably less stable than Camera Station 1. There was a

particularly large change in the rotation parameters in early September, with a change of

almost two degrees occurring in ω over this period. However the computed elevations

and XY positions shown in section 4.4 showed no sign of this change, suggesting that the

methodology used was sufficiently robust to account for most of the variations in camera

rotations. Figure 4.8 shows the rotation parameters derived for Camera 2 through the spring of 2009. Once again there was a rapid change in the rotation parameters, this time in the middle of June. Again the associated elevation profiles showed no sign of any sudden change over this period.

In measurement year two, Camera 1 showed only small changes in rotation

parameters (see Figure 4.9). Since photography from Camera 2 was not used, no rotations were calculated for this year. In measurement year three, both Camera 1 and Camera 3 showed only small rotation changes (see Figure 4.10). The elevation profiles shown in section 4.4 show little sign of any changes associated with any camera rotations, so it is believed that any residual effect from incorrectly applied camera rotations was small.

4.5.6 Snow cover and poor visibility

The presence of heavy snow on the glacier in the winter months often resulted in

targets being partially or fully obscured. Analysis of the photos from Camera 1 suggested

that most of the targets were at least partially obscured in the latter part of the winter in

each of the three years. While fully-obscured targets could not be observed, partially-

obscured targets could potentially introduce significant measurement errors, since snow

171 would tend to obscure the lower part of the target, causing the apparent centre to be higher than its correct position. For targets which were half obscured by snow, this could potentially introduce a 15 cm elevation error in target elevation. It is likely that such errors had an effect on many of the target heights observed between March and June in each of the three years. However this effect is difficult to quantify, since it depends on the depth of snow obscuring the bottom of the target.

To reduce the effect of partially-obscured targets, the measurement strategy was amended. In cases where the bottom of the target could not be seen, measurements were made to the estimated centre of the target. Since the target size was already known from observations in snow-free conditions, the position of the centre, relative to the top of the target could be estimated. This method obviously introduces some inaccuracies, but the estimated target centre is likely to be closer to its true position than if snow accumulation was not accounted for. Even after adopting this strategy, it is estimated that partially- obscured targets could have introduced a vertical error of between 5 cm and 10 cm to each observation.

Another consideration was the effect of poor visibility on the measurement of the target positions. A number of the observations, particularly in autumn and winter were made under poor conditions when it was difficult to discern the target extents. Under such conditions, it is possible that measurement errors of up to two pixels could be made.

This means that individual target elevations could potentially be in error by up to 20 cm.

Generally such errors were isolated, so although significant, they would not have had a

172 major effect on the overall shape of the elevation profiles. Errors resulting from poor image quality also needed to be accounted for. For example photographs from the spring of 2010 were noticeably out of focus. This introduced an additional uncertainty into the measurement process, particularly for the reference targets, since they were not highlighted against a white backdrop. Measurement errors of up to two pixels in the reference targets are therefore possible, potentially introducing errors of up to 20 cm in the spring target elevations.

4.5.7 GPS errors

The GPS used to survey the targets delivered good relative accuracy. Typically such systems will deliver relative horizontal and vertical accuracies in the one to two centimetre range. A horizontal and vertical accuracy of five centimetres was assumed, to account for the difficulty of precisely measuring the exact centres of the targets. To ensure consistency, all points were corrected to a datum established at the Bylot-1 weather station. However there is the possibility that GPS heights may have been incorrectly measured on a number of occasions. This could arise from poor identification of target centres, or from incorrect antenna heights. Such errors are difficult to quantify, but are obviously significant, since the GPS elevations were used as the reference against which the photogrammetrically-derived elevations were compared. The errors previously noted in the 2010 GPS elevations and in the 2009 elevation of GT2new were likely the result of antenna height errors.

173 4.5.8 Target lean and target collapse

In 2010 and 2011, it was found that most targets had developed a significant

amount of lean or had collapsed completely. Since the centres of the targets were

approximately 50 cm above the ice surface, this could potentially have introduced a

significant error vertical and horizontal error in a number of cases. Targets which had

developed a significant lean, might be between 10 cm and 20 cm lower than would be

expected. While this potentially is a significant source of error, GPS-derived heights and photogrammetric heights would be consistent, since they were both measured to the target centres. Similarly, most targets sunk into the ice surface by around 20 cm over

time. Most of this sinking occurred during the first few days after target placement, with

targets being relatively stable after this time. Once again, GPS and photogrammetric

measurements would be consistent, since measurements were made to the target centres

in both cases. However sinking of the targets would obviously have an effect on the

calculated change in the glacier surface elevation.

Where targets had collapsed completely, GPS measurements were made to the

estimated position of the target had it still been standing. This is an obvious source of

error, since photogrammetric measurements would have been made to the target in its

collapsed position, if it was not obvious that it had collapsed. This could potentially

introduce a vertical error of up to 50 cm. This provides a possible explanation as to why

the year three profile for GT5, described in section 4.4.11, was significantly different

from the other year three profiles.

174 4.5.9 Atmospheric effects

Any photogrammetric measurement can potentially be affected by atmospheric

refraction. This is particularly true for oblique photogrammetry, since light rays passing

at a low angle over a horizontal surface are particularly vulnerable. Atmospheric

refraction occurs because of the different density of air over different surfaces. As air

warms it starts to rise, causing the characteristic shimmering effect seen on roads on

summer days. While this effect would be important in many environments, it is unlikely

to be a significant factor in this case. The cold surface of the glacier remains at or below

freezing at all times, encouraging the development of a cold stable layer of air above the

glacier surface. This provides consistent observation conditions which are ideal for

making accurate measurements.

4.5.10 Overall accuracy

In a worst-case scenario, a combination of the above errors could potentially have

introduced uncertainties of half a metre or greater into the photogrammetrically-derived elevations for each year of the study. However, it is unlikely that all of these effects were present at all targets. It is also unlikely that the effects of the errors described above would have been cumulative, and in many cases errors would have cancelled each other out. It is therefore believed that the calculated profiles can be considered to be substantively correct, giving a realistic view of elevation changes on the glacier surface over the duration of the study. Profiles derived by averaging, such as the averaged year two and year three profiles shown in Figure 4.29, are more likely to be representative of

175 overall conditions, since the effects of individual errors are likely to be considerably

reduced through the averaging process.

4.5.11 Potential errors in the DEMs produced

Most of the errors associated with the production of the three averaged DEMs

described in section 4.4.12 have been described above. All of the DEMs were produced

using a spatial autocorrelation algorithm. In cases where the surfaces appeared different

in each photo, point matching would have been poor. This would be the case in snow

covered areas, which were present on the June image pairs. The relatively short, 84 m

baseline would also have introduced potential errors in the XY position, varying from

roughly 30 cm in the foreground, to around 1 m at the furthest extents of the DEM, and

resulting in potential vertical errors of between 5 cm and 20 cm.

The DEMs produced were not true surface models, since the algorithm used

involved a certain amount of interpolation and filtering. While this gave a good overall

representation of the glacier surface, it meant that small features, such as bumps and

hollows may have been smoothed out. Overall the purpose was to see how the glacier surface changed between the three dates, so minor surface details were not considered important. In addition, the fact that each DEM was created by averaging five daily DEMs

is likely to have reduced any errors associated with individual DEMs.

176 4.6 Discussion and conclusions

While the techniques outlined above proved successful in meeting most of the objectives outlined in section 4.2, there were a number of shortcomings which would need to be addressed before they could be more widely adopted. In particular there was a significant difference in the accuracy of target measurement between the 940 m baseline separating Camera Station 1 and Camera Station 2, and the 84 m baseline separating

Camera Station 1 and Camera Station 3. The original baseline allowed distances to the intersected targets to be calculated with a relative accuracy of better than 10 cm in all cases, whereas the shorter baseline gave results which were an order of magnitude poorer, and which were generally not of sufficient accuracy to allow accurate target tracking. However the narrow baseline was required for the generation of DEMs. A possible modification to the system would be the addition of a third camera, so that accurate intersected positions could be calculated and DEMs produced from the same set of data.

Target stability is another area which needs to be addressed. Field visits in 2010 and 2011 showed that most targets had developed significant leans, or had collapsed completely. This has an obvious effect on accuracy of the final results. A possible solution would be to replace the flat targets with spherical 3D targets, such as inflatable exercise balls or mooring buoys. Such targets would appear the same from any angle, regardless of any possible lean. It would also help if a means of stabilising the targets could be developed, to ensure that they consistently remained the same height above the glacier surface.

177 The design of the camera stations could also be modified. Camera 2 in particular

showed significant rotational instabilities. If the cameras could be secured to major rock

outcrops, then changes in camera rotations could potentially be eliminated, simplifying

the process of deriving camera rotation parameters still further. The presence of an

external USB port on the camera enclosures would also be a useful addition, since it

would have allowed photographs to be retrieved without disturbing the cameras. The

necessity of physically removing the cameras and repositioning them made it extremely

difficult to directly compare photographs taken before and after they were moved and

meant that there were gaps of several days between photos taken in measurement years one, two, three. These gaps had to be filled by assuming averaged daily melt rates, introducing another potential source of inaccuracy into the data.

The issue of focal length drift caused problems in processing the data. This manifested itself as a gradual change of scale and focus over time and appears to have been temperature related. It is difficult to suggest a practical solution to this problem.

Clearly different camera / lens combinations will respond differently to the effects of temperature over time. Without extensive field testing it is difficult to know whether different cameras and / or lenses would have performed better or worse than the Canon

XTi cameras used. The best recommendation is to have multiple reference targets available so that relative scale factors can be reliably calculated.

With regard to processing, it is significant that elevations calculated from interpolated coordinates using a single camera agreed closely with those calculated using

178 intersected coordinates. This suggests that in the case of Fountain Glacier and many other

slow-moving glaciers, accurate information on surface elevation change can be obtained

from a single camera, with supporting GPS measurements. The close agreement also

suggests that the single camera method is robust and can effectively be used in situations

when intersected data is not available.

This chapter has shown how ground-based photogrammetry may be used in a

number of ways to make measurements of the dynamics and surface changes of a slow- moving arctic glacier. The use of GPS and photogrammetric measurements are naturally

complementary, with the GPS measurements providing a reference framework which can

be used to constrain the photogrammetric observations, and the photogrammetric

measurements themselves providing detailed information on surface motion, and surface

elevation changes throughout the year, especially at times when it is not practical for

researchers to be present in the field.

While individual measurements were typically subject to errors which were

greater than the changes which were being measured, combining multiple measurements

over multiple days gave a representative picture of change at each of the targets on the

glacier surface, allowing the longer term picture of changes through the year to emerge.

By generating DEMs from the ground-based photography, it was also possible to look at

the broader spatial picture over the northern part of terminus. Combining the spatial and

temporal information derived in this way provides a powerful new way of analysing

changes in the glacier terminus region.

179 The information on glacier surface changes described in this chapter forms an important component of the work outlined in this thesis. While this chapter has focussed largely on the technical issues associated with measuring glacier surface parameters, the glaciological implications have yet to be explored. In Chapter 6, the various measurements derived in this chapter and in the other chapters will be combined, with a view to providing a description of the long and short term surface dynamic and surface melting processes affecting Fountain Glacier.

180 Chapter 5: Using a Combined SAR Interferometry and Feature Tracking

Approach to Measure Glacier Surface Displacement

5.1 Introduction

Radar has been used to measure glacier surface motion since the launch of the

ERS-1 satellite in 1991. The ability of this satellite to repeat the same orbit over a comparatively short time period made it possible to make extremely accurate measurements of Line Of Sight (LOS) displacement, over the period between image acquisitions. Although the technique of SAR interferometry is well suited to the measurement of slow-moving arctic glaciers, maintaining coherence on faster-moving temperate glaciers has often proved problematic. In recent years, the advent of high- resolution radar images from satellites such as TerraSAR-X has lead to the widespread adoption of speckle-tracking and amplitude-correlation techniques. These techniques, while not as accurate as SAR interferometry, can provide reliable estimates of surface displacement in situations where surface motion is comparatively rapid.

Synthetic Aperture Radar Interferometry, or InSAR, is a technique which is often capable of measuring both surface elevations and LOS surface displacements from the phase differences between two or more complex radar scenes which cover the same area.

Using interferometric techniques, it is often possible to measure LOS surface displacements to sub-centimetre levels of accuracy. This makes InSAR extremely useful for glacial motion studies. By combining multiple image pairs from different orbits, and

181 with different imaging geometries, it is often possible to obtain both the horizontal and vertical components of motion and to derive the direction of flow.

5.1.1 Single-pass interferometry

There are two main approaches to SAR interferometry. Single-pass interferometry

uses a combined transmitting / receiving antenna, along with a second receiving antenna,

which is displaced by a known amount in the range direction. When a pulse is

transmitted from the main antenna, it is reflected off the ground target, and the return

signal is picked up by both receiving antennas. Because of the offset between the two

antennas, there is a slight difference in the time that the signal is registered at each

receiver. The time difference results in a phase shift between the two signals. This shift is

related to the angle of incidence at the ground point, which is a function of the distance

and of the surface topography. By compensating for the change of incidence angle caused

by increasing range, it is therefore possible to calculate the surface elevation of the target

point.

Single-pass interferometry is most commonly used for DEM generation. Because

both returns are generated from the same pulse, the terrain is captured instantaneously.

Also, since the precise offset between the two antennas is known, the geometric

characteristics of such a system are well known. A number of specially equipped aircraft

have been developed to carry out 3D surveys, producing both detailed radar imagery and

high resolution DEM. The offset between the antennas on an aircraft mounted system is

generally between 2 m and 5 m. For example the Canada Centre for Remote Sensing CV-

182 580 SAR has two antennas separated by 2.8 m in the cross-track direction (Vachon et al.

1996). Single-pass interferometry has also been used in space. In February of 2000, the

Shuttle Radar Topography Mission (SRTM) was used to generate interferometric imagery and DEM of the whole Earth, between 60°N and 60°S, over a period of only 11 days. The DEM produced from this campaign had a spatial resolution of 30 m and were an order of magnitude more detailed than previous global DEMs. For this mission, the

receiving antenna was separated from the main antenna by a 60 m long mast, which was

extended when the shuttle was in orbit.

5.1.2 Repeat-pass interferometry

Repeat-pass interferometry uses multiple passes of a single radar transmitter /

receiver. When an area is imaged, both the amplitude and phase information for that area

are stored as complex data. A second radar scene is then acquired at a later time, from a

position close to that of the first. The phase difference between the two scenes can be

used to obtain topographic information in the same way as for single-pass interferometry.

However in repeat-pass interferometry the baseline is not fixed and can vary

considerably. While repeat-pass interferometry can be carried out from aircraft, the

technique is more commonly associated with satellite imaging. A number of radar

satellites, such as ERS-1/2, and TerraSAR-X, are designed to acquire interferometric

pairs from repeating orbits. Because of the time difference between acquisitions, repeat- pass interferometry can also be used to measure LOS displacement between the two scenes, from which down-glacier velocity can be calculated. This technique is thus extremely useful for measuring ice motion.

183 5.1.3 Generation of interferograms

Both single-pass and repeat-pass interferometry involve the creation of interferograms. An interferogram is created by multiplying the complex phase component of the primary or master scene by the complex conjugate of the secondary or slave scene.

The interferogram is thus a measure of the phase difference occurring at each point in the scene. An interferogram consists of a series of fringes, each of which contains the full range of possible phase values between 0 and 2π. Each fringe therefore represents a full phase cycle, within which accurate measurements can be made of topography or surface displacement.

The phase difference changes depending on the position of the target, and as a result of any surface displacement occurring during the time interval between which the two scenes are acquired. The dominant effect is caused by the incidence angle changing as the range increases, but this effect can be easily calculated and removed. An interferogram that has been processed in this way is known as a flattened interferogram.

The effects of flattening an interferogram are shown in Figure 5.1. After geometric effects have been accounted for, the next most significant effect is usually due to topographic variation.

Where surface motion occurs over the time period between the acquisition of the two scenes, the resulting interferogram will contain a component caused by this motion.

The most commonly used procedure to extract this motion-dependent phase is to use an existing DEM to create a synthetic interferogram of topographic-only phase, which is

184 then subtracted from the original interferogram. The resulting differenced interferogram

reflects surface displacement in the radar LOS direction over the time period between the

acquisition of the two images. This process is illustrated in Figure 5.1.

Figure 5.1: Formation of a displacement interferogram; (a): TerraSAR-X amplitude

image © DLR 2009, (b): Raw-unflattened interferogram, (c) Flattened and filtered

interferogram containing both topographic and motion fringes, (d) Motion-only

interferogram after topographic fringes have been removed using a DEM.

5.1.4 Image pair selection

With satellite InSAR, the choice of the scenes which make up an interferometric

pair determines whether the resulting interferogram is optimal for the measurement of

topography or displacement. Polar-orbiting satellites repeat the same orbits over a set

period. For example, RADARSAT-2 has an orbital period of 24 days, whereas

TerraSAR-X has an orbital period of only 11 days. Although successive orbits nominally follow the same orbital track, in practice the position from which the images are taken in space may vary by hundreds of metres. The difference between the radar positions in the cross-track or range direction is known as the interferometric baseline.

185 To measure surface displacement, the ideal situation would be to have a zero-

length baseline. Any phase shift would then relate only to surface displacement, and the

resulting interferogram would have no sensitivity to topography. Short baselines of only a

few metres will thus give the best results for measuring surface motion. As the baseline

gets longer, topographic effects will tend become more significant and the interferogram

will become less sensitive to surface displacement.

5.1.5 Interferogram unwrapping

Interferograms contain a series of discrete fringes, each of which represents a

complete phase cycle. While this yields sub-centimetre relative accuracy within the fringe, each fringe is essentially independent of the others. In order to resolve the phase ambiguity, the interferogram must first be unwrapped. Unwrapping is a process whereby the range of values contained within each fringe is sequentially added to those of other fringes in order to build up a continuous surface. Unwrapped interferograms may then be calibrated using GCPs in order to yield absolute values of elevation, or surface displacement.

5.1.6 InSAR geometry

The following section on InSAR geometry is based on two papers by Joughin,

Kwok, and Fahnstock (Joughin et al. 1996; Joughin et al. 1998). The basic geometry for

repeat-pass interferometry is illustrated in Figure 5.2. Two scenes are acquired at

positions S1 and S2, separated by baseline B. Position S1 is height H above the ground.

From S1, the range r0 and look angle θ are defined by the ground range xs and elevation z

186 of the target above the reference ellipsoid. The range to the ground point from S2 varies

by Δ, so that the distance from point S2 to the ground point is r0 + Δ. A reference look

direction θc (normally the centre look angle) is defined, and the baseline may be expressed in terms of Bp and Bn, which are the components of the baseline parallel to and normal to this reference direction.

Figure 5.2: InSAR Geometry.

The relationship between the range difference Δ, the unwrapped phase difference

φunwrap , and the wavelength λ can be expressed as follows:

φ λ ∆ = unwrap = φ 2k 4π unwrap [5.1]

2π Where k is the radar wave number, defined as . λ

187 Thus if the unwrapped phase difference and the wavelength is known, it is

possible to find the difference in distance from each of the two points S1 and S2 to the

ground point. After the interferogram has been flattened and unwrapped the phase

difference may be expressed as:

φ = φ + φ Unwrap topography displacement [5.2]

(Ignoring any errors introduced by differing atmospheric conditions and processing)

5.1.6.1 Extracting topography

When extracting topography, all phase differences in the interferogram are

assumed to be the result of elevation changes, or changes in range. From Figure 5.2, the

following equation may be used to relate the baseline to the range difference caused by

the combined effect of topography and changing ground range:

2 2 ∆ topography B θ + θ = −∆ − + Bn sin d Bp cos d topography [5.3] 2r0 2r0

∆2 Ignoring the topography term in equation 5.3 which is small, the range difference 2r0 can be approximated as:

B 2 ∆ topography ≈ −Bn sinθ d − B p cosθ d + [5.4] 2r0

188 The phase component due to topography can now be calculated using equation 5.1 and equation 5.4:

φ = 2k− r + r 2 − 2r (B sinθ + B cosθ ) + B 2  [5.5] topography  0 0 0 n d p d 

This may be approximated by:

 B 2  φ ≈ −  θ + θ −  topography 2k Bn sin d B p cos d  [5.6]  2r0 

The deviation of the look angle θd from the reference look angle is related to

range and surface elevation. From Figure 5.2 it can be seen that:

θ d = θ −θ c [5.7]

The radar position S1, the centre of the Earth, and the ground point form a triangle

and it is possible to use the cosine rule to solve for θ:

 2 2 2  (H + Re ) + r0 − (Re + z) θ d = arccos  −θ c [5.8]  2(Re + H )r0 

Equation 5.8 may be expressed as:

189  2 2 2  r0 + 2Re (H − z) + H − z θ d = arccos  −θ c [5.9]  2(Re + H )r0 

Where Re denotes the radius of the Earth.

Once ∆topography is determined, equation 5.4 and equation 5.9 may be used to

determine the height and ground range of each point in the image.

5.1.6.2 Extracting LOS displacement

Where surface displacement occurs, the contribution of motion to the unwrapped phase is given by:

φ = 2k(∆ sinψ − ∆ cos ψ ) [5.10] displacement d ,xs d ,z

Where ψ defines angle between the satellite and the normal to the reference ellipsoid at the ground point, ∆ is the cross-track component of the range difference, d ,xs

tangential to the reference ellipsoid (horizontal), and ∆ d ,z is component of the range

difference normal to the reference ellipsoid (vertical). If motion is smooth and continuous

then this contribution can be expressed in terms of the velocities v and v over the time xs z

period dT between the two images. Equation 5.10 now becomes:

φ = 2kdT(v sinψ − v cosψ ) displacement xs z [5.11]

190 Therefore if topographic phase difference can be eliminated, LOS velocity can be

calculated from the residual phase difference of the interferogram. However, since the

horizontal and vertical components of motion are likely to vary over time, it is often

preferable to express glacier surface motion in terms of horizontal and vertical

displacements, rather than as averaged velocities.

5.1.7 Sources of error associated with SAR interferometry

5.1.7.1 Effects of DEM and baseline errors on displacement estimates

Errors in baseline and topographic height will cause residual fringes which will result in inaccuracies in the estimation of surface motion. Vachon et al. (1996) developed an equation to quantify the RMS phase error arising from topographic height errors.

Referring to Figure 5.2, this can be written as:

2kBn σ dφ = σ dz [5.12] r0 sinθ

Where σ dφ is the RMS phase error, k is the radar wave number, Bn is the normal

component of the baseline, r0 is the slant range to the ground point, θ is the local

incidence angle, and σ dz is the RMS height error associated with the DEM. If nominal

values (for ERS-1/2 data) of 850 km for r0, and 23° for θ are substituted into equation

5.12, it now becomes:

191 −4 σ dφ = 6.76(10) Bnσ dz [5.13]

For a DEM with an RMS error of 5 m, this would result in an RMS phase error

−3 σ dφ of 3.38(10) Bn . Assuming a baseline of 300m, this would correspond to a phase

error of approximately 1 radian, which gives an error in flow estimation of approximately

4 mm per day (Vachon et al. 1996). The effect of a systematic error in baseline, dBn can

also be calculated. In this case equation 5.12 becomes:

2kdB dΦ = n [∆ cosθ + dz] δBn [5.14] r0 sinθ

Where dΦ is the effect of the baseline error on differential phase and Δ is the δBn

difference in distance between the two radar positions and the target.

Again substituting nominal parameters:

dΦ = 6.76(10) −4 dB [0.92∆ + dz] δBn n [5.15]

Therefore, if precise orbital information is used, the effect of baseline errors on velocity estimates is comparatively small. Researchers at TU Delft have been able to produce precise orbits for both ERS-1 and ERS-2, using a combination of laser tracking and radar altimetry. The precise orbits can position the sensor in space with an estimated

192 radial error of better than 7 cm (Scharroo and Visser 1998). For TerraSAR-X, the satellite position is known to better than 4.1 cm (Eineder et al. 2011). Of the satellites used in this study, only RADARSAT-2 does not have precise orbital information available.

According to MDA Corporation who operate the RADARSAT-2 satellite, orbital positions are typically better than 5 m, but this uncertainty is potentially a source of inaccuracy when compared to TerraSAR-X and ERS-1/2.

5.1.7.2 Errors arising from atmospheric conditions

A number of authors have investigated the effects of atmospheric conditions on

estimated position e.g. (Meyer et al. 2006; Ding et al. 2008; Eineder et al. 2011).

Microwaves are affected by conditions in both the ionosphere and the troposphere. In the

ionosphere, microwaves are affected by the total electron content within the cylinder of

atmosphere which they travel through. According to Eineder et al. (2011) the effect of the

ionosphere on microwaves in the X-band is generally small and can be discounted.

However for C-band radars in higher orbits, ionospheric effects may have a small, but

measureable effect on the overall accuracy.

Generally the path delay introduced in the troposphere is the more significant

atmospheric effect. It consists of two parts, the larger hydrostatic delay, which is caused

by dry gasses in the atmosphere, and the smaller wet delay, caused by water vapour

(Eineder et al. 2011). The hydrostatic delay can introduce an error of 2.3 m at sea level

for X-band microwaves, with the wet delay potentially introducing up to another 0.4 m of

error (Eineder et al. 2011). Although this delay is significant, the hydrostatic component

193 can be modeled and thus largely eliminated. Also during the dry arctic winter,

atmospheric moisture content is low, so that the wet delay also tends to be small and to

show little variation.

5.1.7.3 Variations in penetration depth

The different radar satellites used in this study have different wavelengths and polarizations. For glaciers which are covered by a thick layer of firn, volumetric scattering is likely to account for a significant fraction of the received backscatter. Where volumetric scattering occurs, the effective penetration depth will vary depending on the polarization and on the wavelength of the radar sensor. In the case of Fountain Glacier however, the area of interest is largely confined to the ablation area, which is typically covered by no more than a metre of dry snow in the winter. Under such conditions it is likely that backscatter will occur almost exclusively from the ice surface. The polarization and wavelength of the sensor is therefore likely to have little effect on the penetration depth.

5.1.7.4 Spatial and temporal decorrelation

In many cases it can be difficult or impossible to form a usable interferogram.

Decorrelation is caused by a loss of coherence for a ground resolution cell, due to

changes in ground conditions. Though the ground target is normally considered to be a single point, the true situation is more complex, since scattering from natural terrain is the coherent sum of returns from many individual scatterers within any given resolution cell

(Rosen et al. 2000).

194 Spatial decorrelation occurs when a ground resolution cell moves more than a

certain critical threshold relative to its neighbouring cells. Temporal decorrelation occurs

as a result of changes over time, such as ice melt, or changes to the water content of the

surface snow layer. In both cases the returns from the various scatterers comprising the

ground cell will be affected, reducing the coherence for that point. Rosen et al. (2000)

state that complete decorrelation occurs when the interferometric phase varies by one full

cycle across the range resolution cell. Therefore the change in displacement must be less

than λ/2 between adjacent cells (Vachon et al. 1996). Even partial decorrelation can lead to problems in unwrapping interferograms and may limit the information that can be

extracted from an interferogram. The short repeat cycles of both the ERS-1 phase-B imagery and the ERS-1/2 Tandem imagery considerably reduce the chances of significant spatial or temporal decorrelation occurring. The 11-day repeat period of TerraSAR-X is

also comparatively short, increasing the probability of maintaining coherence over the

acquisition period.

5.1.8 Deriving motion vectors from LOS displacements

Repeat-pass InSAR makes it possible to determine ice velocity in the LOS

direction. However in order to convert this into X, Y, and Z components of down-glacier

velocity, it is necessary to make some assumptions. By assuming surface-parallel flow,

Joughin et al (1998) showed that was possible to derive the down-glacier component of

velocity using a combination of ascending and descending-path ERS-1 and ERS-2

imagery. They noted however that many high-latitude areas are covered by only

ascending-pass or descending-pass imagery. This is the case for Bylot Island, where there

195 are a number of ascending-pass ERS-1 images available, but no descending-pass images.

In such cases, a second assumption is needed to determine the primary direction of flow.

Either glacier flow is assumed to follow the line of the steepest gradient, or its direction

can be inferred from external information, such as the line of a medial moraine

(Cumming and Zhang 2000).

To reproject LOS data from single-track scenes, the magnitude of down-glacier surface displacement can be calculated by the method described by Cumming and Zhang

(2000). Down-glacier displacement can be calculated using the following formula:

R D = [5.16] sin µ cosθ + sin γ cos µ sinθ

Where R is the change in LOS displacement, μ is the slope of the glacier surface below horizontal, γ is the angle between the satellite track and the glacier flow direction and θ is the incidence angle.

Since Fountain Glacier has flow rates of only one or two metres per year at the margins, and since summer melt rates may exceed this amount, horizontal (XY) down- glacier displacement, rather than 3D (XYZ) down-glacier displacement is used throughout this chapter to avoid confusion.

For single-track image pairs, the direction of glacier flow can be estimated independently, using the direction of flow stripes on the glacier surface. Where both

196 ascending and descending-pass image pairs are available, the correct value of γ will give the same value of D for both cases, and this value can therefore be found iteratively.

5.1.8.1 Determination of the full 3D displacement field using interferograms

from multiple look directions

There are a number of circumstances in which determination of displacement from paired ascending and descending passes may not give good results. The projection geometry described by Cumming and Zhang (2000) is very sensitive to the glacier flow direction. In cases where the satellite orbital track lies within 15° to 20° of the glacier flow direction the projected displacements become extremely unreliable. This is because the horizontal component of surface motion towards or away from the satellite becomes small, relative to the overall down-glacier displacement. This is the case with Fountain

Glacier, which turns through 90°, from a predominantly north / south orientation to an east / west orientation. The imaging geometry effectively means that right-looking descending-pass interferograms will not give reliable estimates of down-glacier displacements for the middle and upper parts of the glacier. Similarly ascending-pass interferograms cannot be reliably projected over much of the transition zone between the middle and lower glacier, where the glacier flow direction changes rapidly. It is therefore only possible to use paired ascending and descending-pass interferograms to derive displacements for the lower third of the glacier.

Another limitation is that displacements in the north / south direction tend to be much less accurately determined than those in the east / west direction, as a result of the

197 near-polar orbital tracks of the main radar satellites (Rocca 2003; Gray 2011). Once again

this is a limiting factor for measuring the surface displacements over much of Fountain

Glacier, since the middle and upper sections of glacier are oriented north / south. A third

problem is the assumption of surface-parallel flow. Many glaciers show areas of localised

surface elevation change, which can introduce significant errors to displacement

estimates if vertical motion is not accounted for. This effect is especially pronounced

where the glacier flow rate is slow relative to the rate of surface elevation change.

To fully determine the 3D displacement field, a minimum of three temporally-

matched interferograms are required, obtained from different look directions. This

configuration can then be used to derive the components of displacement in the East,

North, and Up (ENU) directions. In order to obtain the most accurate estimation of

displacement, a strong intersection is needed, which can be achieved by using a

combination of ascending and descending passes, and low and high incidence angles.

Using a combination of right-looking ascending and descending images, and high and low incidence angles, Gray (2011) suggested that reasonable results could be obtained

only for latitudes greater than 80°. However by incorporating a left-looking

interferogram, the geometry is improved considerably and reasonable results can be

achieved for latitudes higher than 65° (Gray 2011).

Where a minimum of three interferograms with well separated LOS vectors are

available, the ENU displacement components can be calculated from the unit vectors

198 associated with each look direction. The basic methodology is described by Wright et al.

(2004).

The look direction from the satellite to the centre point of a specific interferogram

can be expressed in terms of its unit vector: P = (ρ x , ρ y ,ρ z )

Where ρx, ρy, and ρz represent the components in the East, North, and Up directions

respectively.

These components are given by:

ρ = sin i *sinθ x

ρ = sini *cosθ y [5.17]

ρ z = −cosi

Where i is the incidence angle, and θ is the angle between the look direction and north. Since the incidence angle is always downward, ρz is always negative.

By using the LOS displacements and the unit vectors associated with each look

direction, a system of linear equations can be formed which can then be used to calculate

the ENU components of displacement. In practice however it is simpler to use matrices to resolve the displacement components.

For three look directions, the unit vectors form a 3*3 LOS matrix:

199 ρ1x ρ1y ρ1z    ρ ρ ρ LOS=  2x 2 y 2z  ρ ρ ρ   3x 3y 3z 

If the LOS matrix is then inverted the full displacement field for the glacier surface in the ENU coordinate system can be found from:

R1  -1 T   Displacement [X, Y, Z] =[LOS ] R2  [5.18]   R3 

Where R1, R2, and R3 represent the change in LOS distance for each of the three

look directions.

In cases where there are more than three look directions, the solution will be over- determined and the final result may be determined either by taking an average of multiple solutions or by least squares.

5.1.9 Feature tracking

The current constellation of radar satellites offers ground resolutions as fine as

one metre in certain modes. This improvement in spatial resolution has lead to the

widespread adoption of feature tracking techniques for determining glacial motion. There

are a number of different techniques which have been used successfully. Speckle tracking

relies on measuring the changes in the coherent speckle between two radar images.

Because speckle can only be tracked as long as coherence is maintained, this application

200 is generally limited to acquisitions which are separated by only a short time interval, or to

regions with cold stable climates, such as Antarctica (Short and Gray 2005). Speckle

tracking does however have the advantage that velocities can be tracked over featureless

surfaces which lack sufficient texture for successful amplitude tracking (Floricioiu et al.

2008).

Another approach is the use of amplitude correlation, which is also known as

intensity tracking. This approach uses the cross correlations measured at regularly-spaced intervals in order to determine the change in relative surface position over the time interval between the images. The principle behind this technique is described in detail by

Scambos et al (1992). With the widespread availability of high-resolution radar imagery amplitude correlation has now become the most commonly used measurement tool for determining surface displacements for fast-moving valley glaciers and outlet glaciers.

The advantages of amplitude correlation over SAR interferometry for motion studies of temperate glaciers were summarised by Floricioiu et al. (2008). These include the fact that it is insensitive to phase decorrelation. Temporal decorrelation can be a major problem when making InSAR measurements of fast-moving temperate glaciers, with successful measurements only being possible over short time intervals, such as during the ERS-1/2 Tandem campaign. Another advantage is that there is no need for phase unwrapping when using amplitude-correlation techniques. Unwrapping errors can be a major problem in areas of high shear, often leading to incorrect estimates of surface velocity. With InSAR there is also the problem that only the component of motion along

201 the LOS vector is derived. This means that to determine the direction and magnitude of down-glacier motion normally requires a number of additional assumptions to be made,

such as surface-parallel flow. By contrast, with amplitude correlation the full horizontal

motion field can be derived from a pair of previously orthorectified images.

While there are many advantages to amplitude correlation, there are also some

disadvantages specific to measuring displacements of slow-moving glaciers. Typical

accuracies are of the order of a tenth of a pixel (Fallourd et al. 2011). After

georeferencing and resampling, TerraSAR-X images of Fountain Glacier typically have a

pixel size between three and five metres, which introduces a sizeable potential error when

the slow flow rates are taken into account. Floricioiu et al. (2008) estimated that errors

arising from feature tracking could potentially amount to 3.6 cm per day over the 11-day

repeat cycle of TerraSAR-X. This potential error exceeds flow rates close to the terminus

of Fountain Glacier, which are typically less than one centimetre per day. It is possible to

compensate for the lower accuracy by tracking over a longer time period. However arctic

glaciers do not suffer from the rapid decorrelation observed on temperate glaciers, so are

often better suited to the application of interferometric techniques.

5.1.10 Radar satellites suitable for interferometry

ERS-1 was launched in 1991 and was the first satellite designed with

interferometry in mind. Since its launch, both ERS-1 and ERS-2 have provided an extremely useful source of information for glaciological studies. The specifications of the

ERS-1 satellite are listed in Table 5.1. The normal 35-day repeat period for the ERS

202 satellites is longer than ideal for measuring displacement, even for slow-moving polar glaciers. However a number of special campaigns have provided imagery with shorter repeat periods. The ERS-1 ice phase (mission phase B) took place over a four month period between December 1991 and April 1992. During this phase, ERS-1 was placed in

a three-day repeating orbital cycle, covering a limited number of orbits. Track 32 from

this phase covered Fountain Glacier. Good interferometric coverage with a three-day

repeat period and short perpendicular baselines was available over this most of this time.

A second ice phase (mission phase-D) occurred two years later, but no data was collected

over Bylot Island during this period. The ERS Tandem mission, which took place over a

nine month period between 1995 and 1996 provided imagery with a one-day repeat

period over many parts of the world. However no Tandem data is available covering

Fountain Glacier.

203 Table 5.1: Specifications of ERS-1.

(Source: European Space Agency - Earthnet on line: https://earth.esa.int/web/guest/missions/esa-operational-eo-missions/ers).

Launch Date 17 July 1991

Frequency 5.3 GHz

Wavelength 56 mm (C-band)

Polarization VV

Orbital Height 785 km at equator

Orbital Inclination 98.52°

Time for one orbit 100 minutes

1 day (Tandem), 3 day (ice phase), Orbital Repeat Period 35 day (standard)

Incidence Angle Range Nominal 23°

Look Direction Right

Ground Resolution 30 m

Scene width 100 km

There are a number of other satellites which are capable of interferometry.

However many of these have long repeat periods. The successor to the ERS-1 and ERS-2

satellites is ENVISAT, which carries the ASAR imaging radar. In many ways it is similar

to the ERS satellites in terms of orbital characteristics and resolution. Like both ERS

satellites, it has a 35-day repeat period. This is too long to maintain coherence over most

204 glaciers, except under exceptional conditions. Similarly the Japanese JERS-1 and ALOS

satellites both have orbital periods of 44 days. Vachon et al. (1997) tested a number of

JERS-1 image pairs for an area of southern Bylot Island and found that the orbital repeat period was too long to achieve correlation in areas where there was a significant amount of surface movement, as is the case over glaciers.

Many interferometric studies have made use of RADARSAT data. RADARSAT-

1 was launched in November 1995. It features a variety of different imaging modes, and provides an optimal resolution of approximately 10 m in fine beam mode. Its successor,

RADARSAT-2, shares many instrumental and orbital characteristics with RADARSAT-

1. RADARSAT-2 was launched in December 2007 and provides high-resolution coverage, with a ground resolution as small as 1 m in spotlight mode and 3 m in ultrafine mode. Although the orbital repeat period of 24 days is longer than ideal for interferometric purposes RADARSAT-2 offers a wide variety of different imaging modes which can be used to obtain the best possible imaging geometry of the area of interest.

The specifications for RADARSAT-2 are shown in Table 5.2.

TerraSAR-X is another high-resolution radar satellite which was also launched in

2007, and which provides highly detailed coverage at resolutions as small as 1 m. Like

RADARSAT-2, TerraSAR-X has a variety of different beam modes and is capable of obtaining left-looking imagery under special circumstances. However the biggest advantage TerraSAR-X offers for interferometry is its 11-day repeat period, which is shorter than that for any other civilian radar satellite. Along with its sister satellite

“TanDEM-X”, which was launched in 2010, TerraSAR-X now has the capability to

205 produce high-resolution DEMs of anywhere on the Earth’s surface. The specifications of

TerraSAR-X are shown in Table 5.3.

Table 5.2: Specifications of RADARSAT-2 (Source: Canadian Space Agency -

http://www.asc-csa.gc.ca/eng/satellites/radarsat2/inf_data.asp)

Launch Date 14 December 2007

Frequency 5.405 GHz

Wavelength 56 mm (C-band)

Polarization HH VV HV VH

Orbital Height 798 km at equator

Orbital Inclination 98.6°

Time for one orbit 100.7 minutes

Orbital Repeat Period 24 days

Incidence Angle Range 10° - 60° (depending on beam mode)

Look Direction Right (left-looking capability)

Ground Resolution 1 m – 100 m (depending on mode)

Scene width 18 km - 500 km (depending on mode)

206

Table 5.3: Specifications of TerraSAR-X (Source: Astrium 2012 - http://www.astrium- geo.com/na/1249-terrasar-x-technical-documents)

Launch Date 15-Jun-07

Frequency 9.65 GHz

Wavelength 31 mm (X-band)

Polarization HH VV HV VH

Orbital Height 514 km at equator

Orbital Inclination 97.44°

Time for one orbit 95 minutes

Orbital Repeat Period 11 days

Incidence Angle Range 15° - 60°

Look Direction Right (left-looking capability)

1m - 18 m Ground Resolution (depending on mode)

5 km - 100 km Scene width (depending on mode)

There are a number of other high resolution radar satellites which have been launched in recent years, including the Italian COSMO-SkyMed constellation of satellites which are capable of one-metre spatial resolution. Although the repeat period for each of these satellites is 16 days, the four satellites together have an effective repeat period of

207 four days, making them ideal for interferometry. Though COSMO-SkyMed data would

have been ideal for the current project, scientific proposals were not being accepted at the

time required. There is also the German SAR-Lupe system which is a constellation of

five satellites, launched between 2006 and 2008. These satellites are capable of capturing

the ground with a spatial resolution of 0.5 m. However SAR-Lupe is a military system

and as such imagery is not generally available for research purposes.

5.2 Research using InSAR and feature tracking for the study of glacial motion

The following is not intended to be a comprehensive listing, but is rather a sample

illustrating various projects which have used SAR interferometry and feature tracking for

the measurement of glacial motion. Although these techniques have only been used for glacial motion studies over the last twenty years, a considerable amount of literature on this topic has been generated. A comprehensive literature review would therefore be a major project in its own right.

Traditionally InSAR studies of the major continental ice sheets have made use of

ERS-1/2above data, although much of this is now over 20 years old. The basic workflow for deriving glacial motion from single-pass ERS-1/2 imagery was described by Joughin et al. (1996) for the Humboldt Glacier in Greenland. Joughin et al. (1998) also described the use of both ascending and descending-pass ERS-1/2 Tandem imagery to obtain ice flow patterns on the Ryder Glacier, Greenland. These two papers form the basis of section 5.1.6, InSAR Geometry. Other examples include Murray et al. (2002), who used

208 ERS Tandem imagery as part of an investigation of the 1992-1995 surge of Sortebrae in

East Greenland, and Rignot et al. (2002), who used eight ERS image pairs obtained between 1992 and 2000 in order to investigate changes to the mass-balance and ice flow patterns of the Pine Island and Thwaites Glaciers in West Antarctica.

ERS-1/2 data has also been used in the study of valley glaciers. Strozzi et al.

(2002) used SAR interferometry to produce LOS velocity maps for several Swiss alpine

Glaciers. Vachon et al. (1996) used ERS Tandem data to study flow rates on the

Athabasca and Saskatchewan glaciers in the Canadian Rockies. Trouvé et al. (2007), carried out a study of glacier velocities for the Mont Blanc area of the French Alps, while

Bousquet et al. (2004) compared velocities derived from InSAR with observed velocities for the Mer de Glace in the French Alps. Venkataraman et al (2006) used both ERS

Tandem and ENVISAT ASAR image pairs to map velocities of the Gangotri and Siachen glaciers in the Himalayan regions of India.

Another application was demonstrated by Gudmundsson et al. (2002), who used ascending-pass ERS Tandem imagery to produce a time series of ice motion maps showing the infilling of the ice depression which resulted from a 1996 subglacial volcanic eruption under the Vatnajökull ice cap in Iceland. On a much smaller scale,

Kenyi and Kaufmann (2003) were able to use ERS-1/2 data to monitor extremely small deformations for the Dosen Rock Glacier in the Austrian Alps.

Although the study by Kenyi and Kaufmann (2003) covered an extremely small area, this represents an exception. ERS-1/2 data is generally limited to larger glaciers and

209 ice sheets because of its comparatively low spatial resolution of 30 m. Data with

sufficiently short repeat cycles for interferometry is also limited to mission phases B and

D, and to the ERS-1/2 Tandem campaign. This limits the applicability of ERS-1/2 data

for the study of Fountain Glacier, since only ascending-pass data from mission phase B,

covering the winter of 1991-1992 is available.

RADARSAT-1 has also been commonly used for interferometric analysis of ice

flow. For the 1997 RADARSAT Antarctic Mapping Program (RAMP), the satellite was turned around through 180°, allowing full radar coverage over the whole of Antarctica for the first time, although this mission produced only limited interferometric coverage. The

Modified Antarctic Mapping Mission (MAMM), which took place over three months

ending in the November 2000, was a specially designed campaign aimed at obtaining high-quality interferometric coverage of Antarctica, north of 80.1° S. Over the duration of this mission, the satellite position was optimised to give the best possible baselines for

interferometry. The goals and strategy behind the MAMM were summarised by Jezek

(2002). The 24 day repeat period of RADARSAT-1 and 2 is generally only suitable for

InSAR surveys of arctic regions, where conditions remain stable for prolonged periods.

In other parts of the world, RADARSAT data has been predominantly used for feature

tracking, since the interval between acquisitions is generally too long for coherence to be

maintained.

Young and Hyndland (2002) used RADARSAT-1 imagery from the 1997 RAMP

to determine ice velocities and strain rates for the Amery Ice Shelf in East Antarctica.

210 Gray et al. (2002) also used imagery from RAMP, this time to identify grounding zones for parts of the Ross and Filchner ice shelves. Joughin (2002) used RADARSAT-1 imagery from MAMM in order to produce velocities for the entire Lambert Glacier and

Amery Ice Shelf. InSAR was applied in slower-moving regions where the correlation was good. In other areas speckle tracking was used to measure horizontal displacement.

The study by Joughin (2002) shows how InSAR and speckle tracking or amplitude tracking are naturally complementary, and can often be used side by side to obtain good velocity estimates for both fast and slow-moving regions. A similar approach was used by Burgess et al. (2005), who mapped the flow dynamics of the Devon Island ice cap. SAR interferometry was carried out using ERS-1 ice phase B imagery, with

ERS-1/2 Tandem data being used to map the western and southeastern sections. However decorrelation occurred over the fast-moving outlet glaciers, so speckle tracking of

RADARSAT-1 data was used to obtain velocity estimates for these regions.

In the last few years a number of papers have appeared describing the use of

TerraSAR-X for interferometric and feature tracking applications. The high spatial resolution of this satellite has encouraged the use of feature tracking, especially on faster- moving glaciers. Fallourd et al. (2011) describe preliminary experiments using a combination of InSAR and feature tracking over glaciers in the Chamonix area of the

French Alps. Feature tracking using TerraSAR-X was also carried out by Floricioiu et al. (2008), who calculated the velocities of the major outlet glaciers of the Patagonia

Icefield. Surface velocities for the glaciers studied varied from hundreds of metres to

211 thousands of metres per annum. Previous attempts to use InSAR for glaciers travelling at such speeds had produced only fragmentary sections of interferograms, even when using data from the ERS Tandem mission. The errors due to orbital uncertainty and variations in atmospheric path length for the feature tracking approach were estimated to be around

3.6 cm per day.

Floricioiu et al. (2009) described the use of a combined speckle tracking and SAR interferometry approach for a motion analysis of the Recovery glacier in Antarctica. In

2007 and 2008, TerraSAR-X was rotated to image the Antarctic in a left-looking configuration, making it possible to obtain radar imagery over the whole continent.

Speckle tracking was used to estimate velocity over much of the glacier and surrounding ice sheet. However in slow-moving regions, SAR interferometry was used to provide more accurate results. Accuracies obtained from the speckle-tracking approach were found to be around 2.3 cm per day, whereas InSAR-derived velocities were found to be approximately 50 times more accurate.

Kumar et al. (2009) used speckle tracking and SAR interferometry to study the motion of two Himalayan glaciers, using ERS Tandem imagery with a single-day separation and TerraSAR-X imagery. Good interferograms were formed from the ERS image pairs. However the 11-day repeat period of TerraSAR-X was found to be too long to maintain coherence on the glaciers. Contemporary velocities for the glaciers were therefore estimated using a speckle-tracking approach. Amplitude correlation was also compared with InSAR by Kumar et al. (2011). In this case feature tracking was carried

212 out on TerraSAR-X spotlight image pairs of Himalayan glaciers, separated by 11, 22, and

33 days respectively, with the results being compared to velocities obtained using

imagery from the ERS Tandem campaign. Little difference was found in the velocities

obtained from each of the three time periods, and the derived velocities showed good

agreement with those derived from the ERS images.

While the 24 day repeat period for RADARSAT-2 has tended to discourage its

use for SAR interferometry, the wide range of available incidence angles can be

extremely useful for determining 2D and 3D velocity fields in stable arctic and antarctic

environments, where loss of coherence occurs relatively slowly. Using scenes with a

wide range of incidence angles from ascending and descending-pass RADARSAT-2

orbits, Gray (2011) was able to determine the full 3D velocity field of the slow-moving

Henrietta Nesmith Glacier on northern Ellesmere Island. By knowing the surface slope of

the glacier, changes in surface elevation over time could be estimated to an accuracy of

approximately one millimetre per day.

The studies described above highlight the importance of having a short temporal

repeat period for carrying out SAR interferometry. In general, the most commonly

described limitation for TerraSAR-X and RADARSAT-1/2 interferometry was that

coherence could not be maintained on fast-moving temperate glaciers. This has tended to encourage the use of feature-tracking approaches for the measurement of glacial velocities. However the 11 and 24 day repeat periods of TerraSAR-X and RADARSAT-

213 1/2 make InSAR a practical method for measuring velocities over slow-moving arctic glaciers, such as Fountain Glacier.

A significant limitation to both the InSAR studies and feature-tracking studies described has been that the full 3D motion field is generally not directly measured, although it is often derived through supplementary measurements (e.g. Gudmundsson et al. 2002). For many arctic regions, it is theoretically possible to obtain sufficient data to allow both the horizontal and vertical components of motion to be derived. However this generally requires a left-looking interferogram to be included. In the Arctic this causes problems with tasking of acquisitions, since the entire satellite needs to be rotated, which generally means that no other acquisitions can be acquired over the northern hemisphere for the orbit requested.

5.3 Objectives

The overall purpose of using radar imagery was to determine the three- dimensional surface velocity field for the majority of Fountain Glacier, with a view to providing a broader spatial context to the point measurements described in the previous chapter. Within the context of this broad objective were a number of specific objectives which were aimed at providing information on the surface dynamics of Fountain Glacier:

• To determine historic flow rates, using ERS-1 imagery from the 1991 / 1992

mission phase B ice measurement campaign.

214 • To use high-resolution TerraSAR-X and RADARSAT-2 imagery to compare

surface velocities throughout the winter, in order to determine whether winter

velocity is consistent.

• Use of a combination of ascending and descending-pass, and left and right-

looking radar images with different imaging geometries in order to establish both

horizontal and vertical flow rates.

• Identify flow anomalies.

• Use feature tracking techniques to determine annual and winter surface flow and

compare estimates with those derived from InSAR.

5.4 Methodology

5.4.1 Imagery used

Radar imagery from ERS-1, TerraSAR-X, and RADARSAT-2 was used. The individual scenes used are described below:

• ERS-1: Four ascending-pass scenes were provided by the European Space

Agency (ESA) as part of agreement C1P.6184. These scenes are listed in Table

5.4 below:

215 Table 5.4: ERS-1 scenes provided.

Incidence Nominal Date Track Frame Polarization Angle Resolution

18-Feb-92 32 A 1485 23° 30 m VV

24-Feb-92 32 A 1485 23° 30 m VV

7-Mar-92 32 A 1485 23° 30 m VV

13-Mar-92 32 A 1485 23° 30 m VV

• TerraSAR-X: Forty six TerraSAR-X scenes were supplied by the DLR under

agreement LAN-0320. The details of these scenes are listed in Table 5.5 below:

Table 5.5: TerraSAR-X scenes provided.

Orbit Incidence Nominal Date polarization Type (A/D) Angle Resolution

2-May-08 52 D 26.9° HH Stripmap 3 m

5-May-08 104 A 40.6° HH Stripmap 3 m

13-May-08 52 D 26.9° HH Stripmap 3 m

16-May-08 104 A 40.6° HH Stripmap 3 m

Hi res 3-Sep-08 104 A 40.6° HH Spotlight 1 m

Hi res 14-Sep-08 104 A 40.6° HH Spotlight 1 m

Hi res 14-Oct-08 52 D 26.9° HH Spotlight 1 m

216 Orbit Incidence Nominal Date polarization Type (A/D) Angle Resolution

Hi res 17-Oct-08 104 A 40.6° HH Spotlight 1 m

Hi res 25-Oct-08 52 D 26.9° HH Spotlight 1 m

Hi res 28-Oct-08 104 A 40.6° HH Spotlight 1 m

1-Feb-09 52 D 27.1° HH Spotlight 1.5 m

5-Feb-09 119 A 29.3° HH Spotlight 1.5 m

12-Feb-09 52 D 27.1° HH Spotlight 1.5 m

16-Feb-09 119 A 29.3° HH Spotlight 1.5 m

23-Feb-09 52 D 27.1° HH Spotlight 1.5 m

27-Feb-09 119 A 29.3° HH Spotlight 1.5 m

30-Apr-09 52 D 27.1° HH Spotlight 1.5 m

4-May-09 119 A 29.3° HH Spotlight 1.5 m

11-May-09 52 D 27.1° HH Spotlight 1.5 m

15-May-09 119 A 29.3° HH Spotlight 1.5 m

12-Jan-10 119 A 29.1° HH Spotlight 1.5 m

14-Jan-10 143 D 33.5° HH Spotlight 1.5 m

23-Jan-10 119 A 29.1° HH Spotlight 1.5 m

3-Feb-10 119 A 29.1° HH Spotlight 1.5 m

5-Feb-10 143 D 33.5° HH Spotlight 1.5 m

11-Dec-10 158 D 43.9° HH Spotlight 1.5 m

217 Orbit Incidence Nominal Date polarization Type (A/D) Angle Resolution

22-Dec-10 158 D 43.9° HH Spotlight 1.5 m

23-Dec-10 13 A 45.2° HH Spotlight 1.5 m

2-Jan-11 158 D 43.9° HH Spotlight 1.5 m

13-Jan-11 158 D 43.9° HH Spotlight 1.5 m

25-Jan-11 13 A 45.2° HH Spotlight 1.5 m

4-Feb-11 158 D 43.9° HH Spotlight 1.5 m

5-Feb-11 13 A 45.2° HH Spotlight 1.5 m

15-Feb-11 158 D 43.9° HH Spotlight 1.5 m

9-Mar-11 158 D 43.9° HH Spotlight 1.5 m

10-Mar-11 13 A 45.2° HH Spotlight 1.5 m

20-Mar-11 158 D 43.9° HH Spotlight 1.5 m

31-Mar-11 158 D 43.9° HH Spotlight 1.5 m

1-Apr-11 13 A 45.2° HH Spotlight 1.5 m

22-Apr-11 158 D 43.9° HH Spotlight 1.5 m

23-Apr-11 13 A 45.2° HH Spotlight 1.5 m

3-May-11 158 D 43.9° HH Spotlight 1.5 m

4-May-11 13 A 45.2° HH Spotlight 1.5 m

15-May-11 13 A 45.2° HH Spotlight 1.5 m

26-May-11 13 A 45.2° HH Spotlight 1.5 m

6-Jun-11 13 A 45.2° HH Spotlight 1.5 m

218 • RADARSAT-2: Twenty two RADARSAT-2 scenes were supplied by the

Canadian Space Agency as part of SOAR-E project 5013. These scenes are listed

in Table 5.6 below.

Table 5.6: RADARSAT-2 scenes provided.

Orbit Incidence Beam Date Look Polarization Resolution (A/D) Angle Mode

9-Dec-09 198 A 48.7° RL HH Ultrafine (3 m) U27

10-Dec-09 210 A 46.3° LL HH Ultrafine (3 m) U23

10-Dec-09 206 D 21.1° RL HH Ultrafine (3 m) U71

11-Dec-09 226 A 23.1° RL HH Ultrafine (3 m) U73

2-Jan-10 198 A 48.7° RL HH Ultrafine (3 m) U27

3-Jan-10 206 D 21.1° RL HH Ultrafine (3 m) U71

4-Jan-10 226 A 23.1° RL HH Ultrafine (3 m) U73

26-Jan-10 198 A 48.7° RL HH Ultrafine (3 m) U27

27-Jan-10 206 D 21.1° RL HH Ultrafine (3 m) U71

28-Jan-10 226 A 23.1° RL HH Ultrafine (3 m) U73

19-Feb-10 198 A 48.7° RL HH Ultrafine (3 m) U27

20-Feb-10 210 A 46.3° LL HH Ultrafine (3 m) U23

20-Feb-10 206 D 21.1° RL HH Ultrafine (3 m) U71

21-Feb-10 226 A 23.1° RL HH Ultrafine (3 m) U73

15-Mar-10 198 A 48.7° RL HH Ultrafine (3 m) U27

16-Mar-10 210 A 46.3° LL HH Ultrafine (3 m) U23

219 Orbit Incidence Beam Date Look Polarization Resolution (A/D) Angle Mode

16-Mar-10 206 D 21.1° RL HH Ultrafine (3 m) U71

17-Mar-10 226 A 23.1° RL HH Ultrafine (3 m) U73

8-Apr-10 198 A 48.7° RL HH Ultrafine (3 m) U27

9-Apr-10 210 A 46.3° LL HH Ultrafine (3 m) U23

9-Apr-10 206 D 21.1° RL HH Ultrafine (3 m) U71

5.4.2 ERS-1 processing

The processing of the ERS-1 data is illustrative of the processing chain for all radar imagery and is shown in Figure 5.3. Examples from the different stages of the process are shown in Figure 5.4.

220

Figure 5.3: Workflow for measuring down-glacier flow from ERS-1 imagery.

221 From the four ERS-1 scenes, it was possible to create a number of different interferograms with separations of 6, 12, 18, and 24 days. After some experimenting it was found that scenes captured on the 7th and the 13th of March 1992 gave optimal results. These scenes were separated by a baseline of 69 m, and the six-day time separation was sufficiently short to avoid any loss of coherence. ERS-1 scenes are approximately 100 km by 100 km in extent and Fountain Glacier was located at the extreme left-hand-side of both scenes, so in order to make processing more efficient the first step was to crop both scenes to the area immediately surrounding the glacier. The orthorectified amplitude image subset from the 7th of March is shown in Figure 5.4(a).

Figure 5.4: Measurement of displacement from ERS-1 interferogram; (a): Amplitude image from 7 March 1992, © ESA 1992, (b): Filtered and flattened ERS-1 motion interferogram, (c): Coherence raster, and (d): LOS displacement image. All images have been orthorectified for visualization purposes. In the usual processing chain, orthorectification only occurs after phase unwrapping.

All processing was carried out using SARscape, which is an interferometric package which runs under the ENVI image processing suite. Once the images were cropped, a preliminary interferogram was formed, using a multi-look factor of five in the

222 azimuth direction and one in the range direction. In order to obtain the best-possible results, the two images were first co-registered to subpixel accuracy using a cross- correlation algorithm. The initial interferogram was then formed by multiplying the phase component of the master scene by the complex conjugate of the slave scene. This interferogram was unflattened, and in order to measure surface displacements, it was necessary to remove both the background phase fringes, which are a function of the scene geometry, and the topographic phase fringes, which arise from variations in the elevation of the terrain.

Interferogram flattening was carried out using the 1982 DEM, which was first reprojected into the slant-range geometry of the ERS-1 scenes. A synthetic interferogram was then generated from the slant-range DEM. This was used to remove the geometric and topographic phase from the original interferogram, leaving only the phase component arising from surface displacement. After flattening, the interferogram was filtered using a

3*3 Goldstein filter (Goldstein and Werner 1998) and a coherence raster was produced for use in the phase-unwrapping process. The filtered, flattened motion-only interferogram and the coherence raster are shown in Figure 5.4b and c.

Phase unwrapping was carried out using a region-growing algorithm (Ferretti et al. 2007), with a coherence threshold of 0.25. The combination of the six-day separation between the two images and the 56 mm C band wavelength of ERS-1 resulted in comparatively few fringes, so no unwrapping errors were apparent. However in order to obtain useful estimates of motion, it was necessary to calibrate the unwrapped phase.

223 This was achieved by identifying a single GCP in a locally-flat ice-free area adjacent to the glacier, which was then used to determine the unwrapped phase value corresponding to zero motion. The final step was to orthorectify the unwrapped-calibrated interferogram, so that measurements could be made in real-world coordinates. The 1982

DEM was used to reproject the image into a UTM 17 projection with a 25 m pixel resolution. The orthorectified, calibrated LOS image is shown in Figure 5.4d.

Final estimates of horizontal flow in the down-glacier direction were calculated using equation [5.16], with the initial direction of glacier flow being estimated from the direction of flow stripes on a SPOT satellite image from the 3rd of August 2008.

5.4.3 TerraSAR-X processing

From the 46 available TerraSAR-X scenes it was possible to form eight 11-day

ascending and ten 11-day descending-pass interferograms which showed reasonable levels of coherence. These are listed in Table 5.7. The processing chain was very similar to that used for the ERS-1 scenes and described in Figure 5.3, except that in this case a multilook factor of three was applied in both range and azimuth, with resampling being used to give orthorectified pixel resolutions of three metres for the spotlight and high- resolution spotlight image pairs, and ten metres for the stripmap image pairs.

More fringes were present in the TerraSAR-X interferograms due to the

comparatively short 3 cm wavelength and the 11-day repeat period. This caused some problems with phase unwrapping, especially in regions where the fringes were closely spaced, such as around the glacier margins. However in most cases, the central parts of

224 the glacier away from the margins unwrapped well and produced smooth, continuous surfaces.

Table 5.7: TerraSAR-X 11 day interferograms used for analysis. The coherence estimate is qualitative, with coherence values predominantly over 50% being classed as high, and values predominantly under 25% being classed as low.

Coherence Image Image Incidence Normal for upper, Scene A/D dates Mode angle Baseline middle, and orientation lower glacier

Upper: high 5- Feb-09 Middle: high 16-Feb-09 A Spotlight 29.3° 41.71 m Lower: high 338.6°

Upper: high 16-Feb-09 Middle: high 27-Feb-09 A Spotlight 29.3° 3.99 m Lower: high 338.6°

Upper: high 4-May-09 Middle: high 15-May-09 A Spotlight 29.3° 0.78 m Lower: high 338.6°

Upper: high 23-Jan-10 Middle: high 3-Feb-10 A Spotlight 29.1° 35.53 m Lower: high 338.7°

Upper: high 25-Jan-11 Middle: high 5-Feb-11 A Spotlight 45.2° 99.45 m Lower: high 344.8°

225 Coherence Image Image Incidence Normal for upper, Scene A/D dates Mode angle Baseline middle, and orientation lower glacier

Upper: high 23-Apr-11 Middle: high 4-May-11 A Spotlight 45.2° 63.51 m Lower: high 345.0°

Upper: med 4-May-11 Middle: med 15-May-11 A Spotlight 45.2° 253.23 m Lower: high 345.0°

Upper: low 15-May-11 Middle: high 26-May-11 A Spotlight 45.2° 248.98 m Lower: high 345.0°

Upper: high 2-May-08 Middle: high 13-May-08 D Stripmap 26.6° 22.83 m Lower: high 197.1°

Upper: high 1-Feb-09 Middle: high 12-Feb-09 D Spotlight 27.1° 22.15 m Lower: high 197.3°

Upper: med 12-Feb-09 Middle: med 23-Feb-09 D Spotlight 27.1° 132.66 m Lower: high 197.3°

Upper: med 30-Apr-09 Middle: med 11-May-09 D Spotlight 27.1° 162.70 m Lower: med 197.3°

Upper: med 11-Dec-10 Middle: low 22-Dec-10 D Spotlight 43.9° 76.13 m Lower: med 191.0°

226 Coherence Image Image Incidence Normal for upper, Scene A/D dates Mode angle Baseline middle, and orientation lower glacier

Upper: high 2-Jan-11 Middle: high 13-Jan-11 D Spotlight 43.9° 151.67 m Lower: high 191.1°

Upper: high 4- Feb-11 Middle: high 15-Feb-11 D Spotlight 43.9° 65.66 m Lower: high 191.1°

Upper: high 9-Mar-11 Middle: low 20-Mar-11 D Spotlight 43.9° 135.08 m Lower: high 191.0°

Upper: high 20-Mar-11 Middle: high 31-Mar-11 D Spotlight 43.9° 64.86 m Lower: high 191.0°

Upper: high 22-Apr-11 Middle: high 3-May-11 D Spotlight 43.9° 48.88 m Lower: high 191.0°

To correct for the effects of unwrapping errors in the marginal regions, an

ascending-pass interferogram derived from scenes acquired on the 25th of January and

the 5th of February 2011, and a descending-pass interferogram derived from scenes acquired on 9th and the 20th of March 2011 were used to calibrate the remaining ascending and descending-pass interferograms. An inspection of centre-line and cross

profiles showed that these reference interferograms appeared to be free of unwrapping

errors. Centre-line profiles from both of these interferograms were projected using

227 equation [5.16] to give initial estimates for displacement in the down-glacier direction.

Phase offsets were then applied to the remaining LOS interferograms in order to match their projected displacements to those of the reference profiles. Adjustment was based only on the east / west oriented section of the lower glacier because of the favourable projection geometry for this part of the glacier.

Since the values for flow direction were only approximate, the initial estimates for projected displacement showed considerable variation over the middle and upper glacier.

Because of the unfavourable alignment of the upper glacier relative to the satellite orbital tracks, any small error in flow direction had a very exaggerated effect on the overall projected down-glacier displacement. This was especially true for descending-pass

interferograms, since the descending-pass satellite track and the direction of glacier flow were almost coincident.

5.4.4 RADARSAT-2 processing

From the RADARSAT-2 scenes supplied it was possible to form ten 24-day interferograms which showed reasonable levels of coherence. These could be divided into four categories; three ascending-pass interferograms with high incidence angles, three ascending-pass interferograms with low incidence angles, three descending-pass

interferograms with low incidence angles, and one left-looking ascending-pass

interferogram with a high incidence angle. The left-looking interferogram was

particularly useful, since it had a completely different imaging geometry from any of the

228 other available interferograms. The full set of RADARSAT-2 interferograms is described in Table 5.8.

Table 5.8: RADARSAT-2 24 day interferograms used in analysis.

Coherence Image Image Incidence Normal for upper, Scene A/D dates Mode angle Baseline middle, and orientation lower glacier

Upper: med

2-Jan-09 Middle: high 26-Jan-10 A Ultrafine 48.7° 49.75 m Lower: med 349.9°

Upper: low

4-Jan-10 Middle: high 28-Jan-10 A Ultrafine 23.1° 113.57 m Lower: high 336.3°

Upper: med

26-Jan-10 Middle: med 19 Feb 10 A Ultrafine 48.7° 186.29 m Lower: med 349.9°

Upper: med

28-Jan-10 Middle: high 21-Feb-10 A Ultrafine 23.1° 315.34 m Lower: high 336.3°

Upper: low

19-Feb-10 Middle: med 15-Mar-10 A Ultrafine 48.7° 153.24 m Lower: high 349.9°

Ultrafine Upper: med 20-Feb-10 A Left Middle: med 16-Mar-10 looking 46.3° 187.49 m Lower: med 295.6°

229 Coherence Image Image Incidence Normal for upper, Scene A/D dates Mode angle Baseline middle, and orientation lower glacier

Upper: med Middle: high 21-Feb-10 17-Mar-10 A Ultrafine 23.1° 186.99 m Lower: high 336.3°

Upper: low Middle: med 3-Jan-10 27-Jan-10 D Ultrafine 21.1° 137.87 m Lower: med 199.9°

Upper: med

27-Jan-10 Middle: high 20-Feb-10 D Ultrafine 21.1° 77.31 m Lower: high 199.9°

Upper: med

20-Feb-10 Middle: high 16-Mar-10 D Ultrafine 21.1° 114.55 m Lower: high 199.9°

The RADARSAT-2 interferograms were processed in the same way as the

TerraSAR-X interferograms. A multilook factor of three was applied in both range and azimuth, and the final orthorectified interferograms were resampled to a 10 m pixel resolution. The RADARSAT-2 interferograms were scaled in order to match the 11-day separation of the TerraSAR-X interferograms. The interferograms were then calibrated to account for any unwrapping errors at the glacier margins, using phase offsets derived from the reference TerraSAR-X ascending and descending-pass centre-line profiles.

230 5.4.5 Determining the full 3D motion field for Fountain Glacier using multi-track

interferometry

The inclusion of the RADARSAT-2 left-looking interferogram greatly strengthened the imaging geometry, with the angle between the look direction for this interferogram and the look direction for the descending-pass RADARSAT-2

interferograms being close to 90°. The RADARSAT-2 interferograms also offered a mix

of high and low incidence angles, providing good intersections, and further strengthening

the imaging geometry.

The following RADARSAT-2 interferograms were used:

• 19 Feb 2010 - 15 Mar 2010, ascending pass, right looking, high incidence angle

• 20 Feb 2010 - 16 Mar 2010, ascending pass, left looking, high incidence angle

• 20 Feb 2010 - 16 Mar 2010, descending pass, right looking, low incidence angle

• 21 Feb 2010 - 17 Mar 2010, ascending pass, right looking, low incidence angle

An ascending-pass TerraSAR-X interferogram for 23 Jan - 3 Feb 2010 was also used.

This offered an intermediate incidence angle and had better coherence than the

RADARSAT-2 interferograms. The imaging geometry of the different interferograms

used is shown in Figure 5.5.

231

Figure 5.5: Geometry of the five interferograms used to determine 3D motion of Fountain

Glacier. The dotted lines show the X, Y, and Z components of each unit vector.

For each interferogram, the 3D unit vector corresponding to its look angle was calculated, using equations [5.17]. The X, Y, and Z components of glacier flow were then calculated using equation [5.18]. To enable matrix inversion, only three vectors could be solved for at a time. Solutions were therefore computed for the following combinations:

• RADARSAT-2 high incidence, ascending, left looking - RADARSAT-2 low

incidence, descending, right looking - TerraSAR-X medium incidence, ascending,

right looking

232 • RADARSAT-2 high incidence, ascending, right looking - RADARSAT-2 high

incidence, ascending, left looking - RADARSAT-2 low incidence, ascending,

right looking

• RADARSAT-2 high incidence, ascending, right looking - RADARSAT-2 high

incidence, ascending, left looking - RADARSAT-2 low incidence, descending,

right looking

• RADARSAT-2 high incidence, ascending, right looking - RADARSAT-2 high

incidence, ascending, left looking - TerraSAR-X medium incidence, ascending,

right looking

• RADARSAT-2 high incidence, ascending, left looking - RADARSAT-2 low

incidence, descending, right looking - RADARSAT-2 low incidence, ascending,

right looking

Each of the five combinations gave very similar values for X, Y, and Z motion, so a mean was taken of all five to obtain a final estimate. The horizontal down-glacier displacement was calculated from the X and Y values and was scaled to give an annual displacement. An accurate estimate of the direction of flow was also calculated from the arc tangent of ΔN / ΔE.

To reflect the greater variability associated with vertical motion, the Z component

was scaled to match the 11-day period between TerraSAR-X acquisitions. To obtain rates

of surface elevation change it was necessary to first remove the portion of vertical

displacement which arises from regular down-glacier flow. This was done using the

233 method described by Gray (2011). The vertical component was computed from the

horizontal displacement multiplied by the tangent of the surface slope at each point on the

glacier surface. In order to minimise the effect of minor local variations, the surface slope

was filtered using a 15*15 median filter prior to correction.

5.4.6 Feature tracking of TerraSAR-X amplitude images

For comparative purposes, surface displacements were also computed using a feature tracking approach. Imcorr is a software package available from the US National

Snow and Ice Data Centre (NSIDC). It works by matching regularly-spaced image

subsets between a reference and a search image, using a fast-fourier transform version of a normalised cross-covariance method (Scambos et al. 1992). Unlike the Cosi-Corr

package described in Chapter 2, Imcorr can be used with radar images.

Feature tracking was attempted for a number of image pairs. Because of the slow

movement of the glacier, the tracking of coherent speckle was ruled out as an option,

since little surface motion would occur before coherence was lost. Instead tracking was

carried out over prolonged time periods, using texture from orthorectified amplitude

images. The best results were obtained using descending-pass images from the 11th of

December 2010, and the 3rd of May 2011. These images were resampled to a 5 m pixel

size prior to processing, and feature tracking was carried out using a 128*128 pixel

reference window with a 32*32 pixel search window.

Using this image combination, the horizontal displacement over the 143 days

between the two images was successfully measured. Although the accuracy of feature

234 tracking is lower than that of interferometry (Floricioiu et al. 2008), the extended period

between the two images was sufficient to ensure that representative winter flow could be

measured on the faster-moving middle and upper sections of the glacier. However the

slow flow rates close to the terminus of Fountain Glacier meant that the accuracy of the

results for the lower glacier was expected to be relatively low.

5.4.7 Feature tracking of SPOT-5 panchromatic images

Feature tracking of SPOT-5 images was also carried out, using the Cosi-Corr software described in Chapter 2. Orthorectified panchromatic SPOT scenes with a resolution of ten metres were downloaded from the Canadian Council of Geomatic’s

Geobase website. Scenes were available from the 3rd of August 2008, and the 25th of

August 2009. Although both scenes were already orthorectified, an additional first-order polynomial registration was carried out between the images to eliminate any systematic offsets. Cosi-Corr was run using an initial window size of 64*64 and a final window size of 16*16, with a step size of eight pixels.

Although the results were considered to be of comparatively low quality, they were still sufficiently detailed to determine the approximate horizontal displacement of the glacier over the 387 day period between the acquisition of the two SPOT images. To determine the approximate contribution of non-winter motion over this period, the results from the SPOT feature tracking were first scaled to a period of 365 days. The estimated winter-equivalent annual down-glacier displacement derived in section 5.4.5 was then

subtracted, in order to obtain an estimate for non-winter motion. The difference was

235 assumed to be the result of accelerated summer flow rates. It should be noted that the

derived value is likely to be an overestimate, since the second SPOT image was obtained

22 days later in August than the first, meaning that summer displacement will be

overrepresented. However if a three to four month period of accelerated summer flow is

assumed, then it is likely that the difference between this estimate and the true summer

displacement will be less than 20%.

5.4.8 Determining changes in horizontal and vertical motion

Since values for down-glacier flow direction had now been accurately determined

from multi-track interferometry, equation [5.16] could be used to reproject all of the

TerraSAR-X and RADARSAT-2 interferograms, in order to obtain estimates of down- glacier displacement from all available interferograms. This is the usual method of obtaining down-glacier displacement from single-pass SAR interferometry and assumes surface parallel flow. Although the corrected glacier flow directions gave much improved results, only ascending-pass interferograms were used to determine displacement for the upper glacier, and only descending-pass interferograms were used for the section of the glacier where the ascending-pass satellite track was within 20° of the glacier flow direction.

Although the close alignment of the glacier flow direction and both the ascending

and descending-pass satellite tracks made it difficult to obtain good estimates of

horizontal displacement over much of the glacier, the imaging geometry was

advantageous for obtaining the vertical displacement, since the vertical component of

236 motion was disproportionately represented in the LOS interferograms. In order to extract

the vertical displacement from each interferogram, the assumption was made that the XY

down-glacier displacement obtained from multi-track interferometry was definitive, and

that any observed discrepancies represented vertical motion. The XY displacement

derived from multi-track interferometry was reverse-projected, in order to create an LOS

interferogram representing only the horizontal component of motion. Different LOS

interferograms were created for the specific geometries corresponding to each different

satellite track and incidence angle used. The procedure used is shown in Figure 5.6. The

following equation was used to create the LOS interferograms:

R = D *sin γ *sinθ *11/ 365 [5.19]

Where R is the horizontal component of displacement in the radar LOS direction,

D is the horizontal component of down-glacier displacement derived from multi-track interferometry, γ is the angle between the satellite track and the glacier flow direction, and θ is the incidence angle. The factor of 11/365 was applied to match the simulated interferogram to the 11-day TerraSAR-X repeat period. Since it was only the XY component of down-glacier motion which was being reverse-projected, any influence of glacier surface slope could effectively be ignored.

Each of the XY interferograms thus created was subtracted from all the LOS interferograms with the corresponding imaging geometry. This resulted in series of LOS interferograms which were assumed to contain only the residual vertical component of motion. These were then divided by the cosine of the incidence angle to obtain actual

237 vertical displacement. To identify areas of uplift and subsidence it was necessary to

remove the vertical component of down-glacier velocity from each interferogram. This was done using the method described by Gray (2011) and described in 5.4.5. An example of this process is shown in Figure 5.6.

Figure 5.6: Obtaining the vertical component of motion; (a): Horizontal down-glacier displacement derived from multi-track interferometry, (b): Comparison of LOS derived from the XY displacement with actual TerraSAR-X LOS interferogram, and (c): The vertical component of displacement before and after correction for down-glacier motion.

238 5.5 Results

5.5.1 3D motion analysis

The results from the multi-track interferometry are shown in Figure 5.7 and

Figure 5.8. It can be seen that the annual-equivalent winter XY displacement increases with distance up glacier from the terminus, reaching a steady maximum of around 25 m at a distance of approximately 7,500 m from the terminus. At this point the glacier is constricted within a narrow valley. At about 7,000 m from the terminus, the glacier widens significantly as it flows past the main marginal lake which separates Fountain

Glacier from Akteneaq Glacier. This is reflected in the steep decline in velocity visible between 7,500 m and 7,000 m from the terminus. Between 7,000 m and the terminus, the equivalent annual displacement drops smoothly by around 2.5 m per 1,000 m.

From Figure 5.7 it can be seen that the down-glacier directions derived from the multi-track interferometry show a smooth flow, with flow directions predominantly being down glacier. The flow arrows do however show a rotation of the flow vector towards the margins at the edges of the glacier, which is particularly pronounced on the northern side of the glacier, near the terminus. This is the region where the time-lapse measurements described in the previous chapter were made.

239

Figure 5.7: Computed down-glacier displacement; (a): Annual equivalent horizontal winter displacement derived from multi-track interferometry, and (b): 11-day vertical displacement derived from multi-track interferometry. The vertical displacement has been corrected to account for the vertical component of down-glacier motion.

240

Figure 5.8: Displacement along centre-line profile AA'; (a): Horizontal annual- equivalent winter displacement along centre-line profile AA', and (b): 11-day vertical displacement along profile AA'. Vertical displacement has been corrected for the vertical component of down-glacier motion. Points B, C, D, and E represent areas of significant vertical displacement. Their positions are shown on Figure 5.7b.

The adjusted 11-day vertical displacement is predominantly positive, which would be expected under winter conditions, with surface melting not being a significant factor. There are however significant dips at 6,000 m (point C) and at 7,500 m (point E) from the terminus, as well as a significant peak at 6,500 m (point D) from the terminus.

These features may represent a response to bed topography or subsurface hydrology.

241 Figure 5.7b shows higher than average vertical displacement on the eastern side

of the upper glacier, and lower than average vertical displacement on the western side. It

is likely that these do not reflect genuine vertical motion but are caused by unwrapping

errors in the high shear zones along both sides of the upper glacier. Some layover was

also present at the edges of the glacier on the low-incidence RADARSAT-2

interferograms and this could potentially have contributed to the anomalous values in these regions. However the centre of the glacier is believed to be largely unaffected by such errors, as can be evidenced by the smooth appearance of the XY profile AA' in

Figure 5.8a.

5.5.2 Feature tracking

A comparison of down-glacier displacements derived from multiple-tack interferometry, amplitude tracking of TerraSAR-X images, and amplitude tracking of

SPOT-5 images is shown in Figure 5.9 and Figure 5.10. It can be seen that the results obtained from multi-track interferometry and from TerraSAR-X feature tracking are similar, with the feature tracking providing confirmation of the displacements obtained in section 5.4.5. It is also apparent that the feature-tracking approach gives a much less smooth result, with local variations of several metres.

242

Figure 5.9: Comparison of displacement estimates from InSAR and feature tracking; (a): Annual equivalent down-glacier horizontal displacement derived from multiple-track interferometry, (b): Annual equivalent down-glacier horizontal displacement derived from

TerraSAR-X amplitude tracking, and (c): Annual horizontal down-glacier displacement derived from SPOT feature tracking.

243

Figure 5.10: Comparison between centre-line horizontal down-glacier displacements

measured using multi-track interferometry, TerraSAR-X feature tracking and SPOT-5

feature tracking.

The combination of the 10 m resolution along with the step size of 8 used by the

Cosi-Corr package meant that the displacement measured from the two SPOT scenes was sampled with an 80 m grid spacing. The winter feature tracking of TerraSAR-X images

used a different software package (Imcorr), but effectively sampled the displacement at a

40 m grid interval. Typical accuracies from feature tracking are of the order of a tenth of

a pixel (Fallourd et al. 2011). This suggests that feature tracking over the slow-moving

marginal regions of the glacier would not be expected to give good results. Also the

relatively course grid size used for the SPOT images means that areas of poor correlation

can cause large variations between estimated displacements. This effect is apparent when

244 looking at Figure 5.9 and Figure 5.10, where it can be seen that the surfaces derived from

feature tracking are much less smooth than those derived from SAR interferometry. In

spite of this the general trends of the profiles shown in Figure 5.10 agree well with that

derived from InSAR.

Comparison of the displacement profiles in Figure 5.10 shows a consistent

pattern. Overall, annual centre-line displacements are 8 – 10 ma-1 greater than winter

displacements. Allowing for the overrepresentation of summer displacement between the

two SPOT images this suggests that accelerated summer motion contributes an additional

6 – 8 ma-1, close to the centre-line of the glacier. It is therefore possible that the average speed of the glacier may increase by a factor of two or three during the summer months, except in some marginal areas where the glacier remains frozen to its bed. Figure 5.10

also hints at the presence of possible sticky patches at 1,000 m and 6,000 m up glacier,

where summer and winter speeds show little change. The resolution of the SPOT profile

is however too coarse to confirm this.

5.5.3 Projection of centre-line displacements

The corrected glacier flow directions derived in section 5.4.5 flow allowed

projected estimates of 3D (XYZ) down-glacier velocity to be derived from each of the

LOS TerraSAR-X, RADARSAT-2, and ERS-1 interferograms, using equation [5.16].

The projection of down-glacier displacements assumed surface parallel flow, and

therefore velocity estimates were poorer than those derived from multi-track

interferometry. This was especially true for the middle and upper glacier where the

245 imaging geometry was comparatively poor. However the use of projected displacements

allowed temporal comparisons to be made of down-glacier velocity. The projected

ascending-pass centre-line profiles for line AA’ are shown in Figure 5.11, and

descending-pass profiles are shown in Figure 5.12. To minimise problems relating to

poor projection geometry, no information is shown for sections of the glacier where the

differences in angle between the satellite track and the glacier flow direction were less

than 20°.

The centre-line profiles shown in white in Figure 5.11 and Figure 5.12 describe full XYZ down-glacier motion, and as such include a vertical component. Normally this component is small compared with the horizontal component, as can be seen by the comparison with the horizontal (XY) displacement derived by multi-track interferometry

(shown in black in Figure 5.11 and Figure 5.12). In general, the shapes of the profiles do not diverge significantly from the profile derived from multi-track interferometry, suggesting that down-glacier flow varies little through the winter. It can also be seen from Figure 5.11 that the projected displacement from the 1992 ERS-1 interferogram

shows some similarity to the displacement profile derived from multi-track

interferometry, suggesting that winter down-glacier velocity has changed little over

recent years.

246

Figure 5.11: Projected ascending-pass displacements from TerraSAR-X, RADARSAT-2,

and ERS-1 Interferograms. Projected displacements are shown in white. Note that only one set of ascending-pass RADARSAT-2 interferograms is shown, since the other

RADARSAT-2 interferograms cover the same time periods.

247

Figure 5.12: Projected descending-pass displacements from TerraSAR-X, RADARSAT-2, and ERS-1 Interferograms. Projected displacements are shown in white. Note that only one set of descending-pass RADARSAT-2 interferograms is shown, since the other

RADARSAT-2 interferograms cover the same time periods.

248 While overall the centre-line profiles showed little change, there were some significant local variations. In many cases these may simply have reflected residual errors in the glacier flow direction, the satellite track direction, or in the DEM used to orthorectify the interferograms. The most obvious variation can be seen in the descending-pass profiles (Figure 5.12), and occurs between 2,000 m and 4,000 m up glacier from the terminus. This is clearly significant, and almost certainly reflects real changes in the horizontal and / or vertical motion of the glacier surface. Since longitudinal and lateral stress coupling make it unlikely that the horizontal motion of any point on the glacier centre-line will be significantly faster or slower than points immediately up or down glacier of it, it is likely that such significant variations from the average predominantly represent vertical motion of the glacier surface.

5.5.3.1 Projected residual vertical displacements

The corrected 11-day vertical profiles are shown in Figure 5.13 and Figure 5.14.

Consistent peaks represent areas where the glacier surface is rising, whereas consistent troughs represent long-term lowering. It can be seen that at the 6,000 m mark there is deep trough, followed by a sharp peak. This is apparent on all interferograms and may represent a long term change in the glacier surface in this area.

249

Figure 5.13: Residual ascending-pass vertical displacements derived from TerraSAR-X,

RADARSAT-2, and ERS-1 interferograms. Projected vertical displacements are shown in white. Note that only one set of ascending-pass RADARSAT-2 interferograms is shown, since the other RADARSAT-2 interferograms cover the same time periods.

250

Figure 5.14: Residual descending-pass vertical displacements derived from TerraSAR-X,

RADARSAT-2, and ERS-1 interferograms. Projected vertical displacements are shown in white. Note that only one set of descending-pass RADARSAT-2 interferograms is shown, since the other RADARSAT-2 interferograms cover the same time periods.

251 It can be seen from Figure 5.13 and Figure 5.14 that the variable peak noted above between 2,000 m and 4,000 m from the terminus, is apparent on both the reprojected ascending and descending-pass vertical profiles. The residual vertical displacement at this point shows considerable variation between the different interferograms. A large peak is apparent on both ascending and descending-pass interferograms from February 2009. This peak then disappears, but a very similar peak can be seen in both the ascending and descending-pass interferograms from April and

May 2011. In between these dates, this region continued to show considerable variation.

The variation is particularly apparent on the 2009 profiles. Figure 5.15 shows all ascending and descending-pass TerraSAR-X profiles from 2009 together. It can be seen that over most of the glacier, the agreement is good, but the region between 2,000 m and

4,000 m up glacier from the terminus shows considerable variability, with a maximum uplift of around 13 cm being seen in the descending-pass profile between the 12th and the

23rd of February. This will be discussed further in Chapter 6.

Figure 5.15: 2009 vertical centre-line profiles.

252 5.6 Error assessment

5.6.1 Acquisition errors

Errors in orbital position will have an effect on interferometric baselines. This was discussed in section 5.1.7.1. However the accuracy of tracking for both the ERS-1

precise orbits and TerraSAR-X means that any baseline error is unlikely to be significant

for these satellites. While baseline error remains a possibility for RADARSAT-2, the interferograms obtained from RADARSAT-2 agreed closely with those from TerraSAR-

X and showed little sign of any systematic bias.

Atmospheric effects were discussed in section 5.1.7.2 and are not believed to have introduced significant errors into the processed interferograms, since the interferogram generation process effectively cancels out the hydrostatic component of tropospheric delay, and atmospheric conditions are generally stable over Bylot Island through the polar winter, minimising the effect of variations in the smaller wet component.

5.6.2 DEM errors

From the DEM comparisons described in Chapter 2, it is apparent that the glacier

has been losing mass over most of its length in recent years. Although it was not possible

to obtain a contemporary DEM covering the whole glacier, it is likely that the glacier has

thinned significantly since 1982, when the photography for the most recent DEM was

obtained. To assess how this could affect the accuracy of down-glacier flow estimation,

the effect of a 25 m error in the 1982 DEM elevation was calculated for a theoretical

TerraSAR-X interferogram, using equation [5.12] with a nominal incidence angle of 45°,

253 a range of 730 km, and a baseline of 100 m. The error in down-glacier displacement was

found to be approximately 2.5 mm over the 11-day repeat period, or 0.083 ma-1, which

represents an error of less than one percent over the majority of the glacier, although the

error is proportionately higher for slower-moving parts of the glacier close to the terminus, which would also be more likely to have seen significant changes in surface elevations.

It is also likely that the use of the 1982 DEM would also have introduced errors during the orthorectification process. The area surrounding Fountain Glacier is mountainous, and any error in the DEM would introduce positional errors into the unwrapped orthorectified interferograms. It is probable that some of the residual errors apparent in the centre-line profiles described in section 5.5.3 arose from orthorectification errors. Orthorectification errors could also have affected the estimates of 3D motion obtained from multi-track interferometry. Variations in horizontal position resulting from such errors could potentially have introduced errors of several degrees into the estimated flow direction for the upper glacier, causing further inaccuracies when projecting the

TerraSAR-X interferograms.

DEM errors will also have an effect on the determination of the surface slope of the glacier. While the slope is unlikely to have changed significantly over most of the glacier, slopes in marginal areas will have changed in response to the loss of ice over time. Though this effect is likely to be small, it will contribute to errors in the estimation of marginal displacements.

254 5.6.3 Phase unwrapping errors

Another significant source of error results from problems associated with phase unwrapping. Close spacing of interferometric fringes in regions of high shear can cause sudden jumps to occur in the unwrapped interferogram. When unwrapping errors are present profiles will typically show a sudden jump of one or more complete wave cycles.

For an X-band radar, such as TerraSAR-X, a single wave cycle represents a shift of 1.5 cm in the LOS direction, and this can translate into a potential error of one to two metres per annum in down-glacier flow, depending on the satellite orbital configuration and the alignment of the glacier. Unwrapping errors were also an issue for RADARSAT-2 interferograms, with the longer C-band wavelength and the 24 day repeat period resulting in a similar number of fringes.

The calculation of phase offsets for each interferogram, relative to the reference ascending and descending-pass interferograms, was described in section 5.4.3. This methodology relied on the assumption that the speed of the lower glacier remained constant through the winter. Photogrammetrically-measured flow rates described in

Chapter 4 showed there to be little variation throughout the winter close to the terminus.

Residual errors in annual displacements after correction are therefore believed to be small, and are likely to be less than 0.5 ma-1. To avoid any problems due to surface uplift in the region between 2,000 m and 4,000 m up from the terminus, offsets were calculated based only on the first 1,000 m up glacier from the terminus, where possible.

255 5.6.4 Errors affecting the determination of the vertical displacement

The vertical displacement derived from multi-track interferometry was similar for each of the interferogram combinations used. However, since the correction for the vertical component of down-glacier motion was derived from the 1982 DEM, changes to the glacier surface since then could potentially have had a significant effect, especially close to the glacier margins. In addition the slope raster had to be strongly filtered, in order to remove high-frequency noise prior to correction. It is therefore likely that the corrected vertical profile used as a reference contained some residual slope effects.

However, since all profiles had the same correction applied, residual slope errors will not affect the comparison between profiles.

The reverse-projection technique described in section 5.4.8, which was used to create simulated LOS interferograms is vulnerable to errors in the glacier flow direction.

Errors of a few degrees could potentially cause significant inaccuracies in the simulated interferograms used to calculate vertical displacement. The assumption of a constant horizontal down-glacier velocity is also a simplification, and variations in flow speed would have resulted in differences between the simulated and actual LOS interferograms.

However, the similarity of the projected vertical displacements shown in Figure 5.13 and

Figure 5.14 to the vertical displacements derived from multi-track interferometry suggests that any such errors were generally small.

The derived vertical profiles shown in Figure 5.13 and Figure 5.14 show variations in vertical displacement compared to the February / March 2010 reference

256 profile. The assumption was made that such differences represent vertical displacement

only. Once again this is a simplification, and it is likely that some variation in horizontal

displacement will also have occurred in areas of uplift. However the geometric alignment

of the upper and middle glacier with the satellite orbits is such that the effects of vertical

displacement are strongly magnified in this region, relative to horizontal component of

down-glacier motion.

While it is likely that the vertical profiles do contain some residual errors from the

above sources, they are most useful for providing a qualitative comparison of vertical

displacement over different time periods. Most important is the ability of such profiles to

identify parts of the glacier surface which show evidence of consistent surface rise or fall,

and to identify areas which show large variations in vertical displacement. As such the

vertical profiles can be considered to be substantively correct, even though the degree of

thickening or thinning may be over or under-represented in some cases.

5.6.5 Combined error for InSAR measurements

Combining potential acquisition, DEM, baseline, phase unwrapping, and

projection errors could potentially introduce errors in down-glacier XY speed of up to 1

ma-1. However such large errors are only likely to occur in marginal regions, which are

poorly represented by the 1982 DEM, and which are steeply sloping. For the centre of the

glacier it is assumed that errors in XY motion from all sources are unlikely exceed 0.5 ma-1. Errors in vertical motion from all sources are likely to be similar in magnitude, and

will also tend to be at their greatest in steeply-sloping marginal regions. Over the 11 day

257 period between TerraSAR-X acquisitions this would translate to a potential error of 1.5

cm in Z.

5.6.6 Errors associated with feature tracking

The use of feature tracking of both TerraSAR-X and SPOT images provides a

useful comparison with the results obtained from SAR interferometry. Feature tracking is

known to have a relatively low level of accuracy when compared to SAR interferometry

(Strozzi et al. 2002; Floricioiu et al. 2009). However the time interval between the

TerraSAR-X images used was 143 days, whereas the SPOT images were separated by

more than a year. The comparatively long time periods between the images used ensured

that a significant amount of surface motion would have occurred over each of the

tracking periods, helping to improve the accuracy of the overall results.

Assuming that each measurement has an associated accuracy of a tenth of a pixel

(Fallourd et al. 2011) gives an estimated accuracy of 0.5 m for the TerraSAR-X feature

tracking, since the resampled pixel sizes used for feature tracking were 5 m. However

since the measurement period was 143 days this works out at 3.5 mm per day, or

approximately 1.2 ma-1. For SPOT, with a 10 m pixel size, the corresponding values are

2.6 mm per day and 0.95 ma-1. Figure 5.10 also shows that both profiles derived from feature tracking had considerably greater variation than the profile produced from InSAR.

This is likely due to poor signal to noise ratios during the feature tracking process.

However the overall shape of the displacement profiles derived from both techniques are very similar, with the average absolute difference between InSAR and TerraSAR-X

258 feature tracking at each point along centre-line profile AA' being measured at

approximately 1.6 m.

The most important factor to ensure good results from feature tracking is to

ensure that the orthorectification of images is consistent. To ensure reasonable results, the

two TerraSAR-X images used came from the same orbital track, and shared the same

imaging geometry. An additional image registration was carried out using common tie

points in unglaciated areas in order to fine tune the georeferencing. The SPOT images

used were already orthorectified, but an additional image registration was also carried out

to improve the georeferencing.

Another factor that is important in feature tracking is to ensure that the images are

as similar as possible. While the radar images tracked had changed comparatively little

over the course over a single winter, the SPOT images were separated by more than a

year, and showed considerable changes in certain areas. Feature tracking is also

dependent on the size of the primary and search windows. Determination of the optimal

window sizes and pixel resolutions for the source images was largely a matter of trial and

error in both cases, with multiple runs being required to achieve optimal results.

While there is no way to independently verify the results from the SPOT feature tracking, a comparison of the profiles in Figure 5.10 suggests that the displacement estimates obtained by this technique are consistent with those derived from the radar imagery. Because of the timing between the images, it is likely that the SPOT profile

259 overestimates the down-glacier displacement. However the displacement estimates from

the SPOT images provide a useful comparison of summer and winter flow regimes.

5.7 Discussion and conclusion

While SAR interferometry has been largely supplanted by amplitude and speckle-

tracking techniques for many glaciological applications, the results from this chapter

show that it is still the most effective way to measure the winter displacement of slow-

moving polar glaciers. This is especially true when the acquisition geometry allows for

the determination of the full 3D motion field. Obtaining a suitable combination of look

directions requires a left-looking interferogram, except at extremely high latitudes.

Because of the practical difficulty of tasking left-looking radar acquisitions this technique has not been widely used in arctic regions to date. However the increasing prevalence of high-resolution radar satellites means that multi-track interferometry is likely to become more widely used in the future.

The traditional method of determining displacement using two interferograms derived from ascending and descending-pass scenes has a number of drawbacks. In particular, the assumption of surface-parallel flow means that areas of surface elevation change are likely to be misinterpreted as changes to down-glacier velocity. Even if surface elevation change is suspected, it is often difficult to quantify from two-pass interferometry. The geometry of the glacier itself can also have a significant effect on the projected displacement. In the case of Fountain Glacier, descending-pass interferograms

260 could not be used over the upper glacier, due to the alignment of the glacier with the

satellite track.

The other major advantage of the multi-track interferometry approach is that both horizontal and vertical displacements are directly calculated as part of the 3D motion field. The horizontal displacement thus obtained can be reverse-projected to produce a

LOS interferogram conforming to any specified projection geometry and representing the horizontal-only component of velocity. If the assumption is made that down-glacier flow

does not change significantly throughout the winter, then this can be used to calculate the

vertical displacement for any interferogram. By using this technique, several areas of

consistent surface rise and fall were identified. The area identified between 2,000 m and

4,000 m from the terminus showed quite different behaviour, with rapid changes in elevation which were likely due to subglacial hydrological processes. This region will be discussed in more detail in the following chapter.

Although the results from feature tracking showed greater variation than those from multi-track interferometry, the agreement between the winter displacement values derived using each method was encouraging. The slow flow rate of the glacier meant that

features travelled only a short way down glacier in the time between images, resulting in

a lot of noise being present in both the TerraSAR-X and SPOT feature tracking measurements. While the displacements derived from feature tracking of TerraSAR-X

amplitude images agreed well with the results from SAR interferometry, the results from

SPOT feature tracking could not be verified from any other source. As such they must be

261 considered as indicative. However, the close resemblance of the profiles shown in Figure

5.10 shows that the flow rate increased approximately constantly along most of the length of the glacier, suggesting the occurrence of uniformly accelerated flow rates over the summer.

This chapter has focused on the measurement of displacement using both interferometry and feature tracking. Using these techniques it was possible to derive and verify down-glacier winter displacements, and to identify areas where the surface of the glacier was rising or falling, as well as one area where the surface elevation of the glacier was continually varying. Using SPOT feature tracking it was also possible to estimate annual displacement, although this could not be independently verified. By using ERS-1 images, glacier flow rates from 1992 could be compared with those of the present day, revealing that there has been comparatively little change over time. The final chapter will look at combining the measurements derived in this chapter with those from the previous chapters in order to achieve a comprehensive description of the spatial and temporal dynamics of Fountain Glacier.

262 Chapter 6: Integrating Data from Different Sources

6.1 Introduction

In the previous chapters, a number of different techniques were used to observe

and measure the different spatial and temporal characteristics of Fountain Glacier, using

both remotely-sensed and in-situ data. While each of these techniques by itself provides a

piece of the puzzle, the full picture only becomes apparent when the information from all sources is integrated. By combining DEMs and orthophotos from different time periods,

along with surface displacements derived from SAR interferometry and feature tracking,

large-scale spatial patterns become apparent. When this information is supplemented by

detailed temporal measurements of surface change made at point targets then a four-

dimensional picture begins to emerge, describing both seasonal and longer-term glacier

dynamics.

In Chapter 2, DEMs were derived using photography from 1958, 1982, 2010, and

2011. While the latter two DEMs covered only the terminus region of the glacier, a

comparison of the four DEMs was able to give an indication of multi-year surface

melting trends occurring between 1958 and 2011, as well as changes in ice thickness at

the terminus. Orthophotos derived from the multi-year source photography were also

used to measure the retreat of the glacier terminus over the last 50 years. Additionally,

by using manual feature tracking from 2010 and 2011 orthophotos, estimates were

obtained for annual down-glacier flow rates in the terminus region.

263 Chapter 3 introduced the concept of making photogrammetric measurements from

a time series of ground-based photographs, obtained at regular intervals from fixed

positions. Measurements obtained over a two month period were used to produce a series

of orthophotos documenting the seasonal decay of the proglacial icing associated with

Fountain Glacier. This phase of the project was designed to develop a simple, low- accuracy application of ground-based photogrammetry, and to provide a base from which higher-accuracy measurement techniques could be developed.

In Chapter 4, ground-based photogrammetric measurements were made to a number of point targets at the glacier terminus. These measurements were used to determine surface motion and surface change over a period of three years. By using a ground-based photogrammetric approach supported by annual GPS measurements, it was possible to observe summer melt and winter recovery patterns in a way which has hitherto not been possible. The temporal frequency of the photogrammetric measurements made it possible to identify the start and end of the summer melt season to a precision of a single day. By comparing the observed melting patterns to temperature records from the Bylot-1 weather station, a strong correlation was noted between the start and end of summer melting and the days when the average daily minimum temperature crossed the freezing point.

In Chapter 5, SAR interferometry and feature tracking were used to provide a wider spatial context. Winter horizontal and vertical displacements were calculated for the lower ten kilometers of the glacier, with horizontal displacements being verified using

264 feature tracking of TerraSAR-X amplitude images. Interferometric analysis of TerraSAR-

X, RADARSAT-2, and ERS-1 scenes revealed that down-glacier displacement was

subject to only minor local variations throughout the winter, which along with the slow winter rates of flow suggests that surface motion at this time of year likely occurs

primarily as a result of ice creep. However amplitude tracking of SPOT panchromatic

images also showed that surface motion increased significantly through the summer

months. Estimates of vertical displacement showed that there were some areas which

consistently showed surface uplift or subsidence over the duration of the study, and also

that there is a highly variable zone between two and four kilometers up glacier from the

terminus. The variability associated with this part of the glacier is believed to be the

surface expression of subglacial hydrological processes.

In order to make sense of the results as a whole, it is necessary to first compare

the data obtained by different methods, to ensure that a consistent picture emerges of the processes affecting Fountain Glacier. Once the results have been validated in this way, then patterns can be identified, and conclusions drawn about current and likely future trends.

6.2 Comparison of results obtained through independent measurements

Many of the results discussed in previous chapters were complementary, and provided information which could not be obtained from other sources. Examples include summer melt patterns, which were uniquely derived from time-lapse photography, and

265 the measurement of vertical displacement using SAR interferometry. Other results were

compared in specific chapters, such as down-glacier flow estimates derived from SAR

interferometry and from SAR amplitude tracking discussed in Chapter 5, or annual

changes in surface elevations obtained from ground-based photogrammetry and GPS

measurements described in Chapter 4.

Some results were derived using different data sources, and were presented in

different chapters. Before any conclusions can be drawn on overall glacier behavior, it is

necessary to ensure that results derived from different sources show a certain level of

agreement. Of particular interest in this context is how the point source measurements

derived for individual targets on the glacier surface agree with the more generalised flow

rates derived from SAR interferometry and manual feature tracking.

6.2.1 Comparison of down-glacier flow estimates

A comparison of results obtained from GPS measurements of targets between

2009 and 2010, and from multi-track SAR interferometry over the winter of 2010, is

shown in Table 6.1. The target positions are shown in Figure 4.3 and Figure 4.4. The

results from the photogrammetric analysis of time-lapse photography are not included, since these were already compared to GPS measurements in Chapter 4 and found to be generally consistent.

266 Table 6.1: Comparison of interferometric and GPS displacements close to the terminus.

InSAR InSAR GPS GPS % InSAR distance direction direction distance distance / Target from winter from winter 2009 - 2009 - GPS 2010 data 2010 data 2010 2010 (m) distance (m) (m)

GT2 3.01 3.33 90.4 53.5° 90.1°

GT4 3.18 3.86 82.4 55.4° 88.2°

GT5 3.12 4.11 75.9 59.5° 96.4°

GT6 3.96 4.57 86.7 80.4° 98.7°

GT7 3.75 5.18 72.4 71.1° 94.3°

GT8 2.53 2.13 118.8 18.9° 68.0°

GT9 2.70 2.36 114.4 27.4° 63.3°

In Chapter 2, displacements for the terminus region were obtained by manually tracking features on 2010 and 2011 orthophotos. In Table 6.2, these displacements are compared with GPS-derived displacements for the same period.

From Table 6.1 and Table 6.2, it can be seen that measured displacements obtained using the three different methods are generally similar. Where accelerated motion occurs during the summer, the overall annual displacement measured by GPS would be expected to be greater than that derived from SAR interferometry, which represents the annual-equivalent displacement based on winter flow rates. This pattern can be seen for the targets which are higher up or closer to the centre of the glacier. GT2,

267 GT4, GT5, GT6, and GT7 show displacements derived from SAR interferometry which are between 70% and 90% of those derived from GPS measurements, whereas the results from manual feature tracking for these targets generally show better agreement with the

GPS measurements. By way of comparison GT8 and GT9, close to the terminus of the glacier, do not show this pattern, and indeed have calculated InSAR displacements which are slightly greater than those derived from GPS measurements. This disparity suggests a seasonal speed up of the glacier in the upper terminus region, with differences between winter flow rates and annual flow rates being between 10% and 30%, whereas flow rates show little variation at the terminus itself.

Table 6.2: Comparison of displacements from GPS and manual feature tracking

Distance from Direction GPS % Feature manual from GPS distance tracking Target feature manual direction distance / tracking 2010 2010 - feature GPS distance 2010 - 2011 - 2011(m) 2011 (m) tracking

GT2 2.65 3.16 83.9 94.0° 92.4°

GT5 3.31 3.15 105.1 95.9° 94.9°

GT6 4.16 4.15 100.2 100.4° 101.3°

GT7 4.16 4.55 91.4 100.4° 93.0°

GT8 2.02 1.82 111.0 43.5° 66.7°

GT9 1.83 2.48 73.8 47.1° 75.1°

268 It can be seen from Table 6.1 and Table 6.2 that the flow directions obtained from

SAR interferometry are typically 30° to 40° more northerly those obtained from GPS measurement and from manual feature tracking. This is likely due to changes in the glacier surface close to the margins since 1982, the year when the photography for the

DEM was obtained. While incorrect values for slope are likely to have only a small effect on the absolute displacement, the combination of incorrectly modeled surface slope and slow flow rates in marginal regions, along with orthorectification errors introduced by changes to glacier terminus region since 1982, could be expected to introduce significant errors in the estimated flow direction. The error in flow direction is once again most apparent at GT8 and GT9, which are very close to the terminus.

A comparison was also made between displacement rasters obtained from manual feature tracking and from SAR interferometry. The result of this comparison can be seen in Figure 6.1, which shows the InSAR-derived annual equivalent flow from the winter of

2010 subtracted from the annual flow rate obtained by manual feature tracking. The points used for the manual feature tracking covered a period of 366 days and are shown in Figure 2.4. In Figure 6.2, the estimated displacements derived from SAR interferometry, manual feature tracking, and SPOT feature tracking are compared along centre-line profile BB'.

269

Figure 6.1: Difference between displacements derived from InSAR and manual feature tracking. The InSAR data was from February / March of 2010, and the points used for manual feature tracking were obtained on July the 1st 2010 and July the 2nd 2011.

Figure 6.2: Comparison of annual displacement along centre-line profile BB'.

270 It can be seen from Figure 6.1 and Figure 6.2 that displacements derived from

manual feature tracking are generally higher than those derived from InSAR and this

difference increases with increasing distance from the terminus. However Figure 6.2

suggests that displacements derived from the two sources remain similar up to about 800

m from the terminus. This would suggest that there is a seasonal component of

displacement, which declines significantly close to the terminus. Figure 6.1 also shows

large differences for parts of the southern terminus, close to point B. These differences

are believed reflect errors in the InSAR-derived displacements, which are a result of significant changes to the glacier surface in this region since 1982.

Figure 6.2 also compares the displacements derived from manual feature tracking with those derived from automated feature tracking of SPOT images. It can be seen that there are significant differences between the two profiles. The displacements derived from the SPOT feature tracking show a great deal of variability. This is to be expected, since feature tracking is considerably less accurate than SAR interferometry (Floricioiu et

al. 2008), and the SPOT pixels tracked were 10 m in size. The displacements derived

from the SPOT images are therefore likely to provide useful information only for the faster-moving parts of the glacier, away from the marginal regions.

6.2.2 Comparison of surface elevation change between 2010 and 2011

Surface elevation changes for points close to the glacier terminus were measured

over a three year period, using both ground-based photogrammetry and GPS. A

comparison of the results obtained by these methods is given in Chapter 4. Generally

271 elevation changes derived using the two methods differed by less than 20 cm, once differences in the measurement period had been accounted for. However the DEMs obtained from the UAV overflight in 2010 and from the 2011 helicopter survey also provided an independent estimate of the change in surface elevation for the terminus region. A comparison of estimated surface elevation change between 2010 and 2011 is shown in Table 6.3. While these results are approximate, it can be seen that with the exception of GT5 and GT9 agreement is generally better than half a metre. The DEMs will tend to smooth out local variations in topography, so some variation would be expected. Also in a number of cases GPS target heights had to be estimated, since the target had collapsed.

Table 6.3: Comparison between GPS observations and DEM differences for targets at the glacier terminus.

GPS elevation DEM elevation % DEM difference 2010 difference 2010 difference / Target - 2011 (m) - 2011 (m) GPS difference

GT2 -1.93 -1.99 103.1

GT5 -1.69 -2.36 139.6

GT6 -1.94 -2.40 123.7

GT7 -1.92 -2.07 107.8

GT8 -2.20 -2.50 113.6

GT9 -1.96 -2.81 143.4

272

6.3 Combining information from multiple sources to provide a description of

glacial processes

While the information collected in the previous chapters falls short of providing a full description of the dynamics of Fountain Glacier, it does provide a strong framework from which many of the main characteristics of the glacier may be inferred. The data gathered allowed estimates to be made of the magnitude and direction of down-glacier flow, including historical down-glacier flow rates from 1992. It also allowed estimates to be made of seasonal and long-term ice melt at the glacier terminus, as well as making it possible to quantify changes in the extents of the glacier over the period since 1958. By using a combination of SAR interferometry and feature tracking it was possible to obtain flow rates for the winter period and also through the year. The difference between these two figures strongly suggests that there is a significant increase in the rate of flow over most of the glacier during the summer. From SAR interferometry it was also possible to investigate how both horizontal and vertical displacement varied over the course of the winter.

The following three sections describe different characteristics of the glacier which the availability of data from multiple different sources helped to reveal. These examples are intended to be illustrative and as such they are not described in detail. However each example could form the basis of a comprehensive research project in its own right.

273 6.3.1 Seasonal flow variations and melt patterns

Seasonal flow variations were believed to exist for Fountain Glacier, but prior to the current study these had not been quantified. The glacier has a number of well developed flow stripes as can be seen in Figure 6.3, and these features tend to be associated with basal sliding (Burgess et al. 2005). A comparison of measurements obtained through a combination of ground-based photogrammetry, SAR interferometry, and feature tracking of TerraSAR-X amplitude images suggested that there was little variation in the speed of glacier flow throughout the winter period. However, further measurements, derived from a combination of ground-based photogrammetry, GPS, manual feature tracking, and automated feature tracking of SPOT images revealed that annual flow rates were significantly higher than annual-equivalent winter flow rates over most of the glacier. From this it can be inferred that there is a period of accelerated flow which occurs during the summer.

The relatively slow winter flow rates and the lack of variation in speed noted above suggest that down-glacier flow occurs predominantly through ice creep during the winter months. The higher flow rates seen over the course of a full year are a consequence of significantly increased summer flow rates, which implies that basal sliding may play a significant role over the summer. Measurements from SPOT feature tracking shown in Figure 5.9 and Figure 5.10 suggest that the speed increase is relatively constant close to the centre-line of the glacier, and after compensating for differences in acquisition dates, it typically represents an additional 6 - 8 ma-1 of down-glacier motion.

The observed pattern is consistent with the hypothesis of down-glacier motion arising

274 predominantly from ice creep in the winter, and from a combination of ice creep and basal sliding in the summer months. Although basal sliding in the winter is not ruled out

and the presence of the icing provides evidence that liquid water is present beneath the

glacier year round, it is likely that the glacier will freeze to its bed in marginal regions.

Lateral stress coupling will therefore act to dampen any sliding component in the winter.

Figure 6.3: 2008 SPOT image of Fountain Glacier showing well-developed flow striping.

SPOT image provided by Geobase ®.

275 If summer flow is assumed to occur only through the months of June, July, and

August then it follows that there must be average speed increase in speed of between

200% and 300% over most of the glacier during this period. For the fastest-moving part

of the glacier, the average winter down-glacier horizontal flow speed measured using

multi-track interferometry was 25 ma-1, with an estimated error of less than 0.5 ma-1 (see

section 5.6.5). For the summer, the average flow speed for the same part of the glacier is

estimated to be approximately 50 ma-1. However the contribution of basal sliding to

down-glacier flow is likely to vary throughout the summer, in response to the supply of

water at the glacier bed. This could potentially cause errors of 10 ma-1 or greater in this

estimate.

From a combination of manual feature tracking, along with measurements made by GPS and ground-based photogrammetry, it is apparent that flow rates also increase in

the summer over the upper-terminus region. This can be inferred from Figure 6.1 and

Figure 6.2. However the speed increase is lower in this region than it is further up the

glacier. Measurements of the lower-terminus region show very little difference between

winter and summer flow rates, with seasonal differences only becoming apparent at

distances greater than 800 m up glacier from the terminus. This provides evidence

supporting the hypothesis that Fountain Glacier is polythermal in nature, with the

terminus consisting of cold ice, frozen to the glacier bed.

Measurements obtained through ground-based photogrammetry also allowed

summer melt patterns to be determined for the glacier terminus region. These showed that

276 summer melting was fairly consistent, with surface melting starting in early June in 2009,

and in mid June in 2010 and 2011. In the years studied melting started slowly, reaching a

maximum in early July. By the start of August, the melt rate generally showed a decline,

with melting stopping completely in early September in all years. The observations also showed a strong correspondence between the onset and the end of the melt season and the average daily minimum temperature recorded at the nearby Bylot-1 weather station.

The average surface elevation change over the terminus region was 2.5 m for the year 2009 – 2010 (measurement year 2), and 2.0 m for the year 2010 – 2011

(measurement year 3). Over the winter of each year, the surface elevations at the measured points showed a recovery of between 0.3 m and 0.5 m. The recovery in surface level was measured over the period between the end of the summer melt season in early

September, through to the start of the following melt season in early / mid June, and is believed to be the result of ice flow into the terminus region. Accelerated summer flow rates will result in more ice flowing into the terminus region over the summer months.

However this trend is masked by summer melting of the glacier surface. In total it is therefore estimated that annual ice flow into the terminus region would be double that measured over the winter months, which would be sufficient to raise the surface elevation by an average of approximately 0.8 m at the points measured if no melting were to have

occurred. If an average change in surface elevation of -2.25 m for measurement year 2

and 3 is assumed, then this can be broken down into an ice loss of 3.05 m through surface

melting, and ice gain of 0.8 m through down-glacier flow. Between 2009 and 2011, ice

277 loss at the terminus through surface melting is therefore estimated to have exceeded ice

gain through down-glacier flow by a ratio of approximately 4:1.

6.3.2 Detection of a possible subglacial water body

The role of subglacial and englacial water transit in the formation of the Fountain

Glacier's associated proglacial icing has been noted by several authors, e.g. (Moorman

2003; Moorman 2005; Wainstein et al. 2008; Wainstein et al. 2010). There are three

marginal lakes adjacent to the glacier, with the largest of these being about 6,500 m up

glacier from the terminus (Marginal Lake 1 in Figure 6.4). This ice-dammed lake is about

2,750 m long by about 500 m wide at its widest point, and forms a link between Fountain

Glacier and the adjacent Akteneaq Glacier. The other two lakes are considerably smaller,

but it has been suggested that the three lakes are linked via a subglacial drainage system.

It was noted in Chapter 5 that the glacier surface showed a great deal of vertical variation in the region between 2,000 m and 4,000 m up glacier from the terminus. The extents of this anomaly during the second half of February 2009 can be clearly seen in

Figure 6.4. It is hypothesised that this vertical anomaly is the surface expression of subglacial hydrological processes, with variations in basal water pressure causing the surface to rise and fall (Whitehead et al. 2010). The similarity of events in this region in

both February 2009 and April 2011 was noted in Chapter 5. The fact that in both cases

the 11-day vertical displacement and the extents of the region of change were similar

suggests that basal water movement though this region may occur in discrete pulses.

278

Figure 6.4: The extents of the vertical anomaly obtained from a TerraSAR_X descending-

pass interferogram derived from scenes acquired on 12 and 23 February, 2009. The line

A, B, C represents the location of the ground-penetrating radar profile acquired in the

summer of 2009 and shown in Figure 6.5. The extents of the anomaly are superimposed

on a SPOT image from August 2008. SPOT image provided by Geobase ®.

It can be seen that the anomaly shown in Figure 6.4 appears to terminate in a

straight line on the eastern or down-glacier side. This bounding line closely matches the line defined by the eastern side of the south spur of the glacier. This suggests that the basal topography may play a significant role in regulating the flow of water in this region, with the eastern side of the south spur possibly continuing under the main glacier in the

279 form of a bedrock ridge. While further work would be required to prove or disprove this hypothesis, it would provide a possible explanation for the presence of the anomaly.

In late June of 2009, a GPR survey was carried out in the region of the anomaly

(Whitehead et al. 2010). The line A, B, C shown in Figure 6.4 was surveyed, using a

Pulse Ekko Pro GPR system. The survey was carried out using 50 MHz antennas in a parallel broadside configuration. The 50 MHz frequency allowed penetration to the base of the glacier, which was approximately 200 m deep in the region of the anomaly. The interpreted GPR profile obtained from the region of the anomaly is shown in Figure 6.5.

Two strong reflections are apparent from the base of the glacier between points A and B, suggesting the presence of an additional layer between the bottom of the glacier and the glacier bed. In view of the variability in surface elevation previously noted for this part of the glacier, this layer was interpreted as potentially being a large body of subglacial water

(Whitehead et al. 2010). After recalibrating to account for the speed of propagation through water, it was determined that this possible water layer was approximately 3 m thick.

280

Figure 6.5: Interpreted GPR profile showing the region of the anomaly. The locations of points A, B, and C, are shown in Figure 6.4.

281 The possible subglacial water layer extended approximately 750 m up glacier.

Unfortunately it was not possible to obtain a cross profile, which would have helped to

determine the full spatial extents of this feature. However if it were assumed to be

circular, then a subglacial lake of this size and depth could potentially hold 1,325,000 m3

of water. If a subglacial lake were to occupy the extents shown in Figure 6.4 then it could

potentially hold 3,500,000 m3 of water, assuming an average depth of 3 m. It is worth

noting that even using the lower volume estimate, this volume of water could potentially

cover the main section of the proglacial icing to a depth of over 4 m, and this reservoir

could therefore provide much of the water supply necessary for the regeneration of the icing over the winter months.

6.3.3 Marginal lake drainage event

In July 2009 the large marginal lake between Fountain Glacier and Akteneaq

Glacier (Marginal Lake 1 in Figure 6.4) lost an estimated 30 to 50 million cubic metres of

water, representing approximately three quarters of its volume. During summer fieldwork

in late June / early July of 2009, the lake had been observed to be full. However a SPOT

satellite image acquired two months later on the 25th of August 2009 showed the lake to

have mostly emptied. While the exact routing of the water from the lake is unknown,

there is evidence that a significant amount of this water may have flowed under the

glacier and emerged in the terminus region. This evidence takes the form of a large

deposit of fresh sediments between 2 and 3 metres deep immediately in front of the

glacier terminus (see Figure 6.6).

282 While the exact timing of the lake drainage event is uncertain, evidence from analysis of the time-lapse photography suggests that a rapid increase in basal water pressure at the terminus occurred in the second half of July 2009. Figure 6.7 shows the change in surface elevation of two points on the glacier terminus for the period from the

12th of July to the 4th of August. The relative elevation of Rock-1 was tracked photogrammetrically over this period from Camera Station 1. This rock was situated on the southern side of the main supraglacial stream. The change in surface elevation at target GT4 over the same time interval is also shown by way of comparison. It can be seen that at both points, the surface shows a significant rise. Between the 17th and the

18th of July, Rock-1 shows a drop in surface elevation of 0.7 m. This is because the rock was observed to slide across the surface at this time. However if this movement is accounted for, it can be seen that the glacier surface at this point rose by approximately

30 cm between the 16th and the 22nd of July. This is completely different from the normal melting-driven elevation loss for July, which is described in Chapter 4. While the effect is not so pronounced at GT4, there is still a noticeable increase in surface elevation, which also peaks on the 22nd of July.

283

Figure 6.6: Fountain Glacier terminus in July 2008 and June 2010. The 2010 image shows a deposit of fresh sediments which were estimated to be 2 – 3 metres deep.

284

Figure 6.7: Observed changes in glacier surface elevation; (a): Change in surface

elevation at GT4, (b): Change in surface elevation at point Rock-1, and (c): Location of points shown.

Further evidence of increased basal water pressure over this period was provided by the presence of a spring approximately 100 m up glacier of point GT8, which is shown in Figure 6.8. This spring was visible between the 15th and the 24th of July on photographs taken by Camera 1. Although photographs from Camera 2 covered the icing, all photos captured by this camera over measurement year two were out of focus. This is

285 unfortunate, as increased water levels on the icing would have provided strong additional evidence as to the timing of this event.

Figure 6.8: Spring visible on northern terminus from 15 – 24 July 2009.

The Marginal Lake 1 remained at very low levels throughout the winter of 2009 -

2010, and water levels only started to recover the following summer. During the winter period, the vertical anomaly discussed in section 6.3.2 showed very little variation compared to the winters preceding and following it (see Figure 5.13 and Figure 5.14).

This suggests that water supplied from this lake could be the source of much of the variation in vertical displacement observed for this region of the glacier surface.

286 6.4 Summary of glacier characteristics

From the evidence assembled from the different sources it is now possible to describe many of the characteristics of Fountain Glacier. The evidence suggests that winter flow arises primarily from ice creep, and that it shows little variation through the eight or nine months of winter. Winter flow rates are very slow at the terminus and increase by approximately 2.5 ma-1 for every 1,000 m up the glacier, until about 7,000 m

from the terminus. At 7,500 m from the terminus, the glacier is constricted by a narrow

valley and reaches its maximum winter flow rate of approximately 25 ma-1. Winter flow

directions are generally down glacier, except close to the edges, where the flow direction

tends to be deflected towards the margins. Flow rates were also determined for the winter

of 1992 and found to be similar to current values.

The measurement of annual flow rates using SPOT imagery suggests that annual

down-glacier flow speeds are typically between 6 ma-1 and 8 ma-1 faster than winter flow

rates. This implies that for most of the glacier, the average speed over the months of June,

July, and August is typically two or three times greater than during the winter. It is

believed that most of the extra motion is due to basal sliding, and this is supported by the

observation that the speed increase is similar in magnitude over the length of the glacier

(see Figure 5.9 and Figure 5.10). For the terminus region, accelerated summer flow could

be seen for points more than 800 m up glacier from the terminus itself. Points closer to

the terminus showed little variation between summer and winter flow rates, providing

evidence that the glacier is polythermal in nature, with the cold ice of the terminus being

frozen to the glacier bed.

287 It can be seen from comparing recent melt rates with-long term patterns that ice loss due to surface melting has increased considerably over the last few years. Although

the three years over which measurements were made is not long enough to provide a

representative sample, current melt rates do appear to be at least double those measured

from 1958 to 1982. Similarly the terminus of the glacier has retreated by around 200 m

and has also thinned by around 50 m since 1958. It is unclear whether the rest of the

glacier has seen a similar loss of ice over the same period, since no contemporary DEM

was available for comparison. From the time-lapse photography and the weather records

from the nearby Bylot-1 weather station it can be seen that the typical melt season runs

from early June to early September.

From the analysis of time-lapse photography it was possible to see the seasonal

melt cycle occurring at a number of points on the glacier surface. It could be seen how

surface melting began slowly in early June, reached maximum intensity in early July, and

gradually tailed off towards the end of August in both years for which a full set of

summer measurements were available. An increase in surface elevation at the terminus

was also apparent over the winter. This is thought to be due to inflow of ice into the

terminus region from higher up the glacier. Increased summer flow rates would imply

that more ice would flow into the terminus region over the summer months. However this

component is masked by surface melting over the summer months. From section 6.3.1 it

can be seen that between 2009 and 2011 ice loss from surface melting is estimated to

have exceeded ice gain due to inflow into the terminus region by a ratio of approximately

288 4:1. Yearly GPS measurements at each of the points were able to verify photogrammetrically-derived changes in surface elevation.

Using SAR interferometry, it was possible to identify vertical displacement of the glacier surface at different times (see Figure 5.13 and Figure 5.14). From this it could be seen that the glacier surface elevation shows a rising trend 6,500 m up from the terminus, with corresponding regions of surface lowering occurring at 6,000 m and 7,500 m up from the terminus. Since this effect was observed on all interferograms, it is likely that that this represents a long-term trend. The regions where these trends are occurring are where the glacier emerges from a narrow valley constriction and slows down significantly.

The vertical displacement measurements obtained by SAR interferometry also revealed an area where vertical surface displacement was highly variable. It is believed that the glacier surface variation in this region is due to the influence of water at the base of the glacier, and this may possibly be a key part of the hydrological system underlying the glacier.

6.5 Summary of techniques used

In this section the different measurement techniques used throughout this thesis are summarised in terms of their advantages and disadvantages. The different techniques used are listed below

289 Aerial photogrammetry:

• Good for establishing long-term changes in glacier extents and ice thickness

through the generation of orthophotos and DEMs.

• UAV photography can be used to measure short-term surface changes.

• Dependent on the availability of aerial photography.

Ground-based photogrammetry:

• Allows high accuracy, high temporal frequency measurements to be made for

specific points on the glacier surface.

• If cameras are oriented in a parallel configuration, DEMs and orthophotos can be

produced for any date for which photography is available.

• Convergent photography may preclude the application of automated measurement

techniques.

• Covers limited areas.

SAR interferometry:

• Allows highly-accurate estimates of surface motion over wide areas.

• If a combination of interferograms with different imaging geometries is available

then it may be possible to extract the full 3D motion field for the glacier surface.

Vertical motion can thus be measured.

• Dependent on phase unwrapping, which can potentially introduce significant

errors in areas of high shear if not accounted for.

290 • Projection of down-glacier motion may require the assumption of surface-parallel

flow.

Automated feature tracking:

• Can give reliable estimates of XY motion of the glacier surface over a wide area

from both optical and radar imagery, irrespective of the look direction and

without the need for phase unwrapping.

• Does not require the assumption of surface-parallel flow.

• Can be used at all times of year, since decorrelation is not an issue.

• Comparatively low accuracy may lead to poor results for slow-moving glaciers.

• Cannot provide the vertical component of flow.

Manual feature tracking:

• Can provide estimates of XY surface motion in conditions where automated

techniques give poor results.

• Allows tracking over longer time periods than is possible using automated feature

tracking.

• Labour intensive.

GPS measurement:

• Gives accurate and reliable measurements of 3D point positions at the time of

measurement.

• Can be used to check measurements made using other techniques.

291 • Measurements can only be made during field visits.

6.6 Summary of new knowledge obtained on glacial processes

The work carried out in order to produce this thesis provided new knowledge on many of the processes affecting Fountain Glacier which is summarised below:

• Long-term thinning rates were established for the glacier, from 1958 until the

present day. These show that surface melting has increased considerably in recent

years.

• The retreat of the terminus was measured over the period from 1958 to the present

day.

• It was established that the down-glacier flow rates for Fountain Glacier do not

vary significantly over the winter period.

• From feature tracking it was inferred that down-glacier flow rates in the summer

are between two and three times faster than winter flow rates.

• Detailed measurements were made of the glacier surface elevation change

throughout the ablation season. This allowed ice loss during successive ablation

seasons to be compared. Winter increases in surface levels in the terminus region

allowed estimates to be made of ice loss vs. inflow of ice from further up glacier.

• Variations in vertical surface motion made it possible to detect a body of

subglacial water which is believed to be a key part of the hydrology of Fountain

Glacier system.

292 6.7 Suggestions for further work

Each of the different techniques used was able to contribute to the overall picture.

However to fully characterise the seasonal and long-term dynamics of the glacier, several important pieces of information are still required. Incomplete coverage of both aerial photography and radar images meant that no measurements were obtained for Fountain

Glacier's accumulation zone in this study. Without information from this region it is not possible to state definitively that the mass-balance of the glacier is changing, although measurements from the lower two thirds of the glacier certainly support this hypothesis.

A current DEM covering the whole glacier would be a useful addition to the project, since it would make it possible to see whether the changes in ice thickness seen at the terminus are reflected over the glacier as a whole. With the launch of the TanDEM-

X satellite operating in parallel with TerraSAR-X, it is now possible to generate high accuracy DEMs on demand. This option was not available during the data collection phase of the project, so recent surface elevations were only available from the UAV and helicopter surveys of the terminus carried out in 2010 and 2011.

While winter flow rates appear to change little, it is likely that summer flow rates will vary in response to the amount of water at the base of the glacier. To monitor this, it would be desirable to have a series of high-resolution optical or radar satellite images, obtained every week or two throughout the summer. Estimates of summer flow rates could then be obtained using feature tracking. The frequent coverage would also allow variations in speed to be measured throughout the summer period. In addition to the

293 cross-correlation methods used by programs such as Cosi-Corr, another approach would be to use direct surface matching techniques, whereby individual objects are identified by the software and tracked between images. Such techniques could prove to be more successful at tracking surface motion over longer time periods.

One of the most intriguing findings from the SAR interferometry displacement measurements was the presence of an area, between two and four kilometers up glacier from the terminus, where the glacier surface showed rapid changes in vertical displacement. This variation is likely to be the surface expression of rapidly changing basal water pressures. Ideally this part of the glacier should be monitored using time- lapse photographs from two overlapping cameras mounted on the ridge to the northeast, with about ten targets covering the area of interest. Photogrammetric analysis could then be used to provide information on the patterns of both seasonal and longer-term surface elevation change for this part of the glacier. This measurement campaign could be supported by placing a pressure sensor in the main marginal lake between Fountain

Glacier and Akteneaq Glacier to monitor depth variations of this lake. This would help to establish whether basal water pressure variations in the region of the anomaly are directly linked to the supply of water from this lake.

To complement the time-lapse photography, GPR surveys of the area surrounding the anomaly would provide detail on the basal topography, including the possible presence of the bedrock ridge hypothesised in section 6.3.2. A dense GPR network covering the lower and middle glacier would also be likely to provide valuable clues to

294 the routing of subglacial and englacial drainage networks, as well as allowing the basal

DEM described in Chapter 2 to be extended up glacier.

6.8 Meeting overall Objectives

The overall project objectives were listed in Chapter 1, section 1.3. In this section each objective is described, along with a brief description of how it was met. The objectives are listed below.

Establish long-term patterns of surface change for Fountain Glacier using DEMs derived from all available sources of aerial photography:

• DEMs and orthophotos were generated using photography from 1958, 1982,

2010, and 2011. The difference between the 1958 and 1982 DEMs was used to

measure average annual surface change over this period. In the terminus region,

the difference between the 1982 DEM and the 2010 DEM was used to measure

surface change over the period from 1982 to 2010.

Establish recent patterns of surface change for the terminus region:

• The orthophotos and DEMs generated from the 2010 and 2011 photography were

used to measure the surface change, as well as changes to the glacial extents in

the terminus region.

295 Use ground-based photogrammetry to monitor the seasonal decay of Fountain

Glacier’s proglacial icing:

• This was carried out over the summer of 2008. A series of orthophotos was

generated, which allowed the changing ice extents to be documented over the

duration of this project.

Use ground-based photogrammetry and GPS measurements to measure changes

in the thickness of the glacier close to the terminus, and to measure seasonal

patterns of surface elevation change:

• Three years worth of photogrammetric measurements were made to targets on the

glacier surface. From these measurements it was possible to produce detailed

temporal profiles showing changes to the surface elevation throughout each year

of the study. These measurements were confirmed using annual GPS surveys.

Use ground-based photogrammetry and GPS to measure the horizontal motion

of targets located in the terminus region of the glacier:

• Horizontal target positions were calculated for periods where photographs were

available from two cameras. These were found to be much more accurate in the

initial year of the study, when using a long baseline.

Determine the full 3D winter displacement field for the glacier using a

combination of SAR interferometry and feature tracking:

296 • By using a combination of interferograms produced from right looking and left

looking RADARSAR-2 and TerraSAR-X scenes it was possible to derive the full

X, Y, and Z components of motion for the lower two thirds of the glacier, over

the period between February and March 2010. The estimated down-glacier XY

speed was confirmed using feature tracking of TerraSAR-X images.

Estimate annual displacements for the glacier using feature tracking:

• Automated feature tracking was carried out using SPOT satellite imagery from

August 2008 and August 2009. Although the results were fairly noisy, due to

changes to the glacier surface, it was still possible to estimate the overall surface

displacement between the two images. This made it possible to estimate the

increase in flow rates over the summer,

Determine areas where the glacier surface is undergoing uplift or subsidence

using SAR interferometry:

• Because the full 3D motion field was already known, it was possible to extract

the residual vertical displacement from each interferogram. This relies on the

assumption that flow rates remained the same throughout the winter.

6.9 Conclusion

While no one set of information can fully characterise the dynamics of a complex system such as Fountain Glacier, the use of both remotely-sensed and in-situ sources of

297 data together with the appropriate analysis tools provides a great deal of information

which may be used to better understand the underlying processes. Many of the same

techniques may be applied to other arctic glaciers, with a view to obtaining a broader,

regional perspective of change in the arctic. While remote-sensing techniques have

typically been applied to larger glaciers, oblique photogrammetry as described in the

preceding chapters is more suited to providing detailed observations of small areas. The

approach described in this thesis is therefore appropriate to the study of small, slow-

flowing arctic glaciers.

The use of time-lapse photography for photogrammetric applications is a

comparatively new application of an old technique. The current study is believed to be

the first study to use photogrammetric analysis to measure changes in the position of

permanent targets located on the glacier surface. This posed a number of challenges,

particularly with target design, and also in ensuring that targets stayed fixed in position

on the glacier surface. While the solution adopted was able to provide results in difficult

circumstances, design modifications to the targets could ensure greater stability, ensuring

more reliable results in the future.

With the increasing availability of high-resolution radar imagery, feature tracking approaches have become increasingly popular for measuring glacier flow. However as

Chapter 5 shows, SAR interferometry remains the technique of choice for measuring the

motion of slow-flowing arctic glaciers. The analysis was also helped considerably by the

inclusion of a left-looking interferogram. Left-looking radar images are still a rarity in the

298 arctic, due to the time demands imposed by satellite tasking. However with multi-satellite systems such as COSMO-SkyMed, it may be that future left-looking acquisitions of arctic regions will become more common.

The use of UAVs is a new development which is likely to have a considerable impact on glaciological applications in the future. The availability of on-demand, high- resolution aerial photography makes it possible to produce detailed orthophotos and

DEMs as required, at very little cost. Future applications may involve the use of thermal and hyperspectral sensors, and miniaturised LiDAR systems, in order to provide additional levels of information which are currently unavailable to scientists. Advances in photogrammetric processing software now make producing DEMs and orthophotos a comparatively simple process, and naturally complement the development of UAV technology.

The picture which emerges of Fountain Glacier is one of continuous change.

Although the glacier has thus far shown little sign of retreat when compared with the neighbouring Stagnation Glacier, the change in ice thickness at the glacier terminus since

1958 suggests that within a few decades the glacier will look very different. This is a scenario which is likely to play out across the entire Bylot Island Icefield and further afield, as the glaciers of the Canadian Arctic continue to shrink. It is only by having good baseline data that accurate estimates of ice loss may be made. While the glaciers of arctic

Canada occupy a comparatively small area relative to the neighbouring Greenland

299 Icesheet, their significance in regional terms is that they provide an early indication of many of the changes likely to be seen in the future.

300

References

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