Arctic ice cap velocity variations revealed using ERS SAR interferometry

Beverley Victoria Unwin

A thesis submitted to the University of London in fulfilment of the requirements for the degree of PhD

Mullard Space Science Laboratory Department of Space and Climate Physics University College London

1998 ProQuest Number: 10013365

All rights reserved

INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.

In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest.

ProQuest 10013365

Published by ProQuest LLC(2016). Copyright of the Dissertation is held by the Author.

All rights reserved. This work is protected against unauthorized copying under Title 17, Code. Microform Edition © ProQuest LLC.

ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Abstract

This thesis will examine the velocity structure of Austfonna, a large ice cap in the Svalbard archipelago. The remoteness of its location had previously hindered detailed observation by traditional methods, but indirect evidence suggested that it had the potential to be dynamically interesting. A recently developed remote sensing technique, SAR interferometry (inSAR), has allowed us to obtain the most detailed map of Austfonna's topography to date, plus unprecedented synoptic measurements of its velocity field. A four year time series of data acquired by the European Remote Sensing satellites ERS-1 and ERS-2 has been used to delineate active and inactive areas of the ice cap, which suggest that past ideas about Austfonna's thermal structure may need to be re-examined. It has also revealed large temporal velocity variations in one of its major drainage basins. These are difficult to classify because intermittent sampling has prevented us from determining their temporal wavelength, and also because globally the database of observed glacier velocity variations is so sparse that the range of possible variable flow scenarios is unknown. The work here demonstrates the huge potential for inSAR in helping to resolve such issues, and in providing an invaluable resource for scientists monitoring the stability of the world's ice fields. Acknowledgements

I would like to thank my supervisor Professor Duncan Wingham for his guidance, particularly over the last few months during the writing of this thesis. In addition I'd like to acknowledge the benefits of some useful discussions with Anne-Marie Nuttall and Professor Julian Dowdeswell at Aberystwyth University's Centre for Glaciology. Julian was also instrumental in helping me to obtain external data-sets with which to validate my results. Ian Joughin, at JPL, probably saved me many months' work by allowing me to use his phase-unwrapping software, and I am very grateful for this. I would also like to thank colleagues at MSSL, past and present, who collectively have been a rich source of advice, support and information. I'd particularly like to acknowledge the excellent computer support from which I have benefited throughout my time here. On a personal note, I thank my family, particularly my parents, and my friends, for their support and encouragement. I'm very grateful to my cousin Carol, and her partner Andrew, who welcomed me into their lovely, comfortable home 18 months ago, and are remarkably good humoured about the fact that I'm still there. Finally, I give very special thanks to my boyfriend John whose support has been invaluable and whose talent for making me laugh has taken the edge off some difficult days. Contents

List of figures

List of tables

List of acronyms

List of symbols

Chapter 1 : Introduction 12

LI Background of study 12 1.2 The glaciology of Austfonna 14 1.3 Questions addressed by this thesis 19 1.4 The evolution and glaciological application of InSAR 20 1.5 Structure of thesis 22

Chapter 2 : Principles of the interferometric technique 23

2.1 Basic geometry for topographic estimation 23 2.2 Determination of range-difference 24

2.3 Interferometric imaging of a moving target 25 2.3.1 Isolating the topographic component of the range-difference 27 2.3.2 Isolating the velocity component of the range-difference 31

2.4 Determination of three dimensional target velocity 32

Chapter 3 : Methodology 35

3.1 Data origin 35 3.2 Registration and formation of single-pair interferograms 36 3.3 Determination of ice cap topography 42 3.4 Determination of line-of-sight velocity component v^. 45

3.5 Determination of the three-dimensional velocity vector 47 3.5.1 Determination of v by combining ascending and descending data 47 3.5.2 Determination of v by assuming a flow direction 49

Chapter 4 : Error Model 50

4.1 Phase error 50 4.1.1 Phase errors due to changes in the target's scattering properties 50 4.1.2 Phase errors due to travel-time anomdies 53

4.2 Errors in the computation of target height 55 4.2.1 Relationship between height error and phase error 55 4.2.2 Errors introduced during the processing procedure 56 4.2.3 Height errors due to errors in knowledge of the imaging geometry 57 4.2.4 The effect of spatially variable surface penetration 61

4.3 Errors in the computation of line-of-sight velocity 63 4.3.1 Sensitivity to phase error 63 4.3.2 Sensitivity to height and baseline error 63

4.4 Errors in the computation of the 3D velocity vector 67 4.4.1 Validity of surface parallel flow assumption 67 4.4.2 Problems with the "method b" velocity determination 67

Chapter 5 ; Verification of results 69

5.1 Interferometrically derived DEMs of Austfonna 69 5.1.1 Comparison of the 1992 and 1994 results 69 5.1.2 Comparison of the interferometric DEMs with an external data set 71 5.1.3 The accuracy of the 1994 DEM 72

5.2 Line-of-sight velocity field 73 5.2.1 Accuracy and repeatability of ascending line-of-sight velocity results 73 5.2.2 Accuracy of the descending line-of-sight velocity results 81 5.2.3 Temporà line-of-sight velocity variations 81

5.3 Ice velocity vector v 83 5.3.1 Results obtained by combining ascending and descending data 83 5.3.2 Results obtained by assuming a flow direction 87

Chapter 6 : Discussion 91

6 .1 Summary of results 91 6.2 Discussion of Austfonna's velocity structure 94 6.3 Discussion of the observed velocity variations 99 6.4 Some comments on Austfonna's mass balance 102

Chapter 7 : Conclusions 104

References 110

Appendix 1 : Justification of use of a spherical coordinate svstem 116

Appendix 2 : Baseline constraint using tie-points 119 List of figures

1.1 The Svalbard archipelago 15 1.2 Austfonna's major drainage basins 16 1.3 Ice surface on Austfonna 17 1.4 Austfonna's subglacial bedrock 18 1.5 Austfonna's ice thickness 18 1.6 The pattern of driving stresses on Austfonna 19 2.1 Interferometric imaging geometry for a stationary target 23 2.2 Interferometric imaging geometry for a moving target 26 2.3 Baseline components 27 2.4 Geometry for topographic phase isolation 28 2.5 Geometry of the differential system 30 2.6 The measured velocity component 32 2.7 Components of ice surface velocity 33 2.8 Relationship between two look geometries 33 3.1 ERS SAR imaging geometry 35 3.2 ERS SAR frames used in this research 36 3.3 Amplitude component of Austfonna SAR image 37 3.4 Wrapped, flattened phase-difference image 40 3.5 Correlation images for each interferometric pair 41 3.6 Topographic phase-difference images 44 3.7 Phase-difference images showing only motion effects 47 3.8 Descending SAR imagery 48 4.1 Relationship between phase error and correlation 51 4.2 Phase scatter error for image pair acquired 13th/16th February 1992 52 4.3 Overlapping ascending/descending correlation images 53 4.4 Height error due to phase scatter error 56 4.5 Predicted height error per centimetre of baseline error 58 4.6 Height error that was obtained from experiment 3 61 4.7 Line-of-sight velocity error that is due to phase scatter error 64 4.8 Error in line-of-sight velocity that arises due to topographic error 65 4.9 Predicted line-of-sight velocity error per centimetre of baseline error 67 4.10 Percentage error introduced by "method b" velocity determination 68 5.1 Height difference between the 1992 and 1994 interferometric DEMs 70 5.2 Correlation related height errors across the CD profile 70 5.3 Details of NP-SPRI radio echo sounding survey 71 5.4 Difference between interferometric DEMs and RES heights 72 5.5 Line-of-sight velocity field for each image pair 74 5 .6 Line-of-sight velocity along the KL profile 7 5 5.7 Difference between each line-of-sight velocity result and a reference 7 6 5 .8 Profiles across the velocity-difference results of Figure 5.7 77 5.9 Velocity difference produced using a deliberately mal-registered DEM 78 5.10 The effect of using the 1992 DEM in computing the velocity results 7 9 5.11 Descending line-of-sight velocity 80 5.12 Phase-difference images for three prominent drainage basins 82 5.13 Line-of-sight velocity profiles for three prominent drainage basins 83 5.14 Velocity field obtained by combining ascending/descending data 84 5.15 Flow azimuth of "method a" velocity field 85 5.16 Position of surveyed velocity profiles 86 5.17 Comparison between interferometric and surveyed velocities 87 5.18 Flow direction taken as direction of maximum slope 88 5.19 Velocity field obtained by assuming a flow direction 89 5.20 Velocity conversion factor 89 5.21 Difference between velocity results derived using different methods 90 5.22 Difference between velocity results along the IJ profile 90 6.1 Digital elevation model of Austfonna 92 6.2 Austfonna's interferometrically derived velocity component 93 6.3 Time series of velocity profiles for Basin 3 94 6.4 Proposed thermal model of Austfonna 94 6.5 Summary of measured temperatures within Austfonna 95 6 .6 Preliminary interferometric results for Vestfonna 98 6.7 Preliminary interferometric results for Academy Nauk 98 6.8 Preliminary interferometric results for Franz Josef Land 99 6.9 Landsat images of the Basin 3 area 100 6.10 Estimated mass lost via iceberg calving along Austfonna's margin 103 7.1 ERS SAR coverage of the Svalbard archipelago 108 A1.1 Relationship between spherical and elhpsoidal coordinate systems 116 A 1.2 Plot of coordinate-system dependent height error 118 List of tables

2.1 Typical values for ERS interferometric parameters 24 3.1 Interferometric pairs used in this research 38 3.2 Scenes selected for differential processing 42 3.3 Details of descending Austfonna images 48 4.1 Results of simulation experiments 59 4.2 Line-of-sight velocity error per metre of topographic error 66

List of acronyms

CEOS Committee for Observing Satellites DEM Digital elevation model DPAF German processing and archiving facility ERS-1/2 European Remote Sensing satelhtes ESA European Space Agency inSAR Interferometric synthetic aperture radar IPCC Intergovernmental Panel on Climate Change JPL Jet Propulsion Laboratory NASA National Aeronautics and Space Administration NP Norsk Polarinstitutt PDF Probability density function RES Radio echo sounding SAR Synthetic aperture radar s.d. Standard deviation SEASAT US-SAR satellite (flown 1978) SLC Single-look complex SPRI Scott Polar Research Institute UD Travelhng ionospheric disturbance List of symbols

A ,, A 2, A 3 Amplitudes of radar echoes received from T at Si, Si and S 3. a When appended as a subscript to velocity parameters, indicates that they were calculated using method a) in section 2.4. «12, «23 Sensitivity of i 2 and ^ 3 to changes in target height. See equation (4.5).

B i 2 Baseline distance between S] and S 2. See Figure 2.1. B 23 Baseline distance between S 2 and S 3. See Figure 2.4.

B„i2, Bp^2 Components of B 12 that are respectively normal and parallel to look direction r^. See Figure 2.3.

B„23’ ^p2 3 Components of B^i that are respectively normal and parallel to look direction ^ 2. 5i23, ^ „ ,23> ^pi23 Differential baseline parameters. See equation (2.21). ^«*123» ^p*i23 Values of B^^^^ and ^^^23 scene centre. See equation (A2.1). b When appended to velocity parameters, indicates that they were calculated using method b) in section 2.4. C 12 Correlation between Pi and P 2. See equation (3.6). e j Subscripts used in Chapter A \e= 1 ,2 ;/= 2,3. F Denotes "flattening" when appended as a subscript to interferogram, phase-difference and range-difference parameters, e.g. see equation 3.4. g I Ground-range distance between the point on the ref. sphere surface below satellite Si and the target T. i Number of pixels in a single-look complex SAR image.

/j 2, 1 2 3 Complex interferograms formed as in equations (2.5) and (2.15). j Number of pixels in a multilooked complex SAR image. K See equation (2.37). k Wavenumber of the SAR signal. Ly y dimension of SAR image. See equation (A2.1). rUy Multilook averaging parameters. See equation 3.1. » i2, «123, «V Unwrapping integers. See equations (2.6), (2.27) and (2.30). «C12’ ^ci23' Minimum values of «, 2, «123, «v Hl Number of looks. See section 4.1.1. o When appended as a subscript to baseline parameters, indicates that they were calculated using orbit data. O Centre of reference sphere. See Figure 2.1. P ], P 2, P 3 Complex radar signals received from T at Si, S 2 and S 3.

^ 5LCi» BsLC2 y Single-look complex radar signals received at Si, S 2 and S 3. p Number of pixels in regularly gridded SAR imagery. (2i23 See equation (2.17). 0 ti23 Complex differential interferogram. See equation (2.26).

Ti, V2 , Range distance between target T and satellites Sj, S 2 and S3. u When appended as a subscript to phase-difference parameters, indicates that they have been "unwrapped", e.g. see equation (3.13). R] 2 Complex displacement interferogram. See equation (2.29). R e Radius of reference sphere. See Figure 2.1. Ri Altitude of satellite Si above reference sphere centre O. See Figure 2 . 1. Si, S2, S3 Position of satellite at times ti, (ti+At) and {ti+2At). See Figure 2.4. ti Time of first observation of the target T. T Resolution cell within SAR image. See Figure 2.1. V Three dimensional velocity vector at T. See figure 2.7. Component of v that is in the satellite's look direction. See Figure

2 . 6 . v^, Vy, Components of v in the jc,y,z directions. See Figure 2.7. Vf, Component of v in the x-y plane. See Figure 2.7. x,y,z Cartesian coordinate system, defined in Section 2.4. x ',y ',z Cartesian coordinate system rotated in jc-y plane with respect to x,y,z. See Figure 2.8. y* y coordinate at scene centre. See equation (A2.1). Zt Height of target T above reference sphere. See Figure 2.1. «1 Local incidence angle at T with respect to Si. See Figure 2.6. j3 Local surface slope at T. See Figure 2.7. Ab See equation (2.25). See equation (3.2). Af.,23, ^/?i23 See equation (3.10). A7-23 Topography dependent range-differences. See equation (2.3). At’j23 Topography dependent range-difference in differential system. See equation (2.23). Av Velocity dependent range-difference. See equation (2.7). 4B„,23, Errors in and ARi Error in Ri. Ari Error in n. At Temporal baseline. Time gap between observations of the target T. AVrc Error in Vr that is caused by Azt- See equation (4.16). AVrz Error in that is caused by A0^^. See equation (4.15). AVrB Error in that is caused by AB„^^ and ABp^^. See equation (4.17). AzBn Height error that is caused by See equation (4.13).

10 Azr Height error that is caused by AR^. See equation (4.11). Azr Height error that is caused by Avi. See equation (4.12). Azt Total height error. Azbp Height error that is caused by See equation (4.14). Az<^ Height error that is caused by A0^^ and A0^y See equation (4.7).

Az^s Height error that is caused by A 0 ^i2 A 0 s2y See equation (4.8).

A0^^, A0^^ Total errors in 0 i2 and 023. A0(^^, A0f^^ Errors in (Pi 2 and 023 due to travel time uncertainties. See section 4.1.

A0s^^, A 0 S2 J Errors in 0^ and 023 due to temporal changes in scattering properties. See section 4.1. ^^pi23 See equation (A2.1). e,2 Angle between baseline B 12 and the local horizontal.

£23 Angle between baseline B 23 and the local horizontal. 0; Phase of scattered radar signal at T. 012 Phase-difference between radar returns at Si and S 2. 023 Phase-difference between radar returns at S 2 and S 3. 0123 See equation (2.18).

0 wi2 ^ 0^123 Wrapped version of 012 and 0123, obtained as in equations (2.6) and (2.27). 0 ^ See equation (2.30). 7 Azimuth of velocity vector. See Figure 2.7. 77 Angle between coordinate systems x,y,z and x\y\z. See Figure 2 . 8 .

01, 02, 03 Look-angles between local vertical and look directions ri, V2 and 7-3. See Figure 2.1. 0cp 0 C2» 0C3 Look-angles at scene centre. See Figure 2.3.

0 ^1, 0^2’ ^d3 Difference between look-angle at T and look-angle at scene centre. See Figure 2.3. As for 0jj but for the special case of Zt = 0.

Ç12 Angle between n and ^ 2. See Figure 2.2. ' Denotes geometry of descending SAR imagery.

11 1. Introduction

1.1 Background of study In 1995, the Intergovernmental Panel on Climate Change (IPCC) reported that global mean sea level has risen by 10 - 25 cm over the last 100 years, and that this is likely to be related to a corresponding increase in global temperature (Warrick et al., 1995). A significant proportion (c2 - 5cm) of this sea level rise was attributed to enhanced melting in glaciated regions, though these figures remain a major source of uncertainty. The two polar ice sheets, and , together account for 99% of the world's ice and are hence expected to be the major contributors to the observed effects. However the input of smaller ice caps and glaciers is not thought to be insignificant because their response to climate change is potentially much more rapid than that of the ice sheets (Warrick et al., 1995). A net loss of material from a particular ice body to the imphes that it has a negative mass-balance, where mass-balance is defined as mass input minus output (Paterson, 1994). Mass is accumulated mainly via the conversion of precipitated snow to ice and the refreezing of surface meltwater. It is lost through melting and, in marine- terminated ice masses, by iceberg calving. Calving is acknowledged to be the dominant form of ablation from the major ice sheets (Warrick et al., 1995), yet its contribution is not well quantified. Isolated measurements of calving rates have been obtained via the tracking of icebergs in satellite imagery (e.g. Losev, 1973), but are made difficult by inadequate data coverage and uncertainties in assessing the lifetime of bergs. Most iceberg calving occurs at the margins of ice streams, which are areas of quasi-continuous fast flow that drain the ice sheets of huge volumes of material. They occupy just 13% of the Antarctic coastline, yet their enhanced flow regimes ensure that they are responsible for up to 90% of ice drainage from the sheet's interior (Morgan et al., 1982). The flux through Greenland's 20 ice streams is similarly a major factor in controlling that region's mass balance (Bauer, 1961). Calving rate estimates can be obtained via measurements of velocity at the margins of these streams. Ice velocity has traditionally been measured via the repeated surveying of ground-stakes, but the relative inaccessibility of glaciated regions, and the huge geographical scales of the ice sheets have resulted in logistical and financial restrictions on data collection, and hence a sparcity of results. There have recently been great advances in technologies that allow the remote monitoring of the world's ice fields from space (Bindschadler, 1998). Synthetic aperture radar interferometry (inSAR) is one such technique, which facilitates measurement of ice velocity on regional scales. Results are averaged over just a few days, have a resolution of a few tens of metres, and an accuracy of a few metres per

12 year. Though various operational and processing issues are still to be resolved (Chapter 7), the technique's potential for measuring ice stream flow rates, and hence calving rates, is clear, and will be demonstrated in this thesis. Though measurements of current ablation rates are important, it is also desirable to know how these components are likely to change in the future. Variations in glacier mass-balance and/or velocity result in changes in area and surface profile (Paterson, 1994), and hence potentially produce feedback loops. Models of long term changes in ice bodies with respect to climate therefore require the inclusion of flow processes (Warrick et al, 1995). A physical relationship between calving rates, glacier geometry, ice flow and climate has not yet been found (Reeh, 1994), and this is largely because the mechanisms that control ice stream flow are poorly known. Though theoretical models (e.g. MacAyeal, 1989; Echelmeyer et al., 1994) have helped to improve our understanding, their validation is hampered by the lack of observational data. This is clearly another area that will benefit from the acquisition of high resolution regional velocity measurements by SAR interferometry. Climate-induced changes in the dynamics of the major ice sheets are expected to occur on timescales of centuries (Warrick et al, 1995). Smaller ice caps and glaciers would be expected to respond much more rapidly and hence potentially provide a laboratory for the study of such phenomena. The most dramatic form of glacier instability is known as a "surge". Surges are temporary fast flow events that occur within a small, though unknown, proportion of the 's valley glaciers and ice cap drainage basins (Meier and Post, 1969). These short bursts of activity occur on a quasi-periodic basis, between which a glacier will lie quiescent, growing steeper and accumulating mass in an upper "reservoir" area. The surge itself will last no more than a few years, compared to a quiescent period of decades. Large volumes of ice will be transported from the reservoir area to a "receiving" area down-glacier. After the surge the glacier's profile will have lowered significantly and its surface will be highly crevassed. Surge-type behaviour is not specific to a particular size of glacier, or a distinctive thermal regime, and both hard- and soft-bedded glaciers can be affected. There is no clear correlation between surge activity and climatic change, but as only a handful of surge-type glaciers have been systematically monitored it has not been possible to establish what the causal mechanism might be (Raymond, 1987). It is generally agreed that disruption of the normal subglacial drainage system is a common factor (Paterson, 1994). While glaciers and ice cap drainage basins are often categorised as either "normal" (exhibiting steady flow) or "surge-type", some authors have suggested that surging is just an extreme end member in an entire spectrum of velocity variations (e.g. Meier and Post, 1969), and others extend this spectrum to include stream-flow,

13 likening it to a state of continuous surge (Weertman, 1964). Temperate valley glaciers, which are at their melting point throughout (Paterson, 1994), allow surface meltwater to penetrate to the glacier bed, and have therefore demonstrated significant temperature related velocity variations on daily or seasonal timescales (e.g. Hodge, 1974). However, observations of velocity variations within non-temperate ice bodies, which more closely resemble the major ice streams, are rare (e.g. Andreason, 1985), with the exception of the very dramatic surge-type behaviour described above. It is possible that this simply reflects the lack of velocity variations generally, with the remoteness of most glaciated areas ensuring that only the most dramatic instabilities tend to be observed. If so, then inSAR contributions to the database of velocity variations should help to identify the extent to which a continuum of variable flow behaviour is a reality. This thesis will use SAR interferometry to investigate the velocity regime of Austfonna, one of the largest ice caps outside of Greenland and Antarctica. It is located on the of Nordaustlandet, within the Svalbard archipelago (Figure 1.1). The region was chosen because it is thought to be dynamically diverse, and susceptible to surge activity, and also because previous work has yielded a satisfactory amount of ground-control data with which to validate the interferometric results. We will employ a four year time series of data from the European Remote Sensing satellites ERS-1 and ERS-2 in examining spatial and temporal aspects of Austfonna's velocity field. Specific questions to be addressed are outlined in Section 1.3, but the broad aim is to demonstrate the valuable contribution that can be made by interferometry in addressing some of the glaciological issues outlined above.

1.2 The glaciology of Austfonna Austfonna covers an area of 8100 km^. Its main , Austdomen, is at 790m above sea level, and corresponds to a maximum ice thickness of around 580m (Dowdeswell et al., 1986). A subsidiary summit, Sprdomen, reaches 680m above sea level. The south-eastern margin of the cap terminates at ice cliffs of height 20 - 30m, which calve into marine waters about 80 - 100m deep (Dowdeswell and Drewry, 1989). To the north-west the ice cap terminates at bedrock. Austfonna's local climate is poorly documented because Svalbard's four weather stations are confined to low lying regions on the western coast of Spitsbergen. These areas record relatively mild temperatures, due to the influence of the West Spitsbergen Current, a branch of the North Atlantic Drift which flows north along Spitsbergen's west coast (Hisdal, 1985). Mean annual temperature is - 6°C, with average July temperatures being about 5°C, and those for January being about -15°C (Hagen et al., 1993). The limited number of temperature measurements recorded by expeditions to central and eastern parts of the archipelago have been used to derive an

14 estimated lapse rate of 0.6 - 1.0°C per 100km from the Western coast. Major fluctuations in temperature have been observed to occur over short periods, particularly in winter (Hisdal, 1985). Increases of 20 - 25°C over 2 -3 days are not uncommon, though as these are related to cyclonic systems originating in the south-west, their effect on temperatures in the region of Austfonna is unknown. Precipitation may fall as rain or snow in any season (Hisdal, 1985). The long term mean on the west Spitsbergen coast is about 400 mm/yr, and in central lowland areas rates are approximately half of this. Precipitation is higher in the glaciated mountainous regions, due to orographic effects, but is thought to seldom exceed 2 - 4m of snow per year (Hagen, 1993).

SVALBARD Nordaustlandet

SON Spitsbergen E3 Bedrock V estfonna □ Ice A ustfonna . 40km _

79N

BarentsOya

78N

(-g Svalbard

Greenland ^ y

E d g eô y a' ainlaatn 77N \ Euroiyv X

Iceland

Figure 1.1 The Svalbard archipelago and (inset) its location in the European Arctic.

15 Dowdeswell and Drewry (1985) used Landsat images to delineate Austfonna's major ice divides and drainage basins. As only a few of these basins had previously been named, they proposed a numbering system with which to reference other parts of the cap, and this is shown in Figure 1.2. Two of Austfonna's basins, Brasvellbreen and Etonbreen, were observed to have surged in the late 1930s (Hagen et al., 1993). The Brasvellbreen surge is thought to be the largest ever recorded, with the terminus advancing 20km beyond its previous limit along a 30km front. Suggestions that two other basins, Leighbreen and Basin 3, may also be of surge-type (Dowdeswell, 1986), are discussed in Chapter 6 .

Named basins I Brasvellbreen 9 Worsleybreen 10 Leighbreen II Normanbreen 12 Nilsenbreen 13 Schweigaardbreen 14 Duvebreen 17 Etonbreen

Ausidoiwn

Sordomen

, 20km ,

24 I

Figure 1.2 Austfonna's major drainage basins and ice divides. After Dowdeswell and Drewry (1985).

The most detailed glaciological investigation of Austfonna was performed in 1983 by a team comprising workers from the Norsk Polarinstitutt (NP) and Scott Polar Research Institute (SPRI). They used airborne radio echo sounding (RES) data to map the region's surface and basal topography along flightlines a nominal 5km apart (Figure 5.3). Hence they were able to calculate ice thickness. The results were published by Dowdeswell et al. (1986) and are shown in Figures 1.3 to 1.5. Dowdeswell (1986) used the RES derived topography and thickness information to map the pattern of driving stresses on Austfonna, and this result is shown in Figure 1.6.

16 There have been no direct observations of Austfonna's substratum, but offshore geological investigations, and evidence of debris-rich subglacial meltwater (Dowdeswell and Drewry, 1989) have indicated that much of the cap's south-eastern margin may be underlain by unlithified marine sediments, thought to have been deposited during periods of ice cap retreat. Austfonna's thermal structure is also poorly known, with very few temperature measurements having been obtained (Figure 6.5).

This issue will be discussed in more detail in Chapter 6 . Studies of drainage basin topography (Dowdeswell, 1986), and observations of surge behaviour, have indicated that Austfonna has a potentially diverse dynamic regime. However, the remoteness of the location has resulted in a sparcity of velocity measurements. Basin 5 was surveyed in the late eighties (Dowdeswell and Drewry, 1989), and some poorly documented observations were made in 1983 (Drewry and Liestpl, 1985), but otherwise the ice cap's velocity structure is not well known.

79.5 2 _ J _ J O J 5 km

## 80.5

C\

■79.0

80.0

Figure 1.3 Ice surface elevations on Austfonna, after Dowdeswell et al. (1986). Contour interval is 50m. Radio echo sounding derived heights were supplemented by Landsat data which provided detail in areas of complex topography. Average error estimated at ±1 Im. The feature labelled is a small ice dome thought to be associated with a subglacial .

17 -79.5 / w km 100 ‘ r'

80,5 . 200? 300 100

100 200 200

2(X) '300 ■ Leighbreen

100

■79.0 -loo;

E3 Ice free land Basin 3 80.0 E Bedrock below sea level

Figure \ A Austfonna's subglacial bedrock elevation, after Dowdeswell et al. (1986). Contour interval is 100m. Error estimate is ±20m. Two bedrock ridges, rising to over 300m a.s.I. run west to east, separated by a valley which reaches an elevation of 150m. In the south and east, much of the bedrock lies below sea level, by up to 157m. Subglacial bedrock troughs are associated with several drainage basins e.g. Basin 3 and Leighbreen.

79.5 km !oo

300 ■4(X) 200 C4(X) O

'400

400

300

-400 ) •79.0

80.0

Figure \.5 Austfonna's ice thickness, after Dowdeswell et al. (1986). Contour interval is 100m. Errors are estimated at 6 %. The 100m thickness contour is absent in many parts of the cap, because the ice is generally of greater thickness, even at the ice cap's margins.

18 30#::^,/^^

■79.5

.v Y — Basin 3

Driving Stress (kPa) contour interval lOkPa Area above 60kPa p z ] Area below 30kPa Brasvellbreena 3 : / ^ __ 2 1 ______51

Figure 1.6 The pattern of driving stresses on Austfonna, after Dowdeswell (1986). There is a general increase from low stress at the ice divides to high stress at the margins, in agreement with theoretical predictions for an ice cap in balance and undergoing plastic deformation (Paterson, 1994). However, the margins are punctured by regions of anomalously low driving stresses, such as those associated with Brasvellbreen and Basin 3.

1.3 Questions addressed bv this thesis Specific questions that will be addressed by the work in this thesis are as follows : i) Is Austfonna's spatial velocity structure consistent with the predictions that have been made via observations of its topography (Dowdeswell, 1986)? ii) Is the spatial velocity structure consistent with models of Austfonna's thermal regime? iii) Does the spatial velocity structure vary temporally? iv) Are there local temporal variations occurring within individual drainage basins, and, if so, are they consistent with surge-type behaviour?

19 v) Can we derive Austfonna's three-dimensional velocity field and use it to obtain an estimate of the mass lost by iceberg calving at its margin? vi) What does this work tell us about the feasibility of using the inSAR technique to routinely monitor ice velocity on a global basis and hence significantly contribute to studies of ice-sheet mass balance?

1.4 The evolution and glaciological application of InSAR This section will seek to put the work in this thesis into context by reviewing the history of the interferometric technique and its application to glaciology. InSAR is a relatively new technology, that has been developed over the last dozen years, principally by workers at NASA's Jet Propulsion Laboratory. Building on earlier work by Graham (1974), Zebker and Goldstein (1986) were the first to demonstrate that the phase- difference between two complex SAR images could be used to calculate topographic height. Two L-band SARs were mounted on the wings of an aircraft and used to produce an accurate, high resolution, digital elevation model of the San Francisco Bay area. Li and Goldstein (1990) were the first to demonstrate that the technique could be applied to a spaceborne system. They generated phase-difference images, or "interferograms", from pairs of SEASAT scenes, acquired on separate near-repeat orbital passes. Gabriel et al. (1989) recognised that the time delay introduced by this repeat-pass approach facilitated the mapping of geophysical changes at the earth's surface, because the resultant interferograms contained information about both topography and surface displacement. This application was spectacularly demonstrated by Massonet et al. (1993) who used SAR interferometry to map the displacement field of the Landers earthquake. They generated an interferogram temporally spanning the event, and one prior to it that contained no motion, and subtracted one from the other to isolate the displacement component. The excitement that was generated by this work, and the swelling of the SAR data-base by the 1991 launch of ERS-1, produced a surge of interest within the geophysical community. InSAR has since been applied within a number of research fields, such as forestry (e.g. Hagberg et al., 1995), geology (e.g. Peltzer and Rosen, 1995), hazard assessment (e.g. Bénédicte et al., 1997) and wetland monitoring (e.g. Morley et al., 1997). The glaciological application of inSAR was first demonstrated by Goldstein et al. (1993). They produced an interferogram of the Rutford Ice Stream in Antarctica which provided an unprecedented snapshot of its flow regime, and allowed its grounding line to be located. As ice flow is continuous they were unable to use Massonet et al.'s (1993) method to isolate the motion effects, but this did not matter

20 because in this case the ice surface was almost flat. Also the flow direction was approximately in the satellite's line of sight, and so their interferogram could be directly interpreted as a velocity field, which agreed with prior measurements to within lOm/y. This study was closely followed by that of Hartl et al. (1994), who generated interferometric imagery of Antarctica's Hemmen Ice Rise. Their results were more complicated due to topographic effects and vertical motion, but they were able to difference two successive interferograms to accurately estimate the local tidal amplitude. The following year saw publication of the first interferometric results from the northern hemisphere. Joughin et al. (1995) and Rignot et al.(1995) simultaneously presented phase-difference images of Greenland's western flank. These were vastly more complicated than those previously yielded by Antarctica, due to the presence of undulating topography. Though the topographic signature within the interferometric phase was removed by the use of an external DEM, the interferograms were found to be much more sensitive to the vertical component of ice velocity than its horizontal component. Areas of surface roughness therefore generated "bullseye" features which complicated the motion phase. This provided a revealing insight into the relative complexity of ice flow on different length scales. The flow direction within the imagery was oblique to the satellite's line-of-sight, but Rignot et al. (1995) were able to derive an estimate of the three-dimensional velocity by inferring a flow direction and employing the assumption of surface parallel flow. Their results agreed with prior measurements to within 6 %. The next major development came from Kwok and Fahnestock (1996) who showed that it was not necessary to use an external DEM to extract the topographic signal from glaciological interferograms. They coined the phrase "double-differencing" to describe a technique whereby two interferograms with different viewing geometries were differenced to remove motion effects and isolate the topographic phase component. This could then be extracted from one of the individual interferograms to isolate motion effects. Using just three SAR images they were therefore able to produce both a DEM and a velocity map for a location in north-east Greenland. Joughin et al. (1996a) employed this technique in producing a DEM for part of Western Greenland, which had an absolute accuracy of 4m, and Joughin et al. (1996b) similarly obtained a single-component velocity field of Greenland's Humboldt Glacier with an accuracy of 2.3m/y. This latter work included a detailed error assessment which highlighted the need for a well planned network of independent velocity tie-points to constrain the accuracy of the interferometric results. Rignot (1996) employed a "quadruple differencing" approach which he used to isolate a third component, tidal uplift, from the interferometric phase. The same year saw publication of the first interferometric observation of glacier instability. Joughin et al. (1996c) generated

21 imagery of a "mini-surge" of Greenland's Ryder Glacier, in which its velocity increased threefold, and then returned to normal, over just a seven week period. To date the literature had been dominated by the work of just a handful of researchers, concentrating on the two major ice sheets, but the two subsequent years have brought increasing diversity, with the publication of results from other glaciated regions, e.g. Canada (Gumming et al., 1997), (Fatland, 1997), (Rignot et al., 1996) and Svalbard (Unwin and Wingham, 1997). This year has seen the first publication of full three dimensional velocity fields that have been generated by the combination of ascending and descending SAR data (Joughin et al., 1998; Mohr et al., 1998). This represents a significant step forward because, as discussed in a later section of this thesis, the use of just one look direction would yield inadequate results for all but the most carefully chosen study areas. In the near future we can expect to see the results of some interesting partnerships between radar glaciologists and theoretical modellers (e.g. MacAyeal et al., in press) who have been using interferometrically derived topography and velocity fields to constrain models of ice sheet flow and hence improve our understanding of the factors controlling the stability of the world's ice fields.

1.5 Structure of thesis The following two chapters will outline the principles on which the interferometric technique is based, and the method by which they have been employed to generate high resolution height and velocity maps of Austfonna. Chapter 4 will provide a detailed error model, quantifying known and potential sources of uncertainty in the interferometric results. This will be followed by a thorough verification of the results, which will check their internal consistency and compare them with external data. Any inconsistencies will be discussed in the context of the error analysis that was laid out in the previous chapter. Chapter 6 will present the results in their final form, and discuss their significance in terms of what they tell us of Austfonna's thermal and velocity structure. Conclusions will be drawn in Chapter 7, and this chapter will also include recommendations for future work.

22 2. Principles of the interferometric technique

This research uses synthetic aperture radar (SAR) data from the European Remote Sensing satellites ERS-1 and ERS-2. The interferometric configuration is therefore that of a spaceborne, repeat-pass, across-track system, operating with a single C-band wavelength. This chapter will illustrate the geometry of such a system and set out the basic theory by which topographic height and surface velocity may be obtained via repeated imaging of a target scene. Several authors have outlined this theory (e.g. Zebker and Goldstein, 1986; Li and Goldstein, 1990). The definitions and conventions used here are based on those of Rodriguez and Martin, (1992). A list of symbols is included at the start of this thesis.

2.1 Basic geometry for topography estimation

Zt

o

Figure 2.1 Interferometric imaging geometry for a stationary-target system.

The co-ordinate system used is that of a sphere of radius Re, as shown in Figure 2.1. The centre of the sphere is at O, and all angles are in the same plane. S, is the position of a synthetic aperture radar at time 6 , and S 2 is its position at time (?, 4- At). The distance between Si and S 2 , B 12, is known as the "baseline" of the interferometric pair. It has a "tilt angle" £ 1 2 with respect to the local horizontal. T is a stationary resolution cell (Schreier,

1993) within the SAR footprint, at a distance r, from S,, and (r, -k Aj^^) from S 2 . The angle 0 , is known as the "look angle" and the distance g, is known as the "ground-range" of the target. The SAR observations of T from S, and S 2 will be referred to as the "primary" and "secondary" observations respectively. Together these observations will be

23 referred to as an "interferometric pair". Table 2.1 gives typical values of the main parameters used.

R e R \ 2 01 Rx r\ £i2 Cl 2 At 6399 km 100 m 0.33 rad 7189 km 840 km 20 m 0.5 rad 300 km 4E-4 rad 3 days Table 2.1 Typical values for ERS inteiferometric parameters.

The heightZ t of T, relative to the reference sphere, is given by :

Zj — ~Re ~ ^^1^1 COS (2.1) Its ground-range gi relative to Si is given by :

& = Re acos 2 R \R e + Zt)

(2.2)

Re is taken as the local geodetic radius at T. Justification of this is given in Appendix 1. Ri is obtained from knowledge of the satellite orbit, and n is obtained from the SAR internal clock. The look angle 0^ is obtained by calculating :

+ - ( n + ^ 712 ) 01 = asin -HE12 2 ^ 12^1

(2.3)

Determination of the baseline parameters 8 ^ 2 and is described in Chapter 2. The range- difference is too small to be determined by the SAR internal clock, and so we must measure it by alternative means, as described in the next section.

2.2 Determination of interferometric range-difference For a distributed target, the return at Si from resolution cell T is a complex random variable Pi of amplitude Ai, given by :

Pi = Ai exp(-/2/:ri) e x p (i0 j

(2.4) The constant k is the wavenumber of the system, and the factor 2 indicates two-way travel along the ri path. The phase is determined by the returns from the many individual scatterers within the resolution cell, and so is uniformly distributed, prohibiting the determination of range information from one complex SAR image.

24 At S2, the return from the same stationary resolution cell would be characterised by :

P^ = A^ exp(-i2 *(r, + 4^,, ))exp(i0 j

We determine by first multiplying Pj by the complex conjugate of P 2 to obtain a complex "interferogram" /12 :

^12 = =AAiexp(i^,2) (2.5)

012 is known as the "interferometric" phase-difference between the two complex returns, and for the stationary target analysis considered above it is given by :

012 = 2 kAj^^

We take the principle argument of /12 to obtain :

^w,2 = arg(/, 2)=

= ^ i 2 + 2 ;mi2 (2.6)

0 H,j2 is known as the "wrapped" interferometric phase-difference, as it is only known modulo-27C. The integer «12 is determined as described in Section 3.4, and we can then use equation (2.6) to calculate 012. For a stationary target, we then have all the information necessary to compute ^i, Zr and g], using equations (2.1), (2.2) and (2.3). The next section, however, considers the more general case, for which 012 ^

2.3 Interferometric imaging of a moving target Referring to Figure 2.2, the interferometric system is now used to view a moving target resolution cell T, whose component of velocity in the look direction of Si is v,. Again, the primary (SJ observation occurs at time fi, and the secondary (S 2) observation occurs at time tx+At. In contrast to the scenario in Figure 2.1, Zt is now the average height of T over the observation interval, and the movement of T extends the distance between S 2 and T by an amount A^, where :

= v,Arcosfi2

= v,Ar + 0 (lO-") (Z7) 25 Figure 2.2 Interferometric imaging geometry for a moving-target system.

The radar return at S, may again be characterised as in equation (2.4), but the return at S 2 becomes :

P, = A, exp(-/2 <:(r, +

(2 .8 ) SO that the interferometric phase-difference

0,2 = +^v) (2.9)

In order to compute useful height and velocity information for a target scene, 0 1 2 must be separated into its two constituent parts. This work uses the method of Kwok and

Fahnestock (1996), which allows isolation of AT^2 under the assumption that the target acceleration is zero. Following Joughin (1995), it is useful to re-express the basic equations in terms of

baseline components and Bp^^, respectively normal and parallel to look angle 0 ^, at scene centre (an arbitrary reference point). So :

(2. 10)

26 7il2 C is a resolution cell at centre range

Zt

Figure 2.3 Baseline components and Bp^^.

From the geometry in Figure 2.3 it can be shown that :

B,2sin( 0, - e , 2) = S„,jSine^,

(2. 11)

By combining equation (2.11) with equation (2.3), and solving for we obtain :

= 5 l -B „ ,2 sin + 0 ( 1 0 -) 2 r (2. 12)

We now proceed with the isolation of Aj^^.

2.3.1 Isolating the topographic component of the range-difference

Suppose we have a third observation S 3, obtained at time + 2At. We can now form a second interferometric pair using S 2 and S3, as shown in Figure 2.4.

Employing the assumption of zero target acceleration, the return at S 3 m ay be characterised by :

P3 = A3 exp(-/2 /:(r2 + Aj^^ + A,))exp(/0 j

(2.13)

27 where = (r, + + A^) and, following the same analysis that was used to obtain equation ( 2 . 1 2 ), but using the geometry of the second interferometric pair, Aj^^ is given by:

sine,, + 0 (10-)

(2.14)

; Ref sphere surface

T o O T o O

Figure 2.4 Geometry for topographic phase isolation.

We can now form a second interferogram given by :

^23 ~ ^2^3 ~ ^2^3 GXp(/023) (2.15)

where the interferometric phase-difference 0 2 3 is given by :

023 = 2k{^Aj^^ + zdj

(2.16)

Now, if we multiply /1 2 by the complex conjugate of I23, we obtain

0123 “ A 2-^23 “ A -^2 A ^ ^ P ( ^ '^ 1 2 3 ) (2.17) 28 where ^123 is given by :

^123 = (^12 - <^23) (2.18)

Using (2.9) and (2.16) we obtain :

^123 — 2 ^ -K - ' 8 .2 3 ^“ ®^2 ) + 0 ( lO - )

B, 23 -( 8 m “ s 0„-B,, 3 Cos 6I^J 2 ^ 0 (2.19) which, for typical ERS-1 geometries (Table 2.1), reduces to :

0123 = 2k - « , , 2 3 Sin 0,, - cos0,, + 0(10-")

(2.20)

where : ■^“123 ^"]2 “ ^"23 ^P123 ~ ^P12 ” ^P23 (2.21)

If we define differential baseline B 123, such that 5j23^ =B„^^^ + then equation (2 .20) becomes :

- 0.,33 Sin 0 , , - COS 0 „ + ^-8.23+8,,3^,33 ^23" 0,23 = 2 A: + 0 (1 0 ^ ) 2 r, 1 (2.22)

We also define ^ 7 ,23» such that :

^ r ,23 = ^~ 8.123 8,, - S„33 COS 0 „ +

= ^ - 8.123 8„ - B„33 COS0 ,3 + O ( I O - )

(2.23)

Comparing this with equation (2.12), it can be seen that is the range-difference which would occur for the imaginary stationary-target system whose baseline is B, 23, the vectorial 29 difference between 5 , 2 and as shown in Figure 2.5. This will be referred to as the differential system.

Ref sphere surface

T o O

Figure 2.5 Geometry of the differential system. B 123 is the baseline of an imaginary interferometric pair.

Equation (2.22) now becomes :

0,23 - + zdg)

(2.24) where :

(2.25)

We calculate As, and using equations (2.17) and (2.24) we remove it from g i 23 to produce a "differential" interferogram g r ,23 whose phase is solely dependent on the differential range-difference 2 lr,23 •

6r,,, =G i2,exp(-i2M g)

= AA-"^3exp(r2i4r,2,) (2.26)

30 We take the principle argument of Qt^^v give us the "wrapped" differential phase- difference :

^wi23 - ^g(&i23 ) - (^^"^T’,23 ) m od(2;r) = ^^^ri23 +27^123 (2.27)

The integer « 1 2 3 is obtained as described in section 3.3, so allowing us to calculate ^t’] 2 3 - As in equation (2.3), but using the geometry of the differential system, we are then able to

compute look angle 0 i, using :

^123^+^l^~(^l + ^ 7^123) = asin ^123 ^■^123^1

(2.28)

Target height Zt and ground-range gj can then be calculated using (2.1) and (2.2) as before.

2.3.2 Isolating the velocity component of the range-difference

Having obtained the target height Zt, it is now possible, using equations (2.1) and (2.3), to

calculate Using equations (2.5) and (2.9), this is then removed from / 12, to produce a

"displacement" interferogram, /?i 2 , whose phase component is solely related to target m otion :

/Î.2 = /,2exp (-i2i4^ iJ

= Aj A 2 exp(/2 A;A J

(2.29)

We now take the principle argument of to give us the "wrapped" displacement phase- difference ■

= arg(«i2) = (2 W v )^ ( 2,)

= 2 kA^ + 2 %%y (2.30)

The integer is determined as described in section 3.4. Having therefore obtained A^, the surface velocity component v„ in the look direction of the primary observation, may be calculated using equation (2.7).

31 2,4 Determination of three dimensional target velocity We wish to determine the three dimensional target velocity vector v. Note that the "target" is an individual resolution cell of the SAR imagery, and v is a temporal average over the interferometric repeat period At. We define a right-handed Cartesian coordinate system (%,y,z) where the plane is in the plane of the reference sphere, and thexy plane is tangential to the reference sphere surface at T (Figure 2.6). The components of v in the %, y and z directions are, respectively, v^, v,, and :

y = v^x + v j -t- v^z = v„+v^z (2.31) and V;, is the horizontal velocity component in the direction of flow (Figure 2.7).

Ref sphere surface

T o O

Figure 2.6 The measured velocity component

The measured velocity component may be expressed as

sm a^ - cos a, (2.32)

where Of, is the local incidence angle.

32 View in xN plane View in v/,/z plane

Target surface

♦V:

Ref. sphere surface

Figure 2.7 Components of ice surface velocity v.

This work employs two methods to determine v. Both methods are based on the assumption that y lies in the plane of the target surface (Figure 2.7). The implications of this assumption are discussed in section 4.4.1.

Method a Where a target is viewable from two different look directions, then two velocity components are measurable, and this information may be combined with the aforementioned surface-parallel flow assumption to determine all three components of v. The second look direction is defined by the coordinate system (V, y', z), which is rotated with respect to (%,y,z) by some angle 77 (Figure 2.8).

Figure 2.8 Relationship between two look geometries.

The three components of v, may then be obtained using the following set of equations, which was derived by Joughin et al. (1998). All primed variables refer to the second look geometry :

33 '’■ = v,~ z{x,y) + v^-^z{x,y)

(2.33)

vJsm a^' = {i - a b c )'ab v '/sin a ,'

(2.34) where : 1 O' 1 = 0 1

1 COS 7] A = 0 sin 7]

1 1 1 -c o s rj B = ,sin^77. -COS rj 1 dz ^ dz ^ ——coto^i -—cot Of] dx dy C = dz , dz . —— co t Of] —— co t Of] dx dy

Flow azimuth is computed using :

/ \ V 7 = atan

(2.35)

Method b If a second look geometry is unavailable, but the flow azimuth y and surface slope P are known, then it may still be possible to determine v, the magnitude of which is given by :

K (2.36) where : K = cosj9cosysinof] - s'mpcosa^ (2.37)

The limitations of this method are discussed in section 4.4.2.

34 3. Methodology

This chapter describes how, using the principles outlined in the previous chapter, SAR images were processed to allow measurement of the surface height and line-of-sight velocity component of Austfonna, the largest ice cap in Nordaustlandet. Methods used to compute Austfonna's full three dimensional velocity field are then described. Though it has recently become possible to perform most of the following procedures using commercial software, this option was unavailable at the beginning of this project, and so the algorithms were encoded by the author. The exception to this is the phase-unwrapping routine, for which software was provided by I. Joughin.

3.1 Data Origin The SAR images used in this work were acquired by the first and second European Remote Sensing satellites, ERS-1 and ERS-2. These are identical, single band, right-looking, radars, operating at a wavelength of 5.71cm. The imaging geometry is as shown in Figure 3.1.

orbital velocity c 7 4 6 6 m /s SAR (S,)

ground track

Swath width c l0 0 k m

Figure 3.1 ERS SAR imaging geography. Symbols and coordinate system as defined in Chapter 1. x will often be referred to as the look direction, and y as the azimuth direction.

For the principles of synthetic aperture radar imaging, see Barber (1985). The images were obtained in Single Look Complex (SEC) format from the German Processing and

35 Archiving Facility (D-PAF). Details of the raw-to-SLC data processing procedure may be found in Schreier (1993). Each SLC image or "frame" consists of i pixels, covers an area of approximately lOOxlOOkm, and is in slant-range/azimuth coordinates (see Figure 3.1). The pixel size in the azimuth direction (y) is 3.96m. In the look direction (x) the pixel size varies with the topography, because the data is binned into slant-range (r,) pixels of size 7.91m. Each pixel is characterised by a complex number. Attached to each image is a standard CEOS header (ESA, 1995). This work uses data from ERS Ts First (28.12.91 - 30.03.92) and Second (01.01.94 - 31.03.94) Ice Phases, when the instrument was in 3-day-repeat mode, and from the Tandem Phase (17.08.95 - 30.06.96), when the two satellites were orbiting one day apart, each in 35-day-repeat mode. Figure 3.2 shows the geographical location of three image frames in the region of Nordaustlandet that will be referred to in the text.

Vestfonn; Austfonna,

Figure 3.2 Shows the position and orientation of three 100x100km ERS SAR frames used in this research, and referred to in the text.

3.2 Registration and formation of single-pair interferograms Frame A in Figure 3.2 is the ascending ERS SAR frame which is principally used in this work. It is frame 1629 of Ice Phase track 13 and Tandem Phase track 70. The lOOxlOOkm scene covers most of Austfonna (Figure 3.3). Fifteen repeats of this image were obtained from DPAF, and used to form nine interferometric pairs. These are listed in Table 3.1. The primary{Psicf and secondary {Psicf) images of each pair were first co-located, or "registered". This was a two stage process. The so-called "gross" registration stage aligned the images to within one or two pixels, by a process of manual feature matching, and in this way, all of the images were registered onto approximately the same grid. The

36 "fine" registration process then improved the co-location so that, within each pair, the images were aligned to an estimated accuracy of one tenth of a pixel. This was achieved using the algorithm of Gabriel and Goldstein (1988) which seeks to maximise the correlation between images. In the case of the two trios of images that were later to be used for topographic isolation (see Section 3.3), the second two images were both registered to the first, i.e. Psicji^) was registered to resulting in a resampled version of to whichPsLc-^ii) was then registered.

21E 22E 23E 24E

V e s t f o i m a

IS percolation z o n e m i

zone' ^ L e i g h b r e e n

20km Lx / am plitude

Figure 3.3 Amplitude component of the SAR image that was acquired over Austfonna on 9th January '9^ Image brightness has been normalised for optimum contrast. Boxes mark prominent drainage basins referred to later in the text. Black lines crudely delineate the Benson Zones, discussed in Section 4.2.4.

37 Primary Secondary At ^nO] 2 ^POJl image PsLc,(i) image PsLCo(i) (m) (m) (days) First Ice Phase 13th Feb. '92 16th Feb. '92 -60 -10 3 16th Feb. '92 19th Feb. '92 174 72 3 20th Mar. '92 23rd Mar. '92 -71 8 3

Second Ice Phase 6 th Jan. '94 9th Jan. '94 -68 27 3 9th Jan. '94 12th Jan. '94 86 33 3 12th Jan. '94 15th Jan. '94 136 45 3 24th Jan. '94 27th Jan. '94 113 42 3 5th Feb. '94 8 th Feb. '94 -6 4 3

Tandem Phase 15th Dec. '95 16th Dec. '95 61 31 1

Table 3.1 Interferometric pairs used in this research. The baseline parameters given relate to the mid-azimuth position within the scene, and are obtained from the best available orbit data (see text).

Each complex pixel withinPsLcfO was multiplied by the complex conjugate of its counterpart in the resampled PsicfJ)' order to reduce speckle, this product was spatially averaged over m^ range-pixels and my azimuth-pixels to produce what is termed a "multilooked interferogram" fiif) comprised of j "multilooked pixels" where :

P I l f SLCi ^SLCi h i - m . X m .

(3.1) Referring to section 2.2, each multilooked pixel of 7] 2(7 ) represents an individual target resolution cell T. Pj and P 2 are therefore multilooked versions of Pslc^ and Psicr

All interferograms produced in this work were averaged over m=A pixels in range and my= 2 0 pixels in azimuth, as these dimensions were found to effectively reduce speckle and to yield multi-look pixels that were approximately square (of size ~80x80m, though, as stated above, the actual size of each pixel in x depends on the topography). The intention was to retrieve the phase component d>i 2 of each pixel, which, referring to equation (2.9) comprised a topographic term 21cAt^^ and a velocity term 2kA^. However, Aj^^ may be subdivided into a term Ar ^^ that would be present in the special case of Zt = 0 , and a superimposed finite topography term Ap^^, i.e. :

0 J2 = 2k{^Ap^^ + A^j

= ^^{^Rll +^Fi2 +^v) (3.2) 38 where

As 2kAr ^^ has a strong linear dependence on rj, it dominates the interferometric phase, taking the form of a steep ramp in the look direction. Hence, we temporarily removed it, in order to ease the phase-unwrapping procedure. Referring to equation (2.12), A^^^ may be approximated by :

- ^non sin % - %

(3.3)

where is the equivalent of 6 ^^, for the special case when the heightZt of T above the reference sphere is zero, and the subscript "o" attached to the baseline terms indicates that these values are estimated using the best available orbit data. (Note that the accuracy of these estimates was immaterial at this stage because the ramp was only removed temporarily). For ERS-I s First Ice Phase, the best orbits available were the DPAF Revision 1 Precise orbits, which have a radial accuracy of 7cm, and an across-track accuracy of 33cm (Reigber et al., 1997). For the Second Ice Phase and Tandem Phase, Delft DGM-E04 orbits provided a better radial accuracy of 5cm (Scharroo and Visser, in press), and estimated across-track accuracy of 10cm (Personal communication, Remko Scharroo, 1997). The information in the CEOS header relating to acquisition timing was used in conjunction with the orbit data to obtain baseline estimates for the first and last azimuth lines of the interfenoigetric image pair, using the algorithm described in Solaas (1994). As baselines vary) linearly with azimuth, values for all y positions within the frame could now be determined, giving an azimuth dependence to the phase-ramp of equation (3.3). The ramp was removed to produce a "flattened interferogram" /fi 2(î)-

= A^A^Q\ip{i{2kAp^^ +2Mj)

(3.4)

Note that the subscript "F" will henceforth always denote images that have been flattened in this way.

The principle argument was taken of each complex pixel of to obtain the wrapped phase-difference Ofwi2 U)^ where :

39 = 2*(^f ,2 +4„)+2®îf|j

(3.5) where is an integer, equivalent to « 1 2 in equation ( 2 .6 ), but for flattened data.

An example of is shown in Figure 3.4. Numerous wrapped phase-difference images of this type will be presented throughout this work, and so it is appropriate at this point to comment on how they should be viewed. Each cycle from black to white represents a phase-difference cycle from 0 to 2 ti, and will be referred to as a "fringe". For images that contain only topographic components, the fringe spacing is inversely proportional to target height Zt and baseline length 5 , 2 (see equation 4.5). For images that contain only velocity components, the spacing is inversely proportional to v^At (see equation (2.7)). Images containing both components, such as the one shown in Figure 3.4, will combine these two effects.

phase difference 20 km

Figure 3.4 Wrapped, flattened phase-difference image Op^ (j), formed using SAR images that were acquired on the 9th and 12th of January 1994. Greyscale explained in text. White noise occurs in uncorrelated areas. Fringes have the appearance of topographic contours, except where motion effects dominate, such as in the prominent drainage basins marked in Fig 3.3.

40 a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

d) 6th/9th Jan. ‘94 e) 9th/12th Jan. ‘94 f) 12th/15th Jan. ‘94

g) 24th/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

20 km 01 — 1 1 I_____ I correlation

Figure 3.5 Correlation images Cj 2 for each interferometric pair. The dates of the primary and secondary acquisitions are given. Causes of low correlation are discussed in section 4.1. Zero correlation characterises areas of open water, and also areas of very high shear, such as the fast flowing ice stream Bodleybreen on Vestfonna, marked "B" in a). The dark streaks apparent in some of the images are discussed in section 4.1.

41 In order to isolate the motion term from equation (3.5), it was first necessary to determine Ap^^, as described in the next section. Before doing this however, we created a

"correlation image" Ci2 (j) for each pair, where :

^^^SLCi^SLC2 rix my ^ 1 2 ~

I l k SLCil I l k SUC2

(3.6)

Figure 3.5 shows the correlation images for each interferometric pair. Correlation can be used as measure of the quality of an interferometric pair. As discussed in section 4.1, low correlation may result in a complete loss of interferometric phase information, or otherwise result in noise that would hamper the unwrapping procedure and produce errors in the results.

3.3 Determination of Ice Cap Topography This section describes the creation of two digital elevation models of Austfonna, using the principles outlined in section 2.3.1. The procedure requires an input of three repeat-pass SAR images. One trio of images was selected from the First Ice Phase data, and a second from the Second Ice Phase data. Only consecutive images, separated by temporal baselines {At) of three days were selected. There were two reasons for this. Firstly, correlation (see section 4.1) was found to be poor within interferometric pairs with longer temporal baselines. Secondly, minimising the time period spanned by each trio helps to fulfil the assumption that no ice acceleration occurs over the measurement period (see equation (2.13)). The trios that were chosen for use in topographic isolation are shown in Table 3.2.

Mission phase Differential image trio ®noi ®P 0111 P SLC^(f) P5LCo(i) P5LCa(i) (m) (m) First Ice Phase 13th Feb '92 16th Feb '92 19th Feb '92 -234 -82 Second Ice Phase 6th Jan '94 9th Jan '94 12th Jan '94 -154 6

Table 3.2 Scenes selected for differential processing to isolate topographic effects. Each trio of images is used to produce a DEM of Austfonna. The baseline parameters given relate to the mid-azimuth position within the scene, and are obtained using the best available orbit data.

Each SAR image trio was combined to produce a complex differential interferogram Qr^2 -Jd) where :

42 SX (^StC l^StC 2 )(^JtC2^StC3 ) mx my ex p (-,2 M g ,) Ôt-,23 = m^XOT,

(3.7)

As discussed in the previous section each multilooked pixel of <2 7 ,23(7 ) represents an individual target resolution cell T, as defined in Chapter 2, with the complex combination of images being performed before averaging in order to reduce speckle. The term Ago is the equivalent of Ag in equation (2.25), with the "o" subscript indicating that it is an estimate, calculated using the best available orbit information. Section 4.2.2 shows that no significant errors are introduced by this estimation. Referring to equation (2.26), the phase component of ôrijsC/) is dependent only on ^ 7 ,23» the range-difference of the imaginary differential system of Figure 2.5. Retrieving

A t ^ 2 2 will therefore allow us to calculate the target height Z7 , using equations (2.28) and (2.1). The following steps outline the procedure by which this was achieved. As in the previous section ^ 7 ,23(7) was "flattened" to facilitate the phase-unwrapping procedure (see below), i.e. :

23 =67,23 exp(-i2M^^^J

= A,A2 A3 exp^/2/:A^^23 ) (3.8) where :

(3.9) and : “ ^ri23 ^^123 (3.10)

The principle argument of <2 ^123(7) was then taken, resulting in a wrapped differential phase- difference image where :

^ F w i23 ( ^ ^ " ^ F l 2 3 )m od2;r

= 27:A^j23 + 2%%Fi23 (3.11) «7,23 integer, equivalent to «123 in equation (2.27), but for flattened data. An example of is shown in Figure 3.6a.

43 In order to calculate Ay (j), we first need to determine Uy (j). This may be represented as :

(3 J 2 ) where is a constant, equal to the minimum value of and is the relative value of fiy^^^ij) with respect to

We determined using an "unwrapping" algorithm, comprised of the residue- formation algorithm of Goldstein et al., (1988), supplemented by the residue-linking algorithm of Joughin (1995). Hence we obtained an "unwrapped" differential phase- difference image where :

123 C|23 (3.13) An example of 0y„^^^(J) is shown in Figure 3.6b.

•I

52IIS»

phase difference no data mm p max , 20 km , Tie-point

Figure 3.6 a) Wrapped topographic phase-dijference image 0y^.^^^(j), formed using the Second Ice Phase image trio detailed in Table 3.2. In comparison with Fig. 3.4 it can be seen that motion effects in the prominent drainage basins are no longer present. The altered spacing of the topographic fringes reflects the change in baseline between the two systems. In its wrapped state, this image may be viewed as a first approximation to a topographic contour map, and can be compared to Figure 1.3. However, the "contour” spacing is spatially variant, being determined by equation (4.5). b) The unwrapped version of Fig. 3.6a, 0y„i^^(j). The modulo-ljt ambiguity has now been removed, and the phase-difference varies smoothly across the scene. Areas that couldn't be unwrapped are flagged as data-gaps and are coloured black. The positions of the RES height tie-points referred to in the text are marked.

44 Once the unwrapping procedure had been completed, the phase ramp was added back to ^f«i23(/) to give 0 r«]23(/)' where :

^r«i23 ~ ^F ui23 23

(3.14)

So, in order to retrieve ^ 7 ^2 2 ^), it was then only necessary to determine the constant «^ 23-

Our best estimate of the differential baseline parameters was at this stage and

Bpo^2 2 ^ ^ ' Though these values were obtained using the best available orbit information, it was still necessary to improve on their accuracy in order to minimise the eventual topography errors (see section 4.3.2). This was achieved using external topographic tie- points, resulting in more accurately constrained baseline parameters and Bp^^^iy). The same process solved for the constant «^ 23- The tie-points used in this research came from the 1983 NP-SPRI radio echo sounding mission discussed in Section 1.2. The aircraft flight path, from which over 17000 RES height measurements were obtained, can be seen in Figure 5.3a. Every 50th point was extracted from the data set, to give 340 independent height tie-points, spread uniformly across the Austfonna region (Figure 3.6b). These were then used to obtain B^^^^iy), Bp^^jy) and 71^23 using a least-squares algorithm to solve equation (A2.3) in Appendix 2. Having computed «^ 23’ the differential range-difference was obtained using equation (3.14), and used to calculate height zAj) and ground-range gj{j) using equations (2.28), (2.1) and (2.2). Using second order polynomial interpolation, zAj) was then interpolated onto a regular ground-range grid. The new height image, zAp) consisted of p resampled pixels, of size 80x80m. The regular ground-range grid allowed the results to be viewed without the distortions associated with slant-range viewing. The results of this DEM production procedure are evaluated in section 5.1.

3.4 Determination of line-of-sight velocity component Vr This section will describe how the motion term \ in equation (3.2) was isolated, and used to calculate the line-of-sight velocity field vAj) of the nine interferometric pairs listed in Table 3.1. Having determined target height zAj)^ it was then possible to compute using equations (2.1) and (2.3). However, it was first necessary to obtain an accurate assessment of the baseline parameters, R^^^Cv) and which we currently only had estimates obtained using the best available orbit data.

45 Referring to equation (3.5), each Opw^^ij) was unwrapped using the same unwrapping algorithm as in the previous section, and its phase-ramp was added back, to obtain where :

^«12 +^v) + 2»».,2 (3.15) in which the constant is the minimum value of np^^ij).

Because is dependent on both motion and topography, it was necessary to employ tie-points of both height and velocity for the baseline constraint procedure. Height information was taken from the DEM Zj(j), derived in the previous section. Only the Zj{j) that was obtained using Second Ice Phase data (Table 3.2) was used, for the reasons outlined in Section 5.1. 280 tie-points were located on the ridges between drainage basins and within bedrock regions (Figure 3.7b), and assumed to have a Vr of zero. The values of the baseline parameters and and the constant were then constrained using a least-squares algorithm to solve equation (A2.4) in Appendix 2. Having constrained the baseline parameters, could now be calculated using equations (2.1) and (2.3). Again, only the Second Ice Phase DEM ZjH) was used in this procedure. The topography dependent phase-difference term 2kAr^J(j) was not subtracted from the unwrapped phase-difference image (D^^^(/), because the combined effects of topography and velocity in this image had lead to a relatively poor performance of the phase unwrapping procedure. Instead, it was removed from the complex interferogram, Ii2 (j) as in equation (2.29), resulting in a displacement interferogram Rn(j) whose phase was solely related to target motion. As in equation (2.30) the principle argument of Rnii) was taken, resulting in a wrapped phase-difference image An example of is shown in Figure 3.7a.

As previously, 0 ^ (j) was unwrapped to produce (D^»(/), where :

0 ^^= 2 kA^ + 2 m^c (3.22) in which the constant is the minimum value of n^(j). An example of is shown in Figure 3.7b. The constant was obtained using the same set of "zero-velocity" tie-points referred to above (Fig. 3.7b), to solve equation (3.22) using a least squares algorithm. Hence A^(j) was obtained and used to determine v^ij) in equation (2.7). This was interpolated to produce Vr(p), on the same regular ground-range grid as Zjip). The results of this measurement of Austfonna's line-of-sight velocity component are evaluated in section 5.2.

46 I

phase difterence no data min ------^ max

20 km H = no data H Tie-point

Figure 3.7 a) Wrapped phase-difference image showing only effects due to ice motion. The primary/secondary images of the interferometric pair were acquired on 9th/12th Jan 1994. In its wrapped state this image may he viewed as contours of the line-of-sight velocity component with each complete fringe representing a Vr increase of 3.5 m/y. So a great deal of information regarding the relative velocity of different areas of the ice cap may be obtained at this stage simply by "counting fringes". The fringes are closest together in regions of high shear at the edges of prominent outlet glaciers. In the centre of the cap, however, there is little variation in velocity, b) The unwrapped version of Fig 3.7a. Notice that the unwrapping algorithm failed in some of the high-shear regions, where the fringes were very close together. The positions of the "zero velocity" tie-points referred to in the text are marked.

3.5 Determination of the three-dimensional velocity vector Section 2.4 described two ways of doing this, a) by combining data acquired from two different look directions; and b) by using knowledge of the flow direction and surface slope. For the reasons outlined in section 4,^2, the second method is flawed and should only be used when two look geometries are unavailable. As overlapping ascending/descending data was only available for a small part of the area of interest, both methods were attempted. The results are compared in section 5.3.

3.5.1 Determination of v by combining ascending and descending data Figure 3.2 shows the position of a descending SAR frame, labelled "B ", which overlaps a portion of the ascending frame used previously. To date, we have obtained only one interferometric pair from this location, acquired during the First Ice Phase, as detailed in Table 3.3. Primed variables will be used to denote this descending data.

47 D I D I Primary Secondary ^ n o n ^ p o i2 At

image P' s l c .CO image P'sLcfH (m) (m) (days) First Ice Phase 12th Feb. '92 15th Feb. '92 54 32 3

Table 3.3 Details of descending Austfonna images used in this work. The images are repeats of Frame B in Figure 3.2, which is Frame 1971 of Ice Phase track 37.

A 20km X 80km section of each image, shown by the dotted line in Figure 3.2, was extracted. These sub-images, were then processed as for the ascending data, to produce a regularly gridded line-of-sight velocity image v/(p'). Figure 3.8 shows the wrapped phase-difference image from which v/(p') was computed.

Basin 5

mm □max 1 01 1271 am plitude correlation phase difference

Figure 3.8 Descending SAR imagery. The image portion corresponds to the dotted area of Frame B in Figure 3.2. a) SAR amplitude image acquired on 12th February 1992. Bedrock regions were used for tie-pointing, b) Correlation between images acquired 12th/15th February 1992. c) The corresponding motion dependent, wrapped phase-difference image 0 \J f). Comparing to Figure 3.7a, a much greater sensitivity to motion in the x' direction is apparent, particularly in the Basin 5 area.

48 The angle rj between the ascending and descending coordinate systems (Fig. 2.8) was 112.8°. Vrip') was rotated onto the same grid as v^ip). Using equations 2.33 and 2.34, it was then combined with the Vr(p) that was obtained using primary/secondary observations from the 13th/16th February 1992, to produce a "method a" velocity image Va(p)- Flow direction %(p) was computed using equation 2.35.

3.5.2 Determination of v bv assuming a flow direction Ice flow direction may be approximated as the direction of maximum surface slope, averaged over several ice thicknesses (Paterson, 1994). The number of ice thicknesses used varies between 8 (e.g. Bindschadler et al., 1977) and 20 (e.g. Budd, 1968). A value of 10 was selected for this work, on the recommendation of A.M. Nuttall (Personal communication, 1997). Ice thickness information was obtained from the NP-SPRI radio echo sounding data-set (Figure 1.5). The Second Ice Phase DEM Zjip) was then spatially averaged and its direction of maximum surface slope calculated to produce a "method b" flow direction image %(p). Returning to the unsmoothed topography zAp), it was then possible to obtain the local surface slope ft(p) in the assumed flow direction. Together, v^(p), Pb(p) and %(p) were combined as in equation (2.36) to compute a "method b" velocity image v^(p).

49 4. Error Model

This chapter will discuss, and quantify, potential sources of error in the interferometrically derived topography and velocity results. It will begin by discussing phase error, the limiting error source in any interferometric measurement. The effects of this, and other errors, on our ability to measure target height and line-of-sight velocity component will then be quantified. Finally, limitations of the methods used to compute the three dimensional velocity vector will be discussed. This error model will provide a framework against which the interferometric results will be evaluated in the next chapter.

4.1 Phase error The geophysical results presented in this thesis are derived from measurements of the phase-difference Ogf (e=l,2; f=2,3) between two SAR images, and so the error, AOgf, in this measurement is the hmiting factor in their quality.

Equations (2.8) and (2.13) may be rewritten as :

Pf = exp(-i(2*(r^+ + 4 . ) + AO,^ )]exp(î(

(4.1)

SO that equations (2.9) and (2.16) become :

0 ^ = 2 k[AT^^+A,) + A ^ ,,

(4.2) where :

(4 3) The terms and Awill here be referred to as, respectively, the phase "scatter" error and phase "travel" error. The origins of these two types of phase error will now be discussed separately.

4.1.1 Phase errors due to changes in the target's scattering properties Equations (2.8) and (2.13) made the fundamental assumption that the scattered phase 0^ detected at Sf was identical to that detected at Si. Backscatter is the sum of returns from many scatterers randomly positioned within a resolution cell. When the resolution cell is much larger than a wavelength, the phases of the individual scatterers are uniformly random. Therefore only an exact repeat of the viewing scenario will allow our assumption to hold. As an interferometric system views its tarçt from two different positions, and at two different times, the introduction of a#^^^ unavoidable.

50 Zebker and Villasenor (1992) and Hagberg et al. (1995) have discussed the sources of this error in detail. There is an underlying value due to the signal-to-noise ratio of the system, which includes artefacts of the raw-to-SLC processing procedure. In addition there is a baseline-dependent error introduced because the target is viewed from two slightly different angles, resulting in different surface and volume scattering effects. Further errors are introduced if the images are less than perfectly registered. Physical processes acting on the scattering surface, such as wind, precipitation, and surface melting, can cause temporal changes in the distribution of scatterers, and are often the largest source of scatter error. Such effects reduce correlation between images, and so by measuring the correlation, using equation (3.6), we can quantify the scatter error. The relationship between and depends on the probability density function (PDF) of 0^. This has been derived by Joughin et al.(1994) and numerically integrated by Joughin (1995) to obtain Figure 4.1, which shows the relationship between correlation and scatter error for different averaging parameters. The plot agrees well with similar results obtained using Monte Carlo simulations (Li and Goldstein, 1990; Zebker et al., 1994).

2.10

1.75

"3 1.40

1.05

0.70

0.35

0.00 0.0 0.4 0.60.2 1.0 Correlation

Figure 4.1 After Joughin (1995), showing the relationship between phase error and correlation, where n^ is the number of looks. For the data used in this research the equivalent o f 30 looks have been taken.

These results show that increasing the amount of averaging, or "number of looks", can significantly reduce phase error. The concept of taking looks is explained in Barber (1985). The interferograms produced in this work are averaged over 4 pixels in range and 2 0 pixels in azimuth, but as adjacent pixels are not completely independent, this is only equivalent to taking 30 looks (Joughin, 1995). Consequently, we can use the %^=30 curve from Figure 4.1 to quantify the scatter error in our measurements of interferometric phase. Rather than repeating the numerical integration of the backscatter PDF (Joughin, 1995) a thir-i polynomial was fitted to Figure 4.1's «^=30 curve, and used to 51 calculate from the correlation images C^/J) shown in Figure 3.5. An example of is shown in Figure 4.2. This image shows peaks in scatter error relating to dark streaks in the corresponding correlation image. The origin of these effects will now be discussed.

b)

Phase error AOs (rad) 0.701

1 0.35 i Itlil i . I mil : 0.0 4 0 20 4 0 60 80 (km ) t t A B

Phase error AOg

20 km 0.35 0.35 2.10 (rad) /

Figure 4.2 a) Phase scatter error for the image pair acquired 13th/16th February 1992. The corresponding correlation image can be seen in Figure 3.5a. The error was calculated using the 30-look curve from plot 4.1. The image is streaked by local anomalies approximately parallel to the x axis, b) Profile across the AB line, showing that the streaks correspond to small localised peaks in phase error (marked by arrows). The origin of these anomalies is discussed in the text.

Correlation streaks Streaks of low correlation, forming bands that are approximately parallel to the look direction are prominent in several of Figure 3.5's correlation images. Joughin et al. (1996a) and Jezek and Rignot (1994) have seen similar structures in Greenland images. Jezek and Rignot demonstrated that the streaks were related to high frequency variations of up to ±2 pixels in the azimuth fine registration offsets, though their cause is unclear. The intensity of the feature is independent of baseline length. As the bands extend indiscriminately across areas of ice cap, bedrock and fast-ice, they appear not be linked to any surface geophysical process. Figure 4.3 overlays correlation images of overlapping ascending and descending tracks that are almost temporally coincident. This composite clearly shows that the streaks must be an artefact of the data rather than being related to any physical phenomenon, as their orientation is solely related to look-direction. The DPAF raw-to-SLC processing procedure is not a source of the streak effects, as they have appeared in the products of other processors. However, to date they have

52 only been reported in data recorded at the Kiruna Ground Station. It is therefore currently thought that their most likely cause is a problem with the low bit rate tape recorder downlinks at Kiruna (I. Joughin, personal communication, 1997).

correlation

look direction

"^Austfonnia

20 km

Figure 4.3 Overlapping ascending/descending correlation images for locations A and C in Figure 3.2. The ascending observations were acquired on Feb 13th/16th '92, and the descending observations were acquired on Feb 14th/17th '92. Note the change in orientation of the dark correlation streaks in the descending image. All descending pairs viewed to date that have produced correlation streaks have resulted in the same orientation. All ascending pairs have correspondingly shown the same streak orientation as the Austfonna image shown here. The evidence is therefore conclusive that correlation streaks could not be related to any geophysical phenomenon, and must instead be an artefact of the imaging process.

4.1.2 Phase error due to travel-time anomalies Phase travel errors do not cause decorrelation within interferometric pairs, and so cannot be measured directly. There are two main causes; clock timing anomalies and atmospheric attenuation. a) Clock timing errors The slant range term r^, in equation 4.1, is calculated from the associated two-way travel time, as measured by the SAR internal clock. Errors in this measurement will therefore contribute to

53 Such errors can be large, as shown by Massonnet and Vadon (1995) who attributed phase ramps of up to 6 fringes (37 radians) across a 100km SAR frame to a clock drift that was within ERS-l's design tolerances. However, as these errors also tend to have a linear y dependence they may be partially compensated by the baseline constraint procedure (Appendix 2). bl Atmospheric. Variations in the velocity of the radar signal as it travels along its path will also contribute to Spatially and temporally varying atmospheric anomalies can cause the electromagnetic wave to be introducing significant phase errors (e.g. Tarayre and Massonnet, 1996). Hanssen and Feijt (1997) modelled the effects of tropospheric variations in temperature, pressure and relative humidity, and showed that interferometric phase errors can be significant with respect to the wavelength of the ERS radar signal. For instance, they showed that at a temperature of 0°C, a 20% horizontal change in relative humidity would produce a half cycle phase error in an interferogram. Such changes are common in the vicinity of cumulus clouds. Horizontal pressure changes consistent with meteorological frontal zones were predicted to cause phase errors of a similar magnitude. Tropospheric anomalies can therefore result in phase errors on both sub-kilometre and multi-kilometre spatial scales. Horizontal and temporal variations in electron density in the ionosphere can also produce significant phase travel errors. The two main sorts of irregularity that are thought to be of importance are travelling ionospheric disturbances (TID) and F-irregularities (Tarayre and Massonnet, 1996). TIDs are internal waves that create sinusoidal fluctuations of the electron density over wavelengths of between 30 and 300km, and with amplitudes of the order of 1% of the total electron content. Tarayre and Massonnet (1996) performed simulations which showed that a typical TID creates a 1.2 radian phase error in a standard ionosphere. The same workers showed that F-irregularities have produced phase errors of up to 19 radians. These errors are very distinctive, being aligned on the magnetic field in a cigar shape. Close to the pole the length-to-width ratio is approximately 5, and typical widths vary between several metres to several kilometres. In addition, geomagnetic storms, caused mainly by solar wind events, can cause dramatic changes in the ionosphere, particularly in the poles, and can produce phase errors of the order of a factor of two higher than those discussed above (Callahan, 1984). These would not be expected to display any regularity of form or occurrence.

54 4.2 Errors in the computation of target height This section aims to quantify potential errors in the two DEMs of Austfonna that were obtained as described in section 3.3. The sensitivity of the results to phase error will first be established. Errors introduced in the processing procedure, and effects of uncertainties in the imaging geometry will then be discussed. Finally, the impact of spatially variant radar penetration will be assessed.

4.2.1 Relationship between height error and phase error Using equations (2.3), (2.9) and (2.1), target height Zt can be differentiated with respect to ^ef- Hence we determine the height ambiguity which is a measure of the sensitivity of each single-pair interferogram to changes in target height :

dzj sin 6 ^ a^f= ------^ ------

(4.5)

Note that a^f is inversely proportional to B^f, implying that longer baselines are desirable to reduce height error. As implied in section 4.1, however, baseline decorrelation is a significant source of phase error, and hence longer baselines also increase height error. Rodriguez and Martin (1992) discussed optimisation of baseline length, taking these issues into account. In practice the ERS orbits are managed in order to keep baselines within an acceptable range (Solaas, 1994). The DEMs obtained are the result of combining two interferograms as in equation (2.18), and so the phase-dependent height error Az^, will depend on the height sensitivity of both interferograms :

(4.7)

As discussed in Section 4.1.1, phase error comprises both scattering and travel effects, and we can calculate the scattering component by measuring correlation within interferometric pairs. We can therefore quantify the height errorAz,ps that is due specifically to scattering error :

(^23 ^^523 ) (4^) This contribution to the errors in the two Austfonna DEMs is shown in Figure 4.4.

55 a) Correlation dependent error in 1992 DEM b) Correlation dependent error in 1994 DEM

Y Height error A z^ s 20 km X 0 20 >20 (m) /

Figure 4.4 Height error due to phase scatter error, for each of the two differential systems used to derive interferometric DEMs of Austfonna.

4.2.2 Errors introduced during the processing procedure The procedure used to isolate the topographic component of the interferometric phase- difference potentially introduces two errors, the first because we must employ approximate estimates of the baseline parameters, and the second because we must assume that the target acceleration is zero. This section will show that both of these errors are expected to contribute insignificantly to the results obtained in this thesis. a) Baseline approximation Having measured 0 ,23, we use equation (2.24) to calculate the differential range-difference Ar^^y Before doing this we must calculate the baseline term Ab , using equation (2.25). However, as discussed in section 3.3, at this stage we can only obtain an estimate of Ab based on the best available orbit information. We are therefore effectively introducing an extra phase error. If the errors in and are, respectively, AB,^^y then equation (2.25) becomes :

=

04.9)

56 For baseline errors of the order of half a metre, and baseline lengths of the order of a hundred metres, this reduces to :

(4.10)

This has the effect of introducing an 0(10'^) phase error into equation (2.24), and hence (referring to the previous section) an 0(10'^) height error into our final DEMs. This is negligible compared to the phase-error induced height errors (Figure 4.4). b) Zero acceleration assumption Equation 2.13 assumed that between acquisitions S2 and S3, the target had been displaced by the same distance \ as between acquisitions Si and S 2, i.e. that no acceleration occurred over the time period spanned by the differential system. If this is not the case, then the equivalent of a phase-travel error is introduced into the differential interferogram < ^ 1 2 3 (equation 2.18), and this will produce a height error, as described in Section 4.2.1. However, using equation 4.5, it can be shown that for the differential configurations used in this research, just one metre of height error would require a target acceleration of over 150my^. Such accelerations are possible (e.g. Kamb and Englehardt, 1987) but unusual. If present, this height error would be recognisable by being geographically confined to an individual drainage basin.

4.2.3 Height errors due to errors in knowledge of the imaging geometrv Having obtained a measurement of interferometric phase-difference, the accuracy with which we convert this to target height Zt depends on our knowledge of the geometric parameters, /?i, n, The sensitivity of the height derivation to errors in these parameters may be determined by differentiating Zt with respect to each one. Following Rodriguez and Martin (1992) and Joughin (1995) we obtain :

Azr = AR^ (4.11) AZj. ~ -C O S0, Ar^ (4.12) -r,sin(9,-ejsine,

(4.13) -rj cos(0i - )sin 6^

~ ^ P 1 2 3 ) + &23 " ^q23 ) (4.14) 57 where AR^, Ar^, and are the errors in /?,, r,, and respectively, and Azr , Azn /kg» and Azbp are their associated height errors. The relationships are written as approximations because they were derived for a flat-earth geometry, rather than the spherical geometry used elsewhere in this thesis. Radial accuracies of the DPAF PRC-1 orbits are 7cm (Reigber et al., 1997), and those of the Delft orbits 5cm (Scharoo and Visser, 1998). The contribution to the height error made by Azr is therefore expected to be negligible in comparison to the phase errors discussed in Section 4.2.1. Also, errors in /?i might be expected to be constant for a particular scene, or have a slight linear dependence on y, in which case they would be minimised by the baseline constraint procedure. As discussed in section 4.1.2, errors in slant range r, are caused by inaccuracies of the SAR internal clock. The associated height errors would tend to be linear, and so again would be compensated by the baseline constraint procedure. Figure 4.5 shows plots of the expected height error per centimetre of baseline error for the two differential interferometric measurements made in this research. The errors take the form of ramps with a strong range dependency, though clearly if the baseline errors vary with azimuth this will give the ramps an azimuth dependence too. In order to produce DEMs with an accuracy of just a few metres, baseline accuracies of just a few centimetres are needed. It is because current orbital accuracies do not meet this stringent requirement (see section 3.3), that it is necessary to constrain the accuracy of the baselines by the use of tie-points. The accuracy to which baseline parameters may be constrained depends on the quality and distribution of the available tie-points (Joughin et al., 1996b), and this will be discussed in the following sub-section.

a) AzBn (m) b) Azbp - av(AzBp) (m) 3 0.6 2 0.4

0.2 0 0.0 1 - 0.2

- 0.4 2 1994 DEM - 0.6 ■3 7min *7 max Ocl

Figure 4.5 a) Predicted height error per centimetre of error in baseline component for the two topographic measurements made in this research, b) Similarly, the predicted height error per centimetre of error in baseline component Bp. This has had a large zero-offset removed, since any such offset would be compensated in the computation of the unwrapping constant by the use of tie-points (see Appendix 2).

58 Baseline estimation accuracy Joughin et al. (1996b) carried out various simulations to investigate factors controlling the amount of residual baseline-related height error, after the baseline constraint procedure. They showed that, in general, the residual errors are inversely proportional to the square root of the number of tie-points used, and inversely proportional to the area spanned by the tie-points. As described in Section 3.3, 340 tie-points, distributed as shown in Figure 3.6b, were used to constrain the baseline parameters for the two DEMs derived in this work. This section describes an experiment that was performed to estimate the success of this procedure, and hence the residual baseline-related height errors in the final results. The experiment involved the simulation of a topographic interferogram from a known DEM, using known baseline parameters. As with the real data, the baseline parameters were then re-constructed using tie-points to solve equation (A2.3) using a least squares algorithm. The new baseline parameters were used to compute a new DEM from the interferogram, and the magnitude of the difference between this and the original DEM was taken as the experimental height error We similarly computed ABnh^.^, and respectively the experimental errors in the baseline parameters and SBp^^y which are defined in Appendix 2. We do not compute an error for because, as described in Appendix 2, the value of this is fixed to that of the input baseline parameters. One of the interferometrically derived Austfonna DEMs was used as the known DEM, and interferograms were simulated using the orbital baseline parameters of both of the differential geometries used in this work (Table 3.2). For each configuration, four variations of the experiment were performed, each using a set of tie-points with the same spatial distribution as the set of RES tie-points used for the real data. The results are shown in Table 4.1.

Configuration Experiment Az sim (m) (m) (m) (m) mean s.cl.

First Ice Phase 1 1.3E-4 2.8E-4 2.7E-4 0.24 0 .1 0 (1992) 2 2.8E-2 1.2E-2 2.4E-3 1.08 1.00 3 1.2E-2 3.1E-2 4.0E-3 1.53 0.84 4 1.7E-3 8.1E-2 1.3E-3 0.83 0.53

Second Ice Phase 1 2.8E-5 1.4E-5 2.9E-5 0 .1 2 0 .0 2 (1994) 2 1.8E-2 8.2E-2 1.6E-3 1.00 0.97 3 1.9E-3 2.8E-2 2.2E-3 1.20 0.76 4 9.4E-4 5.0E-2 1.8E-3 0.65 0.62

Table 4.1 Results of simulation experiments designed to test the performance of the baseline constraint procedure.

59 The first experiment used "exact" tie-points, extracted from the known DEM. These allowed the baseline parameters to be constrained very accurately, resulting in mean height errors of the order of 10cm. For the second experiment, random errors with an average magnitude of 11m were added to the exact tie-points, mimicking the errors in the RES tie-points (see Section 5.1.3). The mean height error then increased to about one metre, confirming Joughin et al's (1996b) conclusion that residual height errors after baseline-constraint are much smaller than the errors in the tie-points, provided a large number of tie-points are used. As errors in the interferometric phase also hamper the performance of the constraint procedure, the third experiment included this effect, using the phase-scatter errors that were computed for each image pair in Section 4.1.1. These were added to the simulated interferograms before the baseline-constraint procedure, but removed before the computation of the DEM, because their effect on that process has been considered separately (Section 4.2.1). Again tie-points with an average error of 1 Im were used. The mean height errors in the final DEMs were found to be around 1.5m. The final experiment again included phase noise, but this time the RES tie-points were used. In this case the height errors were less than those obtained using the simulated tie-points. This is probably because the DEM had already been "tied" to this set of tie- points before the experiment began. Although the errors in the two sets of tie-points were of similar magnitude, and so should have constrained the results to the same degree, those in the simulated data set were randomly distributed, whereas the errors in the RES data set were not (see section 5.1.3). By constraining our results using a slightly biased set of tie- points we have apparently introduced height errors of the order of a few tens of centimetres. These are in addition to the effects of tie-point error and phase noise, which have been shown to yield a mean height error of around 1.5m. The two-dimensional distribution of this height error will now be considered. Each of the experiments conducted constrained the baseline parameters to within a few centimetres at most. An examination of Table 4.1 shows that the relative contribution of each parameter to the total baseline error changed in each case, due to changes in the distribution of the input errors. The two-dimensional form of the residual height error depends on these relative contributions. As shown in Figure 4.6, any profile parallel to the x or y axis will yield a ramp, as predicted by Figure 4.5. However the ramp gradient is dependent on the relative contribution of Azsp and which changes with azimuth. Consequently, a diagonal profile will tend to yield a parabola.

60 a) b) ^sim (m ) 4 AE

BF

a # CG i

HD

^sim (m)

20 km 40 80 120km

Figure 4.6 a) Height error Azsim(j) that was obtained from experiment 3, using the Second Ice Phase baseline configuration, b) Profiles across Aisim(j)> highlighting its spatial variation. Profiles parallel to the x and y axes take the form of a ramp, whereas diagonal profiles are parabolic. The BF profile, which is parallel to the x axis at mid-azimuth, has a near-zero gradient. This is because the error in Bph ,23 zero for this experiment, and, as shown by Figure 4.5, this parameter is the dominant contributor to baseline-dependent height errors.

4.2.4 The effect of spatially variable surface penetration This error arises from the frequently incorrect assumption that the radar target T lies at the earth's surface. If the radar signal penetrates the surface, we are in fact measuring the height (and velocity) of some other datum. If the amount of penetration is constant for a whole SAR image, then this will be rectified in the baseline constraint procedure, but if it is spatially varying, local height errors will be introduced. Note that tem poral changes in penetration will also produce height errors because a loss of correlation will produce phase errors. The scattering properties of an ice cap vary according to its zonal distribution of accumulation and ablation, as categorised by Benson (1961). Fahnestock et al. (1993) were able to map these zones in Greenland using ERS-1 SAR data, and the following discussion of Austfonna's scattering properties is based on that work. Figure 3.3 crudely mapped the Benson Zones onto an ERS SAR amplitude image of Austfonna. High elevation regions at the centre of the world's largest ice sheets are

61 characterised by so-called "dry snow", where, even in Summer, no melting occurs. Fine grain sizes and low particle densities result in deep penetration and very little backscatter at ERS SAR wavelengths, with potential to cause large interferometric phase errors. However, no such zone would be expected for the relatively low elevations of Austfonna, and this is confirmed by the absence of a characteristically dark region in central parts of Figure 3.3. Instead there is a central bright region. This is likely to correspond to a "percolation zone", where some surface melting occurs, but meltwater can only percolate for a short distance before it refreezes to form structures such as ice lenses, layers and pipes (Paterson, 1994). Exceptionally high backscatter occurs at the boundary where refreezing begins because strong layering attenuates radar penetration (Jezek et al., 1994). The depth of this boundary varies according to the season (Paterson, 1994). Summer measurements in Greenland's percolation zone (Jezek et al., 1994), at an elevation of about 200m, revealed that the strongest scattering occurred at a depth of 1.1m. The Austfonna data used in this thesis were acquired in winter, and the percolation zone is at elevations greater than 650m, so penetration estimates of less than one metre are reasonable. Below the percolation zone lies the "wet snow zone" where the entire annual layer of snow will be raised to 0°C by the end of the melt season. Higher temperatures result in greater compaction, and so the fim is denser than in the percolation zone. This reduces radar penetration (Fahnestock et al., 1993), which is probably confined to within a metre of the surface. Consequently, ice lenses and similar structures at depth, are of less importance in the scattering process. Therefore, though backscatter is still high, it is reduced in comparison to the percolation zone. This region of Figure 3.3 can be seen to be of near uniform brightness, though interrupted by "ripples" corresponding to kilometre scale roughness associated with deformation of the ice within major drainage basins (Dowdeswell et al., 1994). Radar-dark regions at the edges of Austfonna correspond to bare ice, produced by both compaction of snow at higher elevations and "superimposed" ice that forms by re­ freezing of meltwater at the base of the fim. This is the ablation zone. In Winter the ice is overlain by fresh snow, and the snow-ice interface acts as a surface scatterer, though the strength of backscatter is low due to its relatively smooth surface (Fahnestock et al., 1993). In summary, winter radar penetration of Austfonna is expected to show very little spatial variation, being everywhere confined to within a metre or two of the surface. This is therefore not expected to be a significant source of height error in the interferometrically derived DEMs.

62 4.3 Errors in the computation of line-of-sight velocity This section aims to quantify potential errors in the nine computations of Austfonna's line- of-sight velocity field that were obtained as described in section 3.4. The sensitivity of the results to phase error will first be established. The effects of topographic error and baseline error will then be discussed.

4.3.1 Sensitivitv to phase error Using equations (2.7) and (2.9), line of sight velocity can be differentiated with respect to the phase-difference 0%2 determine its sensitivity to phase error. Thus we obtain :

(4.15) where Avr0 is the error that is due to phase error.

So for a temporal baseline At of 3 days, a 2;rphase error would produce a 3.5m/yr error in v^. Correspondingly, the same phase error in an interferogram with a 1 day temporal baseline would result in a 10.5m/yr error in v,.. Based on the analysis in Section 4.1.1 Figure 4.7 quantifies the contribution to Vr error that is due to the scattering component of phase error

4.3.2 Sensitivitv to height and baseline errors Again referring to equations (2.7) and (2.9) it can be seen that our ability to calculate also depends on our ability to determine the topographic range-difference At^2 - As shown in equation (3.2) At^^ is comprised of a linear term, Ar^^, that is strongly dependent on baseline, and a superimposed topography dependent term Af^^. Therefore errors in will introduce into a linear, baseline dependent error and a superimposed height- related error Av,^. Joughin et al. (1996b) derive the following expressions for these errors :

(4.16) -(^»,2 sin% + ^g„,cos6>^,)

(4.17) where Azt is the height error in the DEM that was used to extract the topographic effects from each single-pair interferogram. These errors will now be considered separately.

63 ■ _ W"' a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

d) 6th/9th Jan. ‘94 e) 9th/12th Jan. ‘94 0 12th/15th Jan. ‘94

g) 24th/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

Correlation related line of sight velocity error Avr^s 20 km & I_____ I t i 0 0.4 >0.4 (m/y) /

Figure 4.7 Line-of-sight velocity error that is due to phase scatter error, i.e. poor correlation. The associated correlation images can be seen in Figure 3.5. The errors are generally below 0.4m/y.

64 a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

d) 6th/9th Jan. ‘94 e)9 th /1 2 tb Jan. ‘94 0 12th/15th Jan. ‘94

g) 24th/27th Jan. '94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

20 km □ I______I (m /y) > 1

Figure 4.8 Error in line-of-sight velocity that arises due to topographic error, assuming that topographic error is as shown in Figure 4.4h (Section 5.1 will show that this is a reasonable assumption).

65 Sensitivity to height error Table 4.2 quantifies for each of the nine interferometric pairs used in section 3.4 to calculate Austfonna's line-of-sight velocity field. It shows that the results are reasonably insensitive to height error. In section 5.1.3 the mean accuracy of the corresponding DEM is established as 10m, resulting in errors of just a few tens of cm/y, depending on the temporal and spatial baselines of individual image pairs. If phase scatter error is assumed to be the dominant source of height error (Figure 4.4b), then can be quantified more specifically, as shown in Figure 4.8.

Primary Secondary Av,^ / Azt At image PsLci(i) image PsLC2(i) (cm y-i m*0 (days) First Ice Phase 13th Feb. '92 16th Feb. '92 -2.7 3 16th Feb. '92 19th Feb. '92 7.6 3 20th Mar. '92 23rd Mar. '92 -3.1 3

Second Ice Phase 6 th Jan. '94 9th Jan. '94 -3.0 3 9th Jan. '94 12th Jan. '94 3.8 3 12th Jan. '94 15th Jan. '94 6 .0 3 24th Jan. '94 27th Jan. '94 5.0 3 5th Feb. '94 8 th Feb. '94 -0.3 3 Tandem Phase 15th Dec. '95 16th Dec. '95 7.5 1

Table 4.2 Line-of-sight velocity error in cm/y per metre of topographic error for each of the interferometric pairs used in this research. Values are based on mid-scene baseline and range measurements , with variations occurring in the first decimal place.

Sensitivity to baseline error Figure 4.9 is a plot of the baseline dependent error Av^b per centimetre of baseline error (using equation 4.17), assuming equal errors in and Bp^^. As in Figure 4.6, the form of this error is an azimuth varying ramp, though it can be seen that the effect of baseline error on the velocity results is far less than the corresponding error in the topography results. The tie-points used to constrain the baseline parameters of the single-pair interferograms (Figure 3.7b) were not so well distributed as those used to constrain the topography results. In order to determine the effect of this the simulation experiments performed in Section 4.2.3 were repeated using the nine single-pair baseline geometries, and the alternative tie-point distribution. Errors in the assumption of zero velocity at these tie-point locations were also simulated. In all cases the residual baseline errors were, at most, just a few centimetres. We can therefore be confident that baseline error will account for no more than a few cm/y of error in the v^ results.

6 6 Near-range Far-range

Figure 4.9 Predicted v, error per centimetre of baseline error (assuming = in equation 4.17). A large zero-offset has been removed, since any such offset would be compensated in the computation of the unwrapping constant by the use of tie-points (see Appendix 2).

4.4 Errors in the computation of the 3D velocity vector

4.4.1 Validity of the surface-parallel flow assumption This work uses two different methods to compute the full 3 dimensional velocity vector v (see section 2.4), both of which make the assumption that ice is flowing tangentially to the surface topography. In fact, v has a small component perpendicular to the surface, known as the "emergence" velocity in the ablation zone, and "submergence" velocity in the accumulation zone (Paterson, 1994). In steady state it is equal to the local mass balance, which for Austfonna is not expected to exceed a few decimetres per year (Dowdeswell and Die wry, 1989). The impact of this error will be further reduced in areas of bumpy terrain, where the vertical component of surface-parallel motion is relatively large (Joughin et al., 1998).

4.4.2 Problem with the "method b" velocitv determination This section discusses a limitation to the method of determining ice velocity vector v by assuming a flow direction, which is employed when only one SAR look direction is available (see section 3.5.2). Clearly, as the ice flow vector approaches a direction that is perpendicular to the look-direction, the component becomes very small, inhibiting our ability to measure it accurately, even if the flow azimuth and slope are accurately known. In order to investigate this, an "ideal" ice cap (Paterson, 1994), with dimensions similar to those of Austfonna was simulated. Its velocity, uniformly increased from

67 zero at the central ice divide to a maximum at the margin. Flow azimuth was parallel to the direction of maximum slope, and so all possible flow directions were represented. Using typical ERS-1 parameters, synthetic topographic and displacement interferograms were generated for the ice cap and used to compute the line-of-sight velocity component in the same way as described for the real data in Chapter 3. Taking flow direction as the direction of maximum slope, it was then possible to compute "method-b" velocity as described in section 3.5.1. The difference - Vjdeail was calculated, and its value as a percentage of Vjdeai was taken as a measure of velocity error Av^. In Figure 4.10, this is plotted against K, which is defined in equation 2.37. The errors can be seen to increase rapidly as K approaches zero, indicating that areas where the magnitude of K falls below about 0.1 should be avoided.

1500

1000

500

-0.4 0.2 0 .4 0.6

Figure 4.10 Percentage error introduced in simulated data by the "method b" velocity determination technique.

68 5. Verification of results

This chapter will describe how the topography and velocity results obtained in Chapter 3 were validated. Where multiple solutions were obtained, these will be compared to determine their repeatability. The results will also be compared with external data-sets, where these are available. Apparent anomalies will be discussed in the context of the error sources predicted in the previous chapter.

5.1 Interferometrically derived DEMs of Austfonna Two digital elevation models of Austfonna were created, each requiring the input of three ERS-1 SAR images. The first was obtained using First Ice Phase (1992) data, and the second using Second Ice Phase (1994) data, as detailed in Table 3.2. This section will compare the two DEMs and show that one of them contains anomalies, the origin of which will be discussed. The DEMs will also be compared to an external data-set to determine their relative accuracy. The accuracy of the final result will then be established.

5.1.1 Comparison of the 1992 and 1994 topographv results Figure 5.1 presents the magnitude of the height difference between the two interferometrically derived Austfonna DEMs. There are large, isolated patches where the differences have an amplitude of 40 - 60m. Such height changes are too large to represent a real physical change in the ice cap over the two year time gap between the two data-sets, and are hence concluded to be errors. They appear mainly to affect the far-range portion of the image. The profile in Figure 5.1b suggests a possible quasi-periodic structure, with a wavelength of a few tens of kilometres. Their alignment with the direction of the streak anomalies discussed in section 4.1.1 may suggest a common origin. If the long-wavelength height errors were related to measurement errors due to temporal changes in the backscatter cross-section at the surface, we would expect to see corresponding areas of low correlation for at least one of the pairs used. However, an examination of Figure 3.5 shows no clear relationship between poor correlation and height error. More explicitly, section 4.2.1 quantified the expected scatter-related height errors for each DEM. Figure 5.2 shows that there is no correspondence in character or magnitude, with the predicted errors being much smaller than those observed. Joughin (1995) found similar long-wavelength quasi-sinusoidal height errors in interferometrically derived DEMs of Greenland. He suggested that they may be an artefact of the UK-PAF processor which, at that time, was not phase-preserving. However the images used in this research were processed by DPAF, which did have a phase-preserving processor, so the source of the problem must lie elsewhere. The anomalies are most likely to be caused by phase-travel errors (Section 4.1.2). Non-linear orbit perturbations could produce errors of this magnitude. These might be

69 expected to affect the result across its full range-extent, rather than just the far-range portion. However the DEMs are formed by combining two interferograms, and it is plausible that interactions between the two may have cancelled the errors locally. A second possible origin of the anomalies lies in quasi-periodic travelling ionospheric disturbances. A 60m height error would require a phase error of between 2.6 and 5.2 radians, depending on the baseline of the affected image pair. These values are of the same order of magnitude predicted for TID effects by Tarayre and Massonnet (1996).

H eight Difference (m)

60 ft 1 1 40 Cl Î, r / 20 \ n ■ ^ 0 16 32 48 64 D Distance (km)

D Height Difference b)

20 km no data 0 k 60m

Figure 5.1 a) Magnitude of the height difference between the 1992 and 1994 interferometric DEMs. b) Profile across the line CD.

1992 A z0s (m )

^ ujwIüaü u

Distance (km) Distance (km)

Figure 5.2 Correlation related height errors across the CD profile in Figure 5.1 for a) the 1992 DEM and b) the 1994 DEM. Figure 4.4 shows these errors for the full scene. There is no correspondence in character or magnitude to the errors observed in Figure 5.1.

70 5.1.2 Comparison of interferometric DEMs with an external data set The flightlines of the 1983 NP-SPRI radio echo sounding mission, discussed in Chapter 1, are shown in Figure 5.3, and the magnitude of the differences between the 17000 RES height measurements and the two interferometric DEMs are shown in Figure 5.4. The standard deviations of these differences are 28m for the 1992 DEM and 19m for 1994 DEM (the average differences are close to zero, as expected, because any bias was removed during the baseline constraint procedure). Figure 5.4a clearly shows that the higher standard deviation for the 1992 DEM is due to large height differences of 40 - 60m amplitude, in the same regions that similar differences occurred in Eigure 5.2. This suggests that it is the 1992 DEM alone that is affected by the observed large amplitude

a) 80.5N-

;ighbreen

Vestfonna 80.0N-

Xi 79.5N-

22E 26E

b) Nordaustlandet p~] 1 Transponder received r ~ | 2 or more transponders ^—-I received f I Transponder location n) # Transponder and geoceiver

80.0N- 'C / SVALBARD

• Austfonna

& 79.5N-

40km

20E 22E

Figure 5.3 Details of the NP-SPRI radio echo sounding survey, after Dowdeswell et al. (1986). a) Flight lines over the Nordaustlandet ice caps. Dashed lines show where RES bedrock returns were not received, b) Location of transponders and georeceivers on Austfonna, and the area over which the aircraft received range information from transponders.

71 phase-travel errors. For this reason only the 1994 DEM was used in the subsequent procedures to isolate surface displacement and estimate flow azimuth. A comparison of Figures 5.3a and 5.4 shows a clear difference in the number of flight-lines in the RES data-set. Part of the data-set is currently missing (A.M. Nuttall, personal communication). The data-gap is a particular problem in the Basin 3 area, which is of central interest to this thesis.

a) Difference between 1992 DEM and RES data b) Difference between 1994 DEM and RES data

SON

79N

height difference

Figure 5.4 Height differences between the interferometrically derived DEMs and the radio echo sounding height data set of Dowdeswell et al {1986).

5.1.3 The accuracy of the 1994 DEM As stated above, the standard deviation between the 1994 interferometric DEM and the complete radio echo sounding data-set was 19m. However there are zonal biases in both sets of results, which must be taken into account when establishing the accuracy of the interferometric DEM. The accuracy of the RES data was determined by Dowdeswell et al., (1986). A comparison of height measurements at 251 flightline crossover points, gave a mean height- difference magnitude of 11.2m. However, Figure 5.3b shows that geographic location was difficult to establish in some areas of Austfonna, because only one transponder fix was available. Crossover differences in these zones were as high as 40m, with the highest errors occurring in the areas of steepest slope. Therefore, in using the RES data to help establish an accuracy estimate for the 1994 DEM, it was considered useful to isolate RES points from within the zone where two or more transponder fixes were available. 72 1800 RES heights were extracted from this zone, and their comparison with the interferometric DEM gave a standard deviation of 9.85m. It is not clear how this error is apportioned between the two data sets. However, referring to Figure 4.4b, using the same set of 1800 locations, the average predicted correlation-dependent height error in the 1994 interferometric DEM is 6.4m. This implies that phase-scatter error is a dominant source of error in this zone. As shown in the previous section there is no evidence of any local phase-travel errors affecting the 1994 DEM. It may therefore be inferred that the dominance of the phase-scatter error will prevail over the full extent of the ice cap. A first estimate of the errors in the 1994 DEM is therefore provided by Figure 4.4b, which predicts uncertainties of less than 5m in the western part of the ice cap, and up to 15m in the east. On average this error is 8 m (s.d. = 5m). As discussed in Section 4.2.3 there may additionally be, on average, around 2m of baseline-related error. We cannot quantify this explicitly by comparing the interferometric DEM to the RES data, because the interferometric data was "fitted", in a least squares sense, to the RES data during the baseline estimation procedure. However, combining the predicted value with the phase-related height error allows the average accuracy of the 1994 Austfonna DEM to be estimated at 10m.

5.2 Line of sight velocitv field Austfonna's line-of-sight velocity field was computed nine times, using the nine interferometric pairs listed in Table 3.1. This section will compare the results to determine their repeatability. Long wavelength anomalies will be identified in some of the results, and the origin of these will be discussed. Despite these anomalous differences, we will identify real temporal velocity changes within at least one of the ice cap's drainage basins.

5.2.1 Accuracv and repeatability of the ascending line-of-sight velocity results Figure 5.5 shows the nine line-of-sight velocity results. There is a lot of variability, with the exception of 5.5d and 5.5e which are very similar. It is not possible to assess the accuracy of the results in comparison with external ground-truth, as the only previously published velocity profile (Dowdeswell and Drewry, 1989) was aligned perpendicular to the SAR look direction (see Section 5.3.1). However, on comparison with Figure 1.2, which shows the basin geography of Austfonna, it can be seen that the two similar results, 5.5d and 5.5e, also closely resemble the velocity distribution that would be predicted from theory, with near-zero Vr at ice-divides. Also, referring to Figure 5.18, the direction of flow in these two results is also as predicted, with zones in western Austfonna having negative components, and those in the east being positive. It is possible to make a crude assessment of the accuracy of 5.5e and 5.5d. Note that the colour scale in Figure 5.5 is non-linear, and areas with a v,. magnitude of less than 1 have been given one colour. The reason for this can be seen by examining Figure 5.6,

73 a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

d ) 6th/9th Jan. ‘94 e) 9th/12th Jan. ‘94 0 12th/15th Jan. ‘94

k ' g) 24th/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

Vr (m /y) 20 km /V No data -24 -5 -1 1 5 10 15 20 25 30 35 40 80 /

Figure 5.5 Line-of-sight velocity field vfj)for each of the interferometric pairs listed in Table 3.1. Note the non-linear colour scale, which is designed to enhance both low and high velocity features. which is the profile KL from Figure 5.5e. The velocity should be zero in this region of bedrock, but there is a slight ramp across it, amounting to a few tens of cm/y. This is consistent with predictions of the effects of baseline error made in Section 4.4.2 (the high frequency signal is due to the combined effects of topographic error and phase error). The colour scale chosen subsumes this error, to provide blanket coverage of the bedrock region and enhancement of the ice divides in Figures 5.5e, to which we can therefore attach an

74 error estimate of ±lm/y. This value is consistent with predictions made in the previous chapter.

(m /y). 0.4-

0.2

0.0

- 0 . 2-

-0 .4

0km 8km 16km 24km 32km

Figure 5.6 Line of sight velocity along the KL profile in Figure 5.5e.

The same colour scale has been applied to all of the results, but with variable success. Figure 5.5i is an extreme example, showing no correspondence between the v, m inimum and the known position of the ice divides. As we have obtained an assessment of the accuracy of 5.5e, which will be referred to as v/^^(/), the errors in the other results will be quantified with respect to this. The variation of each of the v^. results with respect to is shown in Figure 5.7. With the exception of 5.7d the images can be seen to be affected by regional anomalies, with a maximum amplitude of up 9m/y. In general the anomalies take the form of a west-east trended banding (the superimposed variations, confined to specific drainage basins, are discussed in the next section). There are both positive and negative components but these are not similarly positioned in all pairs. To check that the phenomenon was not a feature of the reference image, similar plots were produced using alternative references, and similarly banded variations appeared. Figure 5.8 shows profiles taken across the velocity variations. Some of the figures (e.g. 5.8b, 5.8g) demonstrate a ramp-like regional trend. This may be accountable for by residual baseline error, though the gradients are much greater than those predicted in Section 4.3.2. The same set of tie-points was used to constrain the baselines of all nine interferometric configurations, but one explanation for a variable performance of this procedure could be that some of the data-sets were affected by phase-travel errors. Apart from the ramp effects there are a lot of similarities between the profiles (though two of the figures, 5.8f and 5.8g, show a sharp discontinuity, which is clearly an artefact of the phase unwrapping procedure). Bearing in mind that the same DEM was used to extract the topographic effects from all data-sets, this may suggestive of topographic error. However, quantitative analysis fails to corroborate this.

75 a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

D d) 6th/9th Jan. ‘94 0 12th/15th Jan. ‘94

g) 24ih/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

Vf difference (m/y) :::a r :i I 20 km & C no data .9 9 30 I______I /

Figure 5.7 The difference vfj) - using each of the line-of-sight velocity results v,(j) shown in Figure 5.5, and where is the reference result that was shown in Figure 5.5e.

For instance, the -3m/y trough in 5.8a would imply a height error in the DEM of 111m (referring to table 4.2). With respect to any existing regional trend, the same DEM error would be expected to produce errors of + 8 m, -3m, -3m, -i-7m, -i- 6 m, -0.3m and -b 8 m in 5.8b, c, d, f, g, h and i respectively. However, the corresponding anomalies in these profiles do not have these predicted amplitudes. Furthermore, as indicated in section 5.1, comparisons with an external data set have indicated that the DEM errors in this region are much smaller than 111m. Figure 4.8 predicted topography-related v, errors of less than

76 Im/y. All of the profiles show very short wavelength variations of this magnitude, which probably represent the topographic component of the error budget. As the two images that are least-affected by errors were formed using the same input data as the DEM (Table 3.2), the possibility of some form of registration error is suggested. As implied in Section 3.2, whereas intra-pair registration was performed to sub-pixel accuracy, the co-location between the interferograms and the DEM was, in most cases, less precise. Uniquely, the data-sets shown in Figures 5.7d and 5.7e are not only precisely registered to each other, but also to the DEM. Slight mis-registrations, of the order of a few pixels, between other image pairs and the DEM may have had the equivalent effect of introducing further topographic errors, the extent of which would vary, depending on the amount of mis-registration.

(m/y)

‘A " S.. . ■■

a) 13th/16th Feb. ‘92 b) 16th/19thFeb. ‘92 c) 20th/23rd Mar. ‘92

JL ! V

d) 6th/9th Jan. ‘94 f) 12th/15th Jan. ‘94

V« \----- ; ■ W •V if------

0 32 0 32 64 (km) g) 24th/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15tb/16tb Dec. ‘95

Figure 5.8 Profiles across the velocity-dijference results of Figure 5.7. The profile is the CD line shown in Figure 5.5e.

To investigate this potential explanation, the DEM was rotated clockwise around its centre point by 0.36°. This is the equivalent of introducing a misregistration at the extremes of the image of 2.5 multilook pixels. Within the unaveraged SLC images this is the equivalent of 10 range pixels and 50 azimuth pixels, so it is clearly far greater than any real misregistration we might expect to find between images (see section 3.2). The rotated DEM was then used to remove the topographic phase component from each /i 2(/) (equation 2.29) and hence to produce a new image vf{j). The difference between v fij) and v fj) was then determined. An example can be seen in Figure 5.9, and clearly shows that even a very dramatic mis-registration of an image pair to the DEM could not be responsible for the character or magnitude of the observed anomalies. Registration offsets in the form of 77 integral xly shifts, as opposed to rotations, were also tried, again with no convincing outcome. Furthermore, as the data-sets corresponding to Figures 5.5e and 5.5f shared a common input image, it was possible to precisely register the latter to the DEM, to see if this reduced the anomalies observed in Figure 5.7f. No change was perceptible, however, indicating that DEM registration could not be the source of the problem. For still further confirmation, the effect of using the First Ice Phase DEM, instead of the Second Ice Phase DEM, for the extraction of topographic effects was investigated. As mis-registration of each data set would then be different to that of the previous situation, and indeed zero for 5.5a and 5.5b, the anomalies would be expected to change accordingly. The resulting v,. images were given the notation v/{j), and their variations, relative to the same reference as used in Figure 5.7, are plotted in Figure 5.10. Comparing with Figure 5.7 and Figure 5.1, it can be seen that the effect has been simply to introduce additional anomalies corresponding to height errors in the First Ice Phase DEM. These can be most clearly seen in 5.10d and 5.10e, for which the equivalent plots in Figure 5.7 remained at or close to the zero level. The magnitudes of the additional effects are as predicted for topography-related errors in Table 4.2, being proportional to the sign and magnitude of the baseline of each interferometric pair.

Vf difference (m/y) 2 0 km m no data -0.5 0.5 0.5 14.0

Figure 5.9 Velocity difference vf(j) - vfj) where vf(j) was produced using a deliberately mal-registered DEM, and both vf(j) and vfj) were formed using the SAR scenes that were acquired on 9th/12th Jan '94.

78 a) 13th/16th Feb. ‘92 b) 16th/19th Feb. ‘92 c) 20th/23rd Mar. ‘92

d) 6th/9th Jan. ‘94 e) 9th/12th Jan. ‘94 0 12th/15th Jan. ‘94

g) 24th/27th Jan. ‘94 h) 5th/8th Feb. ‘94 i) 15th/16th Dec. ‘95

difference (m/y) 20 km ^ no data 9 30 I------1

Figure 5.10 The effect of using the 1992 DEM instead of the 1994 DEM in computing the velocity' results. The plots show v/(j) - Vr'^^^(j) where is the reference result shown in Figure 5.5e, and each v/(j) was computed using the 1992 DEM.

The east-west trend of the anomalies is very reminiscent of the streak effects discussed in section 4.1.2. As these effects are related to fluctuations of up to ±2 pixels in the y- component of the registration offset it is possible that they could bias the fine registration function. Such an effect would be expected to express itself in the correlation images of Figure 3.5, however, yet there is no correspondence between the anomalies and the patterns of low correlation seen in that figure.

79 Having discounted all other potential explanations, it seems that the observed anomalies are most likely to be caused by phase-travel errors. Their similarity in trend to the errors seen in the First Ice Phase DEM (Figure 5.1) suggests a common origin. The regularity of the features, and their approximate alignment with the x axis, suggests that non-linear orbit perturbations could be the problem. Alternatively, travelling ionospheric disturbances could have produced these effects. From Section 4.3.1, a Im/y v, error requires a phase error of 1.8 radians, so the observed velocity errors are of the same order of magnitude predicted for TID effects in Section 4.1.2. Note that the data-sets were obtained over a four year period, and the anomalies affect 7 out of 9 interferometric pairs studied. This is a high "failure" rate, and confirms the findings of other workers (e.g. Massonnet and Feigl, 1995) that phase-travel anomalies are a significant and unpredictable error source in interferometric measurements. Because of the variable nature of the anomalies, and their further complication by the possible presence of real velocity changes (see Section 5.2.3) no attempt was made to remove them.

y

N o data

Figure 5.11 Descending line-of-sight velocity v/(j). The result was formed using an interferometric pair acquired on 12th/15th February 1992. The corresponding amplitude image and interferogram can be seen in Figure 3.8.

80 5.2.2 Accuracy of the descending line-of-sight velocity results As described in Section 3.5.1, a single First Ice Phase interferometric pair was used to compute part of Austfonna's descending line-of-sight velocity field, v/(/'), and this result is shown in Figure 5.11. The accuracy of this descending result cannot be so rigorously assessed as the ascending results as there are no repeat solutions with which to compare it. There are no ice divides within the area of interest, but there are two bedrock regions (Figure 3.8a) which ought in principle to yield zero v/. In these zones the average value of v/ is zero and its standard deviation is 0.7m/y. Comparing Figure 5.11 to Figure 1.2, the pattern of flow appears consistent with the basin geometry of this part of Austfonna. There is therefore no cause to suspect that this data-set is affected by the long wavelength phase- travel anomalies that affected so many of the ascending results. The v/(/) result is therefore assumed to have an error of less than Im/y.

5.2.3 Temporal line-of-sight velocitv variations Referring back to Figure 5.7, it can be seen that in the region known as Basin 3 (see Figure 1.2), the First Ice Phase data sets (a,b,c) and, to a lesser extent, the Tandem data set (i) show an "anomaly" that saturates the colour scale, and is significantly above the level of the previously observed errors. It is always positive, and always occurs in the same position, confined to the region of Basin 3's fast flowing outlet, suggesting that this effect may represent a real change in that basin's flow velocity relative to the measured 1994 levels. Similar, though much more subtle, and therefore less conclusive changes are apparent in some of the other basins too. It should be noted that the observed accelerations are not large enough to introduce significant errors into the topography results, as discussed in section 4.2.2. The apparent changes can be examined further using the corresponding phase- difference images. Figure 5.12 magnifies the region of three of Austfonna's prominent drainage basins, and compares a Second Ice Phase data-set to one from the First Ice Phase. Whereas the fringe patterns for Leighbreen and Duvebreen show little change, in the region of Basin 3 there a marked variation in the fringe rate, suggesting a much lower velocity gradient in 1994 relative to 1992. Figure 5.13 shows line-of-sight velocity profiles beginning at local ice divides and trending along the main axis of each of the three drainage basins (see Fig.5.5e for profile locations). The Basin 3 profile shows a clear split between the First Ice Phase and Second Ice phase profiles, with the 1994 data giving velocities around 50% slower than those of 1992. The Tandem Phase profile plots between the two Ice Phase positions, indicating velocities of around 80% of the 1992 estimates. Apparent intra-annual variations between the profiles occur in all three drainage basins, but correspond to the long wavelength anomalies discussed previously. The dominant presence of these anomalies

81 13th/16th Feb. ‘92 9th/12th Jan. ‘94 a)

20 km phase difference

Figure 5.12 Portions of the motion-only phase-difference images for three of Austfonna's most prominent drainage basins, a) Duvebreen, b) Basin 3 and c) Leighbreen. The positions of these sub-images within the SAR frame are shown in Figure 3.3. The images on the left were formed using acquisitions from 13th/16th Feb. '92, and the corresponding dates for the images on the right are 9th/12th Jan. '94. Each 0 - 271 phase increase represents a v^ increase of 3.5m/y. Duvebreen and Leighbreen exhibit no significant change between the two data-sets. Basin 3, however, displays a significant change between 1992 and 1994. Its fringe rate, and hence its velocity gradient, can be seen to have reduced by a factor of approximately 2. ensures that the possible inter-annual velocity changes that Figure 5.7 suggests may have occurred in Duvebreen and Leighbreen are too subtle to be apparent in Figure 5.13. It should be noted that the large changes in Basin 3's interferometric signature are unlikely to be due to tidal uplift. The area is thought to be grounded (Dowdeswell et al., 1986) despite being associated with bedrock below sea level (Figure 1.4). To corroborate this, the temporal baselines of the multiple results were cross-referenced against local tide tables, and there was no evidence of a correlation (A.M. Nuttall, personal communication). 82 Vf ■t------a) 13/16 Feb ‘92 uuveoreen b) 16/19 Feb ‘92

c) 20/23 Mar ‘92 ) ] d) 06/0 9 Jan ‘94 ) ) e) 09 /1 2 Jan ‘94 0 12/15 Jan ‘94 g) 24/27 Jan ‘94 0km 16km 32km h) 05/08 Feb ‘94 G H 7Q g i ) 15/16 Dec ‘95 6 0 4 - Leighbreen 50 4 0 30 20 10 0 -10 0km 16km 32km 48km

Basin 3 1992

—-/-W4

0km 16km 32km 48km

Figure 5.13 Line-of-sight velocity profiles from the centre line of three of Austfonna's prominent drainage basins (see Figure 5.5efor locations).

5.3 Ice velocity vector v As described in section 3.5, two methods were employed to convert Austfonna's line-of- sight velocity v^ip) to the full three dimensional velocity vector v(/?). The preferred method combined ascending and descending SAR data. This section will begin by discussing the accuracy of the resulting velocity field, and will compare it to an external data-set. The performance of the second method with respect to the first will then be discussed.

5.3.1 Velocitv results obtained by combining ascending and descending SAR data Figure 5.14 shows the "method a" velocity field v^,(p) that was derived by combining ascending and descending SAR data (Section 3.5.1). It also shows the corresponding horizontal and vertical velocity fields, v^(p) and v,(p), calculated using equations (2.31) and (2.33). These results were only obtainable for a small portion of the Austfonna scene 83 N o data Va (m /y)

N o data 0 V/, (m /y)

a m

N o data

Figure 5.14 a) Interferometrically derived velocity field of part of Austfonna, obtained by combining overlapping ascending and descending SAR scenes obtained between the 12th and 15th of February 1992. Lettering will be referred to in Section 6.4. Some coastal detail has been lost in the high velocity regions because the corresponding tightness of the interferometric fringe hindered the unwrapping process, b) Horizontal component of the velocity field. Profdes relate to the velocity survey lines shown in Figure 5.16. c) Vertical component of the velocity field. It should be noted that this is the vertical component of the assumed surface-parallel flow, and not the emergence/submergence velocity (Section 4.4.1). The figure highlights the relative complexity of flow in regions of rough terrain, such as Basin 3 and Basin 5.

84 where overlapping descending data was available (Figure 3.2). To date we have obtained only First Ice Phase descending data (Table 3.3), and so these velocity results were computed only once, using SAR data acquired between the 12th and 15th of February 1992. The accuracy of thev^ip) result will depend on the accuracy of the ascending and descending line-of-sight velocity results, v^ip) and Vr'ip'), from which it was formed, the contribution of each varying according to flow direction and surface slope. Referring to Figure 5.7a, the accuracy of the relevant v^ip) in the area of interest is -2.5m/y relative to the result shown in Figure 5.5e, which in turn has an average accuracy of ±lm/y. An average "worst case" error magnitude for v,{p) can therefore be estimated as 3.5m/y. As discussed in Section 5.2.2, the magnitude of the error in v/(/?') is estimated as Im/y. Using equation (2.34), the corresponding average "worst case" velocity error for v^ip) is 1 Im/y (standard deviation = Im/y). Figure 5.15 shows the flow azimuth %(p), which was calculated using equation (2.35). Comparing with the flow azimuth predicted from theory (Figure 5.18) it can be seen that there are large differences in the low velocity region to the north-east, but good agreement elsewhere. This is because, in percentage terms the errors in and v/ are higher in this region than elsewhere.

20km

^.jg||5sns-*

Figure 5.15 Flow azimuth of the "method a ” velocity field, calculated using equation (2.^.5).

The only previously published velocity data for Austfonna was obtained in the late 1980s (Dowdeswell and Drewry, 1989). Two profiles were obtained from the region of Basin 5 (Figure 5.16). A network of stakes was surveyed in May 1986 and again in May 1988, and so the measured velocities represent a two-year average over this period. The published parameter was horizontal velocity, and Figure 5.17 compares these results to the interferometrically derived horizontal velocity vfp). The surveyed data did not extend to the ice-cap margin because the survey team encountered heavy crevassing half way down the basin. The two data sets therefore overlap by just a few kilometres. Because the survey results are a two-year average, whereas the interferometric results are a three-day average obtained four years later during winter, we would not

85 necessarily expect good agreement between the two data-sets. In fact the results can be seen to agree within about lOm/y. This is comparable with the predicted "worst case" error discussed above, and also with the error magnitudes reported by Mohr et al. (1998) who used this method of combining ascending and descending data in Greenland.

600 7 00

600

5 0 0 .

■403

•3 0 0 -

200-

100

HART0G8UKTA

Figure 5.16 After Dowdeswell and Drewry (1989) showing the position of surveyed velocity profdes obtained between 1986 and 1988. N E profile Vh

1Q IS 17 V" I* ^ ^ l y Q ^ 7 • < • ------i

SW profile

80

60 JA. i r • L6 40 JU. 26- 20

0 0km 8km 16km 24km 32km

Figure 5.17 Comparison between interferometric and surveyed velocities. Numbers refer to survey points in Figure 5.16.

5.3.2 Velocity results obtained by assuming a flow direction The second method of calculating the three dimensional velocity vector required the computation of a flow direction image yb under the assumption that the ice was flowing in the direction of maximum slope, averaged over 10 ice thicknesses. These slopes were obtained using the 1994 interferometric DEM, and the resultant flow direction image is as shown in Figure 5.18. The velocity field v^ip) was then calculated using equation (2.36). Two examples of the result, one from 1992 and the other from 1994, are shown in Figure 5.19. It can be seen that in addition to those drainage basin areas where velocities are known to be high, there are what appear to be anomalously high velocity regions in the centre of the cap. Figure 5.20 is a plot of the velocity conversion factor K (see equation 2.37). As described in section 4.4, the accuracy of the conversion of to diminishes as K tends to zero. The unexpectedly high velocity regions correspond closely to those zones w here K is less than around 0.1, consistent with predictions made in that section. Referring to Figures 1.2 and 5.18, it can be seen that the low K regions are generally related to ice divides (low p) and regions where flow is perpendicular to the look direction (high Ÿ)- Figure 5.21 is a plot of the difference between the two 1992 velocity results, and v^. There are large differences between the two, but the largest errors occur in the low K regions previously observed. If areas where ^<0.1 are ignored then the average velocity difference is 3m/y with a standard deviation of 12m/y.

87 ,'C>n

tS %###%# KK^ ^t3 n'Ù'Ù'Ù'ù^ at^î3î3H

4-<>04>44><^4> -%! R RR ^

v4 V ^ ^ ? * î^ ❖ Ïïî-£ ? s R U K U R « ^î” C? ^ 4^-ÿl Î5-J3-fl î3 a 53 a R a R R R JTÎl 53 R ij ^^u»u\;sK R ^^R R ^^^-^'£i-£iR a5aa?i'S3-£i'ii^-£3a jjjÿj;7jÿj!7J7RRjjaaRX7i;? ,VCt < ^^»^R i^R R U U W K K R C ïl^^^^‘»^'îiï3î3RRa«-ï3^^î3RJ7JÇ.^;7J7^7J7JJRRRnj;?a ^ ^^RRU R ^RK\:i^uwu^ KRt? R awj;7^^w»R»»aaaa RRR

^ ^ R KUv^

^ R aaa^R ^^KUKugi.' -Pai3<^R<>44RRRUUv-

.&BBBBB&&&BB •BBBBBK£f£f£?BB ❖'Î7 .[itttiüiT^ <>'ùi^ •^BBBKKH/iMKB 7i3i)^3 .BK£f£fB A .bbbbbk««bbb î3 'vK> #KÜ8 K# #"6# ^&BBBBBBKBB bbb b b BB*£s | w ,^£f«£f£T tJ ^ tili <).BBBBBBBB\^^^W ,<7#«BB%«#.ÜBB-babb , ^\f£SCtl:sùS£î K ^ t\T^ ■\5>^I^BB B B B B ^ i] i3^. ,B^bb%bbb##Bbbbb 4-^ .^BBAAZY^K a « a \>BBBBBBBB^^-bt]^)._ <7b b a a « a b b b b b b b ^ K Cf B «Mî3 'tJ^VÎ-BB B B B B B \î. ^-ÎJ ^bbb bbbbbbbbü ^ K ff B ■ ■ BBBBBBBB^^'aS'a^^^ ^bbbbbb bbbbbB f; :*.^\>BB ^r^tstsbtùtts « B -Î7 a .BBBBBBB^^^-î7-î7 ^^-b bbbbbbb bBBaa *a ’BBBBBB^-6^-b^^<7 # bbbbbbbbbbBB# _ , B-(7 . ’BBBBBB^^'b«Î7<7<7^^-b bbbb^Sb^bbbbb BBBtî>^5rtt BB B B'tr&&5^<7<7<7<7<7^ b b b b b b b b b BBB bb b b b b K^ï BBBB' ’^ùftltStSt}.___ bbb B gB B B B :^^r£r£r£f£f/^ B B _____ IIIS'’ Bb- BB B bbbbb< 7 &B %KG u s BB^BB '^^•b -b b BBBBB :B^^;t^BB-B-b-baa ^S^l^-î^a^bb-bB BBBBB B B B ^ < 7 b a BBBBB- îiîrcf B-B B B B B ^b bbiBB BBBBB^ ^BBBB^ ■T>-ç> b bbBB B T^ b b b # B ; ^ _ BBBBBr B B B b ^ B B B b b b b b B B - ^

.4^ 20km Lx /

Figure 5.18 F/ow direction yb derived by averaging the 1994 interferometric DEM over ten ice thicknesses and computing the direction of maximum slope.

The differences can be more easily seen in profile form. Figure 5.22 shows the IJ profile (marked on Figure 5.5e) from the centre axis of Basin 3. The 1992 v^ profile can be seen to be very noisy in comparison with the corresponding profile. The figure shows that errors in the assumed flow direction may be responsible for this high frequency noise. No attempts were made to improve the result by varying the number of ice thicknesses over which the slope was averaged. It should be noted, however, that the errors in V/, are small in comparison to the large differences between Basin 3's 1992 and 1994 velocity results which were observed in Section 5.2.3 and which are confirmed by Figure 5.22. a) 1992 velocity b) 1994 velocity

20 km t l x / N o data 0 Vh (m /y)

Figure 5.19 Interferometrically derived velocity field of Austfonna obtained by assuming a flow direction. The results were computed using interferometric pairs obtained on a) I3th/I6th February 1992 and b) 9th/I2th January 1994.

W M m

No data 0.00 0.02 0.04 0.06 0.08 0.10 1.00 lY . 20 km . K

Figure 5.20 The velocity convebion factor K, calculated using equation 2.37.

89 t l . /

N o data 0 Iva - Vbl (m /y) 60

Figure 5.21 Differences between the two three-dimensional velocity results obtained using the two different methods described in Section 3.5.

m/y, k------14C Ik, * Vb 13th/16th Feb ‘92 120 ] iw V/, 09th/12th Jan ‘94 IOC Va 13th/16th Feb ‘92 80 .ilk r Jii. 1 r 60 40 20 0 -20 dc‘ 20 ( 0 y -20 -40 k A J f N l / V - 6(

/ - 8 ( ■ t ' ! -l(X I -I2 (

Figure 5.22 a) Comparison of the three-dimensional velocity’ results for the IJ profile (Fig 5.5e) which is aligned with the central axis of Basin 3. b) Comparison between assumed and calculated flow directions.

90 6. Discussion

This chapter will present the final results, and discuss their significance in terms of Austfonna's glaciological structure. The velocity structure will be considered in terms of previous models of the ice cap's thermal structure, and comparisons will be made with other Arctic ice caps. The observations of unstable flow will then be discussed, and attempts will be made to put them into context with regard to what little is known of glacier velocity variations generally. Finally, some comments on Austfonna's mass balance will be made, based on the interferometrically derived velocity results.

6.1 Summary of results There are three principle results of this thesis; a high resolution digital elevation model of Austfonna (Unwin and Wingham, 1998); synoptic maps of its velocity structure; and evidence of unsteady flow in at least one of its drainage basins (Dowdeswell et al., submitted 1998). Chapter 5 discussed the validity of each of these results, and this section summarises its findings and presents the results in their final form. Figure 6.1 shows the interferometrically derived digital elevation model of Austfonna that was derived using SAR data from ERS-l's Second Ice Phase (1994). Its average accuracy is estimated at 10m (Section 5.1.3). A comparison with Figure 1.2 allows the main features to be identified. Previously, the best available DEM of this area was that obtained by the 1983 NP-SPRI radio echo sounding survey (Figure 1.3). The flightlines for this mission were a nominal 5km apart (Figure 5.3). In contrast, the resolution of the SAR derived DEM presented here is 80m, and so it shows the surface of Austfonna in unprecedented detail. This result is to be used by the Norsk Polarinstitutt as the main data source in a full revision of official maps of the area (J. Amlien, personal communication). Figure 6.2 is a map of Austfonna's line-of-sight velocity field averaged over the period 9th - 12th January 1994. Again its resolution is 80m, and its average accuracy is estimated at Im/y (Section 5.2.1). Attempts to convert this result to a three-dimensional velocity field were hampered by a lack of overlapping SAR data acquired from a descending direction, though this was achieved for a small sub-section of the data (Figure 5.14). If a flow direction was assumed the 3D result for the whole ice cap could be obtained to an estimated average accuracy of 12m/y (Section 5.3.2), provided areas where the conversion factor K was less than 0.1 were rejected. However this is not necessary to the discussion below (Section 6.2), which shows that a significant amount of information can be obtained from the line-of-sight field alone. Figure 6.3 shows a time-series of velocity variations along the centre axis of one of Austfonna's most prominent drainage basins. Basin 3. Again this result is presented in terms of the line-of-sight velocity component in order to minimise the errors, but the

91 equivalent three-dimensional velocity result may be viewed in Figure 5.22. The results indicate that Basin 3's velocity was 50% lower in January 1994 than in February 1992, and that by December 1995 it had recovered up to 80% of its 1992 magnitude. As discussed in Section 5.2.1, the error in the 1994 result is Im/y. In contrast, the errors in the 1992 and 1995 results may be as high as 5m/y (Figure 5.7), but these errors are insignificant compared to the observed variations. The 1992 and 1994 results were derived multiply, but only one solution was obtained for 1995 (Figure 5.13).

Basin 2

80' 30’ Bor 30

80* OO BOfOO

70*30 70 * 30’

Figure 6.1 Digital elevation model of Austfonna a) in shaded surface format and b) contoured at 50m intervals. Its spatial resolution is 80m and its average accuracy is 10m. The result was obtained using three ERS-1 SAR images acquired on 6th/9th/12th January 1994.

92 Austdomeii

Sôrdomen

Vr (m/y) 20km No data -24 -5 -1 1 5 10 15 20 25 30 35 40 45

Figure 6.2 Austfonna's interferometrically derived line-of-sight velocity’ component in m/y, derived using ERS-1 SAR acquisitions from 9th/12th January 1994. Its accuracy is Im/y and its resolution is 80m. Numbers refer to the basin delineation in Figure 1.2. It may be useful to view this figure in conjunction with Figure 3.7a, which is essentially a contour image of the same result.

93 a) 70 f ------; ------13/16 Feb ‘92 60 Basin 3 (m /y) j\ 09/1 2 Jan ‘94 50 40 y ; / 15/16 D ec ‘95 30 ' 20 y 10 0 -10

b)

height 7 0 0 (m ) 6 0 » 5 0 » 4 0 » 300 200 10» 0 0km 16km 32km 48km

Figure 6.3 a) Four year time series of line-of-sight velocity profiles from the centre line of Basin 3 (see Fig 5.5e), showing temporal variations, h) The associated height profile.

6.2 Discussion of Austfonna’s velocitv structure Although vv is only the line-of-sight component of Austfonna's velocity field. Figures 3.7 and 6 .2 contain valuable information about the relative velocity of regions of the ice cap. The interior of the ice cap can be seen to demonstrate very low velocities, with \v,\ generally less than 5m/y. The margins are punctured by fast flowing units. Comparison with Figure

1.2 associates these units with individual drainage basins, which appear to be dynamically independent. Basins 3 and 14 are bounded by zones of high shear at their margins. Several of the faster flowing units extend back into the slower moving ice to within 5-10km of the central divide. Between these high velocity regions, other basins, e.g. Basins 6 and

1 1 , appear largely stagnant, with little or no increase in velocity from crest to coast.

accumulation area

Ice at pressure melting point

Figure 6.4 After Schytt ( 1969). Proposed thermal model of Austfonna.

94 This interferometrically derived snapshot of Austfonna’s velocity distribution is unprecedented, and forces a re-examination of past ideas about Austfonna's thermal structure. To date, only one model for this structure has been proposed. In seeking to suggest a mechanism for the 1938 surge of Brasvellbreen (Basin 1), Schytt (1969) proposed that the cap comprised a central region of temperate ice, surrounded by an outer ring of cold ice (Figure 6.4), where the definitions of "temperate" and "cold" are as given by Paterson (1994). He hypothesised that "occasionally the (temperate) ice from the interior may break through this barrier of cold ice and establish a profile in accordance with its own temperature conditions". Figure 6.5 summarises the available temperature measurements in the region. To date, only one basal temperature measurement has been acquired. This was from a Russian borehole (V. Zagorodnov, personal communication) at Austfonna's summit and was close to zero as predicted. Temperatures measured in the "outer ring" are much colder, but are mostly shallow measurements. The deepest, from a French borehole (Watts et al., 1997), penetrates only half the ice thickness (Figure 1.5). There is consequently no direct evidence that the outer part of Austfonna is frozen to its bed. Possible indirect evidence was put forward by Dowdeswell et al.'s (1986) discussion of a "relative lack" of bedrock returns in central areas of Austfonna during the NP-SPRI radio echo sounding survey. They suggested that warm ice could have lead to greater absorption and more internal scattering of the radar signal, hence reducing the likelihood of receiving echoes from the sub-stratum. However, careful examination of Figure 5.3a shows that in fact bedrock returns were much more likely to be received than not received

French Borehole (F)

D epth(m ) Tem perature (C; 7 (A' ^ 10 -6.2 30 -4.6 45 -T 9 60 -3.7 80 -3.7 101 -4.1 (7m) -6.4 ^ 136 -4.3 (8m) X y V Russian Borehole IR) -8 .6 ^ ' Depth(m) Temperature (C^ >-8.7 10 -3.5 160 -7.8 20km 566 -1.2 I I

Figure 6.5 Summary of measured temperatures within Austfonna. Shallow temperatures from Schytt (1964) and Dowdeswell (1984). French borehole data reproduced from Watts et al, (1997). Russian borehole data from V. Zagorodnov (personal communication).

95 in central Austfonna. The main losses occurred on just two tracks crossing the Leighbreen basin. These were flown at a much higher terrain clearance than other tracks (Dowdeswell et al., 1986), leading to greater signal attenuation and increased surface scattering, therefore reducing the possibility of receiving bedrock echoes. Dowdeswell (1986) examined the characteristics of several of Austfonna's drainage basins, by comparing profiles along their centre line with those predicted from theory for glaciers in equilibrium overlying a rigid bed. He found that a number of Austfonna's basins, numbers 5, 6 , 16 and 19 (Figure 1.2), may be cold bedded, because they have high surface profiles and high marginal driving stresses, implying that they are frozen to their bed. The four other basins in his study, numbers 1, 17, 3 and 10 all demonstrated low surface profiles, indicating that they were either not in equilibrium, or that basal sliding was taking place. As Basins 1 and 17 are both known to have surged this century (Hagen et al., 1993), their low surface profiles were attributed to a post-surge stagnation. The results presented here corroborate this interpretation, showing very low velocities in these two basins. The causes of the low surface profiles in Basins 3 and 10 were previously not known, but as there was some observational evidence that Basin 3 may be of surge type (Nordenskiold, 1875), Dowdeswell (1986) suggested that these two basins may also be in post-surge stagnation. However, the high velocities implied by Figure 6.2 show that these glaciers are not stagnant, and that their low surface profiles are instead likely to be associated with basal sliding (Paterson, 1994), whether over a hard bed or by deformation of an unlithified sub-strata. Some simple calculations confirm that the fast flow units seen at Austfonna's margins are moving too quickly to be accounted for by creep alone. Standard theory predicts that the surface velocity m of an outlet glacier that is frozen to its bed and deforming in simple shear is given by (Paterson, 1994) :

u = (pg sinp)”

(6. 1) where A and n are the flow law parameters, p is depth averaged ice density, g is the acceleration due to gravity, is surface slope and h is ice thickness. For a maximum temperature of 0°C, suitable values of the flow law parameters are n = 3 and A = 6.8E-24 s‘^Pa‘^ (Paterson, 1994). Taking p = 910 kgm"^ (Dowdeswell, 1986), u was calculated for points on the centre flow line as close as possible to the margins of the fast flowing outlets, and compared to the measured values (see Table 6.1). Measured velocities in Basins 3 and 14 were found to be two orders of magnitude greater than those that would be expected from creep alone, and in Basin 10, where the observed point was at the edge of the SAR scene, some 15km from the glacier margin, velocities were twice as high. If Austfonna's fast flowing glaciers are sliding, they cannot be cold bedded (Paterson, 1994). Schytt's model proposed that temperate ice from the centre of Austfonna could temporarily burst, i.e. "surge", through an outer cold ring. However, as such events

96 p h u Uf Vr (degrees) (m) (m/y) (m/y) (m/y) Basin 3 - 1.0 150 0 .2 0.07 47.8 Basin 10 -1.5 360 23 9.4 16.2 Basin 14 - 1.0 200 0 .6 0 .2 24.9 Table 6.1 Predicted surface creep velocity u was calculated using equation 6.1 for three of Austfonna's drainage basins. Ice thickness h was obtained from RES data (Dowdeswell et al, 1986). Slope p, was obtained from the interferometric DEM averaged over 10 ice thicknesses. The line-of-sight component of the creep velocity, Ur, was calculated as in equation 2.37 for comparison with measured line-of-sight velocity Vr. would be expected to be rare it seems unlikely that so many of Austfonna's basins could be "surging" at any one time. In fact there is evidence to suggest that the observed fast flow units are at least semi-permanent temperate features. As shown in Figure 5.5, they are present in the SAR derived results for 1992 and 1995”, as well as 1994. As discussed in section 6.3, high velocities were measured in the Basin 3 area in 1983, though there is evidence that this basin may have been moving more slowly in 1981. Dowdeswell et al. (1986) published a map of Austfonna's bedrock elevation (Figure 1.4), from which it can be seen that the fast flowing units are closely associated with bedrock troughs. McIntyre (1985) demonstrated a similar association in Marie Byrd Land, Antarctica, showing that while the ice-sheet's motion was dominated by internal deformation, the steep gradients of subglacial valley heads initiated the basal sliding and fast velocities seen in its outlet glaciers. He presented evidence that, once established, rapid ice flow through bedrock troughs would become a relatively permanent characteristic, through accentuation of the feature by erosion. The troughs associated with Basins 3, 10 and 13 are up to 157m below sea level, but the ice is not thought to be afloat because surface elevations are an order of magnitude greater than those predicted for an ice shelf (Dowdeswell et al., 1986). The emergence of turbid debris-rich subglacial melt water from these regions (Dowdeswell and Drewry, 1989) indicates that they are underlain by saturated deformable basal sediments. This provides further evidence that their associated outlet glaciers are warm bedded and "shding" by deformation of unlithified marine deposits that are saturated by meltwater from the glacier base. Such a mechanism for enhanced glacier flow was demonstrated by Boulton and Jones (1979). The thermal structure of Austfonna is clearly more complicated than the Schytt model suggests, with the cold outer ring, if it exists, being breached in several locations by warm bedded ice. The temperature measurements shown in Figure 6.5 indicate that the regime in these zones may be polythermal (Paterson, 1994), with a warm basal layer being overlain by cold ice. The preliminary interferometric results shown in Figures 6.6 - 6.8 indicate that a structure of slow moving ice, interspersed with fast flowing outlets is not unusual in Arctic ice caps of similar magnitudes to Austfonna. As mentioned in Chapter 1, such dynamics 97 are also seen in parts of Antarctica, where the transition from internal deformation to fast flow with basal sliding is thought to be of central importance to the ice sheet's stability (McIntyre, 1985).

20 km

Figure 6 . 6 a) ERS-1 SAR amplitude image of Vestfonna, Nordaustlandet, and b) interferogram with near-zero baseline, within which motion ejects dominate. The margins of the cap can be seen to be punctured by fast flowing units in a similar fashion to Austfonna.

0

20 km

Figure 6.7 a) ERS-1 SAR amplitude image of Academy Nauk, Severnaya Zemlya, and b) ERS-1/2 tandem interferogram with near-zero baseline. The southern margin is punctured by fast flowing outlet glaciers, whereas the northern margin appears to be stagnant.

98 10 km

Figure 6.8 a) ERS-1 SAR amplitude image of Zemlya Vilcheka, Franz Josef Land, and b) interferogram with 45m baseline, showing effects due to both topography and motion. Figures c) and d) show the equivalent images of neighbouring ice cap Ostrov Greem-Bell, which is comparatively stagnant.

6.3 Discussion of the observed velocitv variations This section will discuss the time series of velocity changes shown in Figure 6.3. In isolation, the 1992 and 1994 results might suggest that we had observed Basin 3 at the end of a period of surge activity, and that the glacier was in the process of decelerating to its pre-surge velocity profile. However the 1995 acceleration suggests that the reality is rather more complicated.

99 Because the interferometrically derived velocities represent three-day snapshots of velocity, it is not possible to establish whether the observed flow instabilities represent short term pulses, long-term trends or aliased medium-term variations. The only previously published velocity measurement in the Basin 3 region was acquired in the Spring of 1983 by the NP-SPRI expedition (Drewry and Liestpl, 1985), which surveyed a point near the centre line of the glacier, some 8 km from the coast, and found it to have a velocity of 0.82 m/day (300m/y), more than twice the 1992 interferometric measurement. There are reports that the basin may have surged between 1850 and 1873 when a Swedish expedition noted significant crevassing of its surface (Nordenskiold, 1875). The more recent surface characteristics can be examined using Landsat data. Figure 6.9 presents Landsat images from 1981 and 1993. The 1993 image shows a series of rough linear features, defining a flow unit 5 - 6 km wide, traversing from left to right beneath the ice dome. Digital superposition of this image onto the displacement interferogram shown in Figure 3.7a, indicates that the margins of this feature coincide closely with the edges of the observed fast flow unit (A.M. Nuttall, personal communication). In contrast, this feature is absent from the 1981 Landsat image. This shows a relatively smooth surface, with unbroken linear features transversely crossing the region that the more recent observations show to be fast flowing. The indication is that Basin 3 was moving much more slowly in 1981 than in 1993. If the isolated NP-SPRI observation can be relied upon (few details have been published) then the onset of fast flow must have occurred between 1981 and 1983.

J

Figure 6.9 Courtesy ofJ. DowdeswelL Landsat images of the Basin 3 area from 1st August 1981 and 1st August 1993. The pear shaped ice dome (1) is the surface manifestation of a subglacial hill. Radar-derived subglacial bed contours are shown in the 1981 image (Dowdeswell et al, 1986). Differences in brightness are due to variations in the degree of summer melting.

The evidence may arguably point to the fact that Basin 3 began surging between 1981 and 1983, and was still in its "active phase" in 1995. This would be consistent with the findings of Dowdeswell et al. (1991), that the active phase of surge-type glaciers in Svalbard is of greater duration than in other areas. Their survey showed that Svalbard

100 surges typically lasted 3 -1 0 years, in contrast to 1 - 2 years in north-west , Iceland and the Pamirs. However, the basin's behaviour is not consistent with the classic definition of a surge (Meier and Post, 1969). The Landsat images of Figure 6.9 show there has been no significant advance of the glacier's coastal margin. The surface profile of the basin was low in 1983 (Dowdeswell, 1986) and remained low in 1994 (Figure 6.3b), with no evidence of a characteristic wave, or "bulge", transporting large amounts of ice from a reservoir area to a receiving area. Its motion cannot be described as a "catastrophic advance" of the ice cap's margin, but is more consistent with an onset of stream-like flow. An ice stream is defined as a region in a grounded ice sheet in which the ice flows much faster than in the regions on either side (Paterson, 1994). It therefore has clearly defined shear zones at its edges. Most ice streams lie in deep channels with beds below sea level. Their characteristic surface slope is concave upwards, and their velocity increases towards their margins (Paterson, 1994). They are associated with low driving stresses, and may be able to switch between slow and fast modes of flow (Clarke, 1987) The observed flow unit in Basin 3 fulfils all of these criteria. As discussed in the introduction, changes in the dynamic behaviour of ice streams are thought to be strongly linked to the stability of the world's major ice sheets. Although differences in scale may preclude direct comparison, if the observation of the onset of streaming in Basin 3 is real, it is a potentially significant result. The opposite scenario is thought to have occurred in West Antarctica. The feature known as "Ice Stream C " was fast flowing as recently as 130 years ago (Shabtaie and Bentley, 1987), but has since stagnated to a flow velocity of around 5m/y (Whillans et al., 1987). Anandakrishnan and Alley (1997) have shown that this was due to a loss of lubrication at the bed, caused by a redirection of water into the channel below neighbouring Ice Stream B. A similar pairing between the fast flowing Rutford Ice Stream and its slower companion in the Carson Inlet drainage basin has been suggested by Doake et al. (1987). If the missing RES basal topography data (Section 5.1.2) can be relocated, it may be possible to map the hydrological potential in the region of Basin 3 and determine whether a similar event may have resulted in the onset of streaming in that region. As discussed in Chapter 1, Meier and Post (1969) raised the question of whether there was a distinct class of glaciers which surge, as opposed to a complete spectrum of activity from surges to ordinary advances. The continuous fast flow of ice streams has been described as a state of continuous surge (Weertman, 1964). So-called "pulsing" valley glaciers (Mayo, 1978) show velocity variations with yearly (e.g. Heinrichs et al., 1996), seasonal (e.g. Hodge, 1974) or daily (e.g. Kamb and Englehardt, 1987) temporal wavelengths. Our observations of Basin 3 appear to combine these forms of behaviour, as the area demonstrates streaming with a fluctuating velocity, though further monitoring would be required to determine the time-scale of the observed velocity variations. The area's apparent polythermal regime (Section 6.2) would tend to preclude a direct relationship between velocity and surface melting.

101 Alley et al. (1987) suggested that an ice stream moving by bed deformation should be stable against velocity perturbations because an increase in velocity would tend to thin the till layer. Though there are instances of ice streams decelerating (e.g. Stephenson and Bindschadler, 1988) and stagnating (e.g. Shabtaie and Bentley, 1987), reports of pulsing within ice streams are scarce. A notable exception is the observation of a dramatic pulse in the velocity of Greenland's Ryder Glacier, also observed using interferometry (Joughin et al., 1996). In contrast to valley glaciers, ice streams are relatively inaccessible, and so the lack of observations of pulsing may simply reflect the lack of velocity observations generally.

6.4 Some comments on Austfonna*s mass balance Very little is known of Austfonna's mass balance. Analysis of a Soviet core close to the ice cap's summit (Figure 6.5) indicated an accumulation rate of 400 to 500 kgm V^ averaged over a 400 year period (V. Zagorodnov, personal communication). Dowdeswell and Drewry (1989) used these figures to assess the accumulation rate for the Basin 5 area. They arrived at a figure of between 132 and 176 x 10^ m^a‘* for the region above the equilibrium line, but acknowledged that further accumulation occurred below this line via the formation of superimposed ice. It should be noted that their analysis was based on the assumption that the equihbrium line corresponded to a perceived peak in velocity measured along the glacier's longitudinal profile. This can be seen in Figure 5.17, which shows maxima in their surveyed velocities occurring at stakes 15 and 14 in the ne and sw profiles respectively. They predicted from theory (Paterson, 1994) that the velocity within the basin would decline from this location to the margin, and dynamic modelling studies of this basin have since been based upon this assumption (Watts et al., 1997). However, the interferometric results, also shown in Figure 5.17, suggest that in fact the basin's velocity increases towards the margin. This discrepancy arises because a significant amount of mass is lost via iceberg calving at the ice cap's margin, and suggests that the current assumed position of the equilibrium line may need to be revised. Figure 6.10 estimates the annual mass lost through calving along Austfonna's eastern margin, based on the interferometric velocity results in Figure 5.14a, and the NP- SPRI ice thickness data (Figure 1.5). The result is an approximation based on near-surface velocity, as opposed to depth-averaged velocity which might be expected to reduce the figures by around 20% (Paterson, 1994). Also, the interferometric results finish several kilometres short of the coast in some locations (Figure 5.14), due to unwrapping problems, introducing further uncertainty into the results. The fluctuating velocity in Basin 3 will further influence the calving rate, with the results in Figure 6.10 being based on its 1992 velocity. Bearing in mind these notes of caution, the figure indicates that the total calving- related ablation rate integrated along this 60km stretch of coast is 408 x 10^ m^a \ The corresponding values for Basin 3 (the AB stretch) and Basin 5 (the CD stretch) are, respectively, 115 x 10^ m^a‘* and 124 x 10^ m^a \ Mass loss due to calving is therefore a 102 highly significant contributor to Austfonna's mass budget, and it has not previously been quantified. It would be necessary to also quantify the amount of mass lost through meltwater production before determining whether or not the cap is in equilibrium.

M ass loss m 2 a 1

3 0000 !\ O AAAA 1 2 0000 i A S. ÂÜ1, 10000 ^ HJ'V s., ^ E c V 0km 1Okm 210km 3lOkm 410km 50km €»Okm

Figure 6.10 Estimated mass lost via iceberg calving along Austfonna's eastern margin. The profile follows the edge of the interferometric velocity result shown in Figure 5.14a, which does not reach the coast in some locations.

103 7. Conclusions

As outlined in Chapter 1, the objective of this thesis was to exploit a new remote sensing technique in examining the velocity structure of Austfonna, one of the largest ice caps outside of Antarctica and Greenland. Indirect evidence, and isolated observations, had indicated that it had the potential to be dynamically interesting, but few direct measurements had been obtained and the remoteness of the environment had ensured that only the most dramatic instabilities were likely to have ever been observed using traditional methods. As well as being used to derive the most detailed topographic map of Austfonna to date, the interferometric results presented here have provided an unprecedented snapshot of the cap's velocity field, and identified significant temporal instabilities within one of its basins. Section 1.3 listed six questions that would be addressed by the work in this thesis, and these will now be answered: i) Is Austfonna's spatial velocity structure consistent with the predictions that have been made via observations of its topography? Studies of Austfonna's topography had previously allowed its basin geometry to be defined (Dowdeswell and Drewry, 1985) and examination of the interferometrically derived DEM produced here confirmed those results. However, the cap's spatial velocity distribution was not previously known, and the work in this thesis has allowed this to be imaged for the first time. The result, shown in Figure 6.2, needed careful interpretation as it represented only the line-of-sight component of Austfonna's velocity field. However, it allowed the distribution of active and stagnant regions of the cap to be identified. The cap was found to consist largely of ice that was slow moving, but in a number of locations its margins were punctured by units of fast flow, the existence of which had not previously been revealed. Preliminary interferometric work in other areas (Figures 6.6 to 6 .8 ) has indicated that this structure may be typical of Arctic ice caps of this size. Dowdeswell (1986) had inferred the dynamics of several of Austfonna's basins by examining their topographic profiles. The interferometric results presented here were largely in agreement with those results, with the exception of Basins 3 and 10 whose low surface profiles had been thought to imply that they were in a post-surge quiescent phase and therefore stagnant. In fact those basins have been shown to be highly active, and their low surface profiles are probably indicative of basal sliding. ii) Is the spatial velocity structure consistent with models of Austfonna's thermal regime? Schytt (1969) proposed that Austfonna's thermal structure consisted of a warm central annulus surrounded by a cold outer ring (Figure 6.4). The limited number of direct temperature measurements (Figure 6.5) had neither confirmed nor contradicted this model, but observations of turbid subglacial melt-water emerging from the cap's south-eastern margin had raised some doubts of its validity. As the velocity results presented in this thesis suggest that basal sliding

104 is occurring in a number of Austfonna's drainage basins, they apparently confirm that the cap's thermal structure is more complicated than the Schytt model suggests, with at least some areas being characterised by warm-bedded ice. iii) Does the spatial velocity structure vary temporally? Interferometrically derived snapshots of Austfonna's velocity field were obtained using data acquired in the winters of 1992, 1994 and 1995', and show no temporal variation in the spatial distribution of active and stagnant ice. A much longer time series would be needed to establish the permanence of this distribution, but as a relatively high proportion of basins are observed to be active, it is unlikely that they simply represent temporary surge events. Some of these basins are associated with subglacial bedrock troughs, which may provide further evidence of a semi-permanent velocity structure (McIntyre, 1985). In contradiction to this, evidence was presented that Basin 3 may have been stagnant in the early 1980s (Figure 6.9). However, as discussed in the next section, this basin has, in recent years, been relatively unstable compared to other parts of the cap. iv) Are there local temporal variations occurring within individual drainage basins, and, if so, are they consistent with surge-type behaviour? The interferometrically derived velocity results appear to suggest that Basin 3 had slowed by a factor of 2 between 1992 and 1994, and then had regained approximately 80% of its original velocity by 1996 (Figure 6.3). However, as the results represent 3-day snapshots of velocity, obtained at two-year intervals, it is not possible to establish the temporal wavelength of these variations. Examination of Landsat data appears to suggest that the basin may have been stagnant in 1981 (Figure 6.9), but an isolated observation made in 1983 (Drewry and Liest 0 l, 1985) suggested that by then it was active. The available evidence appears to suggest that the basin's behaviour is more consistent with an onset of fluctuating stream-like flow, rather than of surge-type behaviour. The velocity fluctuations are likely to be associated with disruption of the subglacial drainage system (Paterson, 1994), but as local temperature measurements (Figure 6.5) have indicated that the upper layers of ice are sub-polar, a direct relationship between surface melting and velocity does not seem likely. Tidal influences have also been discounted because the region is thought to be grounded, and the results showed no correlation with local tidal data. It has therefore so far not been possible to establish the causal mechanism of the observed phenomenon. v) Can we derive Austfonna's three-dimensional velocity field and use it to obtain an estimate o f the mass lost by iceberg calving at its margin? The inSAR technique was used to obtain the component of Austfonna's velocity field that was parallel to the satellite's line-of-sight. The preferred method of then deriving the three- dimensional field was to combine line-of-sight results from two different look directions. However, the descending coverage of Austfonna was poor during ERS-l's Ice Phases, and

105 only coincided with the ice cap's margins (Figure 3.2). Only a small proportion of Austfonna's three-dimensional velocity field was therefore derived using this method (Figure 5.14). Although an alternative method, using an assumed flow direction, was attempted for the whole ice cap, the accuracy of these results was shown to be highly dependent on their azimuth. As most of Austfonna's calving occurs along its south-easterly margin anyway, only the combined ascending/descending velocity results were used to estimate calving rates, and these results were shown in Figure 6.10. This component of the cap's mass loss was shown to be highly significant with respect to published estimates of accumulation, but there was not enough information to allow calculation of Austfonna's mass balance. vi) What does this work tell us about the feasibility of using the inSAR technique to routinely monitor ice velocity on a global basis and hence significantly contribute to studies of ice-sheet mass balance? Section 1.1 discussed how routine, high resolution measurements of ice velocity, obtained on a global scale, could not only improve current estimates of ice sheet mass-balance, but could also assist modellers in assessing how these might change in the future. The work in this thesis, and similar work by others (Section 1.4), has clearly shown that such velocity measurements are possible on a local scale, but the experience has highlighted various problems that may need to be addressed before routine velocity measurement becomes a reality. The success of interferometric studies of the type presented here is, to a certain extent, at the mercy of surface weather conditions. The nine image-pairs used in this work (Table 3.1) represented just 50% of the total number of pairs obtained from DPAF, the remainder having been rejected due to inadequate correlation. As was shown in Figure 3.5, however, even the pairs that passed this test were partially affected by correlation loss due to changing conditions at Austfonna's surface. With "failure" rates as high as this, large numbers of temporally repeated SAR scenes are clearly required to obtain useful results. If results are also affected by atmospheric effects, or other long wavelength anomalies, such as those shown in Figure 5.7, it may only be possible to remove them by averaging several sets of results (e.g. Joughin, 1995). Clearly this would again increase the number of temporal repeats necessary to obtain a single measurement. Temporal and spatial coverage of existing SAR data is in theory excellent, but in practice variable. For instance, since 1995 the ERS tandem scenario has provided one-day repeat global coverage at 35 day intervals, yet financial and operational constraints have meant that only a small proportion of this data has actually been acquired. As an even smaller proportion of the recorded data has ever been processed, however, the case for improving acquisition density will become clearer as the interferometric community swells and the vast back-catalogue of SAR data is increasingly exploited. The recent appearance of high quality, well documented interferometry software on the commercial market (e.g. Wegmüller and Werner, 1997) will hopefully facilitate increased application of the technique within the geophysical community.

106 It should be noted that the ERS SARs were not originally designed for interferometry, and that their application to this has been entirely serendipitous. Problems arising from this have adversely affected the quality of the results obtained to date. One such problem is sub- optimal baseline planning. Though long baselines are required for topographic analysis (Section 4.2.1), short ones are preferable for obtaining velocities (Section 4.3.2). Though ERS baselines have been kept within limits that prevent baseline decorrelation, within this range they have been very variable (Solaas, 1994). The limited number of good quality pairs available for this research prevented the luxury of a choice of baselines, and so most of the baselines used (Table 3.1) were sub-optimal for both topographic and velocity work. The prospective outlook for interferometric work of this type is clearly dependent on the improved design of future missions. Despite such issues, the interferometric results presented here, and elsewhere, have yielded a large amount of glaciological information, much of which could not easily be obtained by other means. Traditional methods of measuring ice velocity, via the surveying of ground- stakes, are expensive and can provide only limited coverage and resolution. Other remote sensing techniques rely on the tracking of surface features, such as crevasses, and so cannot be used over featureless terrain. Topographic accuracies obtained using interferometry are comparable with those of satellite altimetry, yet the spatial resolution is much better (tens of metres as opposed to tens of kilometres). Interferometry clearly represents a significant advance in glaciological research. However, the reliance on well distributed ground-truth data for tie-pointing (Joughin, 1996b) means that the success of any program to obtain interferometric velocity results on a wide geographical scale may be highly dependent on the pre-planned combination of remote sensing with more traditional glaciological methods.

Recommendations for further work The velocity and topography results presented in this thesis are to be used in a finite element modelling study of Austfonna's dynamics (A. Hubbard, personal communication). This may help us to understand the processes that are controlling Basin 3's velocity perturbations. Re­ location of the missing RES data (Section 5.1.2) may also enhance our understanding by allowing us to map Basin 3's hydrological potential and hence determine what factors may influence disruption of that region's subglacial drainage system (e.g. Anandakrishnan and Alley, 1997). In addition, our knowledge would clearly be improved if the temporal sampling of the phenomenon were to be increased. The requirement to obtain good coherence between the two images of an interferometric pair, restricts us to the use of temporal baselines of no more than a few days. For this reason, only data from ERS-l's First and Second Ice Phases, spanning the winters of 1992 and 1994 respectively, and the ERS-1/2 Tandem Phase (Aug '95 - June '96) have been used in this work. Though ERS-2 has subsequently acquired numerous repeats over Austfonna during 1997 and 1998, these have a temporal baseline of 35 days, and so the

107 chances of using them to obtain useful interferometric results in this region are probably slim. The 1999 launch of the Envisat satellite, which is intended to maintain the continuity of the ERS acquisitions for 5 years, may not provide useful data because currently this is also planned to operate at a 35 day repeat interval. Though the available Ice Phase data have been fully exploited in this project, there may be room for further exploitation of Tandem Phase data. The Tandem Phase provided a 1 day temporal baseline at 35 day intervals, resulting in poorer temporal coverage, but much better spatial eoverage than the Ice Phases (Figure 7.1). Only a small amount of the available Tandem data was used in this project, and the processing of more acquisitions may help to confirm the observation that Basin 3's veloeity had significantly increased by the winter of 1995"with respect to the winter of 1994. The very short temporal baseline also justifies examination of the available non-winter pairs, which may potentially allow the identification of seasonal influences on the behaviour of Basin 3.

,

i i i J U

LW.'

Figure 7.1 ERS SAR coverage of the Svalbard archipelago, a) ERS-1 Ice Phase coverage. The Austfonna scene used in this thesis is shown in bold type, b) ERS-1/2 Tandem descending coverage, c) ERS-1/2 Tandem ascending coverage.

Figure 7.1 shows that the descending coverage of Austfonna was much better for the Tandem Phase than for the Ice Phases. If suitable image pairs could be identified, it may therefore be possible to combine ascending/descending Tandem data to map the three-dimensional velocity field for the whole of Austfonna. This would potentially allow calving rates to be calculated along the full length of Austfonna's eoastline, rather than just for the south-east margin as was demonstrated in this thesis. Iceberg calving is clearly an important negative component of Austfonna's mass balance. However, further work would be needed to more accurately quantify the other components before the region's mass budget could be closed. Also, as discussed in Section 6.4, current assessments of Austfonna's equilibrium line altitude may need to be re-examined. The expertise that has been acquired at MSSL via our interferometric investigations of

Austfonna is to be applied to other large Arctic ice masses (Figures 6 . 6 to 6 .8 ) and also to Antarctica. However, future work should include a full investigation of the long-wavelength 108 anomalies, and "streak" effects, that have compromised the results presented here, and those of other workers (e.g. Joughin et al., 1996a). Though the work in this thesis was not thought to be adversely affected by spatially variant radar penetration (Section 4.2.4), this is likely to be a greater problem in Antarctic and Greenland data, due to the presence of dry snow zones, and is therefore the subject of ongoing research (e.g. Winebrenner et al., 1997). Future results may also be improved by an enhanced capacity to identify atmospheric effects (Section 4.1.2) and so further work in this area would be of great benefit to the interferometric community.

109 References

Alley, R. B., D. D. Blankenship, S. T. Rooney and C. R. Bentley, (1987). Till beneath Ice Stream B: 4. a coupled ice-till flow model. J. Geophys. Res. 92, 8931 - 8940.

Anandakrishnan, S. and R. B. Alley, (1997). Stagnation of ice stream C, West Antarctica by water piracy. Geophys. Res. Lett., 24, 3, 265 - 268.

Andreasen, J-0, (1985). Seasonal surface-velocity variations on a sub-polar glacier in West Greenland. J. Glacial., 31, 109, 319 - 323.

Barber, B. C., (1985). Theory of digital imaging from orbital synthetic-aperture radar. Int. J. Rem. Sens., 6 , 7, 1009 - 1057.

Bauer, A., (1961). Influence de la dynamique des fleuves de glace sur celle de l'islandsis du Groenland. lASH, 54, 578 - 584.

Bénédicte, F., D. Christophe and A. José, (1997). Observation and modelling of the Saint-Etienne-de-Tinée landslide using SAR interferometry. Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Benson, C. S., (1961). Stratigraphie studies in the snow and fim of the Greenland ice sheet. Folia Geographica Danica., 9, 13 -37.

Bindschadler, R. A., (1998). Monitoring ice sheet behaviour from space. Reviews o f Geophysics, 36, 1, 79 - 104.

Bindschadler, R. A., W. D. Harrison, C. F. Raymond, and R. Crosson, (1977). Geometry and dynamics of a surge-type glacier. J. Glacial., 18, 181 - 194.

Boulton, G. S. and A. S. Jones, (1979). Stability of temperate ice caps and ice sheets resting on beds of deformable sediment. J. Glacial, 24, 90, 29-43.

Budd, W. F., (1968), The longitudinal velocity profile of large ice masses. lAHS, 19, 58 - 75.

Callahan, P. S., (1984). Ionospheric variations affecting altimeter measurements: a brief synopsis. Marine Geodesy, 8 , 249 - 263.

Clarke, G. K. C., (1987). Fast glacier flow: ice streams, surging, and tidewater glaciers. J. Geophys. Res., 92, B9, 8835 - 8841.

Gumming, 1., J. L. Valero, P. Vachon, K. Mattar, D. Geudtner and L. Gray, (1997). Glacier flow measurements with ERS Tandem Mission data. Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Doake, C. S. M., R. M. Frolich, D. R. Mantripp, A. M. Smith, and D. G. Vaughan, (1987). Geological studies on the Rutford ice stream, Antarctica. J. Geophys. Res., 92, B9.

Dowdeswell, J. A., (1984). Remote sensing studies of Svalbard glaciers. Unpublished Ph.D. thesis. University of Cambridge.

Dowdeswell, J.A., (1986). Drainage-basin characteristics of Nordaustlandet ice caps, Svalbard. J. Glacial, 32, 110, 31 - 38.

110 Dowdeswell, J. A., B. Unwin, A. M. Nuttall and D. J. Wingham, (Sub. 1998). Velocity structure and flow instability on a large Arctic ice cap from satellite radar interferometry. Submitted to Geophysical Research Letters.

Dowdeswell, J. A., W. G. Rees and A. D. Diament, (1994). ERS-1 SAR investigations of snow and ice facies on ice caps in the European high Arctic. Proceedings of the Second ERS-1 Symposium. ESA SP-361.

Dowdeswell, J. A. and R. L. Collin, (1990). Fast flowing outlet glaciers on Svalbard ice caps. Geology, 18, 778 - 781.

Dowdeswell, J.A., D.J. Drewry, A.P.R. Cooper, M.R. Gorman, O. Liestpl and O. Orheim, (1986). Digital mapping of the Nordaustlandet ice caps from airborne geophysical investigations. Annals of Glaciology, 8 , 51 - 58.

Dowdeswell et al., (1991). The duration of the active phase on surge-type glaciers: contrasts between Svalbard and other regions. J. GlacioL, 37, 127, 388 - 400.

Dowdeswell, J.A. and D.J. Drewry, (1985). Place names on the Nordaustlandet ice caps, Svalbard. Polar Record, 22, 140, 519 - 539.

Dowdeswell, J.A. and D.J. Drewry, (1989). The dynamics of Austfonna, Nordaustlandet, Svalbard: surface velocities, mass balance, and subglacial melt water. Annals o f Glaciology, 12, 37 - 45.

Drewry, D. J. and O. Liestpl, (1985). Glaciological investigations of surging ice caps in Nordaustlandet, Svalbard, 1983. Polar Record, 22, 139, 357 - 378.

Echelmeyer, K., W. D. Harrison, J. E. Mitchell and C. Larsen, (1994). The role of the margins in the dynamics of an active ice stream. J. GlacioL, 40, 136, 527 - 538.

ESA, 1995, Document ER-IS-EPO-GS-5902.3.

Fahnestock, M., R. Bindschadler, R. Kwok and K. Jezek, (1993). Greenland ice sheet surface properties and ice dynamics from ERS-1 SAR imagery. Science, 262, 1530 - 1534.

Fatland, D. R., (1997). InSAR at ASF: Analysis of the 1993 Bering Glacier surge (abs.). Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Gabriel, A. K., R. M. Goldstein and H. A. Zebker, (1989). Mapping small elevation changes over large areas: differential radar interferometry. J. Geophys. Res., 94, B7, 9183-9191.

Gabriel, A. K. and R. M. Goldstein, (1988). Crossed orbit interferometry: theory and experimental results from SIR-B. Int. J. Rem. Sens., 9, 5, 857 - 872.

Goldstein, R. M., H. A. Zebker and C. L. Werner, (1988). Satellite radar interferometry: two-dimensional phase unwrapping. Radio Science, 23, 4, 713 - 720.

Goldstein, R. M., H. Engelhardt, B. Kamb and R. M. Frolich, (1993), Satellite radar interferometry for monitoring ice sheet motion: application to an Antarctic ice stream. Science, 262, 1525 - 1530.

Graham, L. C., (1974). Synthetic interferometer radar for topographic mapping. Proceedings of the IEEE, 62, 6 , 763 - 768.

Hagberg, J. O., L. M. H. Ulander and J. Askne, (1995), Repeat-pass SAR interferometry over forested terrain. IEEE Trans. Geosci. Rem. Sen., 33, 2, 331 - 340.

Ill Hagen, J. O., O. Liest 0l, E. Rowland and T. J 0rgensen, (1993). Glacier atlas of Svalbard and Jan Moyen. Norsk Polarinstitutt, Oslo.

Hanssen, R. and A. Feijt, (1997). A first quantitative evaluation of atmospheric effects on SAR interferometry. Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Hartl, P., K. H. Thiel and X. Wu, (1994), Information extraction from ERS-1 SAR data by means of InSAR and D-InSAR techniques in Antarctic research. Proceedings of the Second ERS-1 Symposium. ESA SP-361.

Heinrichs, T. A., L. R. Mayo, K.A. Echelmeyer and W. D. Harrison, (1996). Quiescent- phase evolution of a surge-type glacier: Black Rapids Glacier, Alaska, U.S.A. J. GlacioL, 42, 140, 110 - 122.

Hisdal, V., (1985). The geography of Svalbard. 2nd edition. Norsk Polarinstitutt, Polarhandbok no. 2.

Hodge, S. M., (1974). Variations in the sliding of temperate glacier. J. GlacioL, 13, 69, 349 - 369.

Hughes, T., (1983), The Jakobshavns Glacier ice drainage system. In Report of the Workshop on Jakobshavns Glacier (Greenland), Northwestern University, Evanston, IB.

Jezek, K. and E. Rignot, (1994). Katabatic wind processes on the Greenland ice sheet. Presented at the AGU Fall Meeting, San Francisco.

Jezek, K. C., P. Gogineni and M. Shanableh, (1994). Radar measurements of melt zones on the Greenland ice sheet. Geophys. Res. Lett., 21, 1, 33-36.

Joughin, I. R., (1995). Estimation of ice-sheet topography and motion using interferometric synthetic aperture radar. Unpublished Ph.D. thesis. University of Wasiiington.

Joughin, I. R., D. P. Winebrenner and D. B. Percival, (1994). Probability density functions for multilook polarimetric signatures. IEEE Trans. Geosci. Rem. Sen., 32, 3, 562 - 574.

Joughin, I. R., D. P. Winebrenner and M. A. Fahnestock, (1995). Observations of ice- sheet motion in Greenland using satellite radar interferometry. Geophys. Res. Lett., 22, 5, 571 -574.

Joughin, I. R., D. P. Winebrenner, M. A. Fahnestock, R. Kwok and W. Krabill, (1996a). Measurement of ice-sheet topography using satellite-radar interferometry. J. GlacioL, 42, 140, 10 - 22.

Joughin, I. R., R. Kwok and M. Fahnestock, (1996b). Estimation of ice sheet motion using satellite radar interferometry: method and error analysis with application to Humboldt Glacier, Greenland. J. GlacioL, 42, 142, 564 - 575.

Joughin, I. R., S. Tulaczyk, M. Fahnestock and R. Kwok, (1996c). A mini-surge on the Ryder Glacier, Greenland, observed by satellite radar interferometry. Science, 274, 5205, 228 - 230.

Joughin, I. R., R. Kwok and M. Fahnestock, (1998). Interferometric estimation of three- dimensional ice-flow using ascending and descending passes. IEEE Trans. Geosci. Rem. Sen., 36, 1, 25 - 37.

Kamb, B. and H. Engelhardt, (1987). Waves of accelerated motion in a glacier approaching surge: the mini-surges of Variegated Glacier, Alaska, U.S.A. J. GlacioL, 33, 113, 27 -46. 112 Kwok, R. and M. A. Fahnestock, (1996). Ice sheet motion and topography from radar interferometry. IEEE Trans. Geosci. Rem. Sen., 34, 1, 189 - 200.

Li, F. K. and R. M. Goldstein, (1990). Studies of multibaseline spaceborne interferometric synthetic aperture radars. IEEE Trans. Geosci. Rem. Sen., 28, 1, 88 - 96.

Losev, K. S., (1973). Estimation of run-off from Antarctic and Greenland ice sheets. lAH S, 95, 253 - 254.

MacAyeal, D. R., (1989). Large-scale ice flow over a viscous basal sediment : Theory and application to Ice Stream B, Antarctica. J. Geophys. Res., 94, 4071 - 4087.

MacAyeal, D. R., E. Rignot and C. L. Hulbe, (in press). Ice shelf dynamics near the front of Filchner-Ronne ice shelf, Antarctica, revealed by SAR interferometry: model/interferogram comparison. J. GlacioL

McIntyre, N. F., (1985). The dynamics of ice-sheet outlets. J. GlacioL, 31, 108, 99 - 107.

Massonnet, D., M. Rossi, C. Carmona, F. Adragna, G. Peltzer, K. Feigl and T. Rabaute, 1993), The displacement field of the Landers earthquake mapped by radar interferometry. Nature, 364, 138 - 142.

Massonnet, D. and K. L. Feigl, (1995). Discrimination of geophysical phenomena in satellite radar interferograms. Geophys. Res. Lett., 22, 12, 1537 - 1540.

Massonnet, D. and H. Vadon, (1995). ERS-1 internal clock drift measured by interferometry. IEEE Trans. Geosci. Rem. Sen., 33, 2, 401 - 408.

Mayo, L. R., (1978). Identification of unstable glaciers intermediate between normal and surging glaciers. Mat. Glyatsiologicheskikh Issled. Khronica Obsuzhdeniya, 33, 133 - 135.

Meier, M. F. and A. Post, (1969). What are glacier surges? Can. J. Earth ScL, 6 , 4, 807 - 817.

Mohr, J. J., N. Reeh and S. N. Madsen, (1998). Three-dimensional glacial flow and surface elevation measured with radar interferometry. Nature, 391, 273 - 276.

Morgan, V. L., T. H. Jacka, G. J. Akerman and A. L. Clarke, (1982). Outlet glacier and mass-budget studies in Enderby, Kemp, and Mac. Robertson Lands, Antarctica. Ann. GlacioL, 3, 204 - 210.

Morley, J., J. P. Muller and S. Madden, (1997). Wetland monitoring in Mali using SAR interferometry. Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Nordenskiold, E., (1875). Den Svenska Polarexpeditionen, 1872 - 1873. K. Svenska Vetenskapsakademiets Handlingar, 2, 18.

Paterson, W. S. B, (1994), The physics of glaciers. Third edition. Pergamon Press.

Peltzer, G. and P. Rosen, (1995). Surface displacements of the 17 May 1993 Eureka Valley, , earthquake observed by SAR interferometry. Science, 268, 5215, 1333 - 1336.

Raymond, C. F., (1987). How do glaciers surge? A review. J. Geophys. Res., 92, B9, 9121 - 9134.

113 Reeh, N., (1994). Calving from Greenland glaciers: observations, balance estimates of calving rates, calving laws. Workshop on the calving rate of West Greenland glaciers in response to climate change. Danish Polar Centre, Copenhagen.

Reigber, C., Y. Xia, H. Kaufmann, F. H. Massmann, L. Timmen, J. Bodechtel and M. Frei, (1997), Impact of precise orbits on SAR interferometry. Proceedings of the "Fringe 96" Workshop on ERS SAR Interferometry. ESA SP-406.

Rignot, E., (1996). Tidal motion, ice velocity and melt rate of Petermann Gletscher, Greenland, measured from radar interferometry. J. GlacioL, 42, 142, 476 - 485.

Rignot, E., K. C. Jesek and H. G. Sohn, (1995). Ice flow dynamics of the Greenland ice sheet from SAR interferometry. Geophys. Res. Lett., 22, 5, 575 - 578.

Rignot, E., R. Forster and B. Isacks, (1996). Interferometric radar observations of Glacier San Rafael, Chile. J. GlacioL, 42, 141, 279 - 291.

Rodriguez, E. and J. M. Martin, (1992). Theory and design of interferometric synthetic aperture radars. IEEE Proceedings, 139, 2, 147 - 159.

Scharroo, R. and P. Visser, (in press). Precise orbit determination and gravity field improvement for the ERS satellites. J. Geophys. Res.

Schreier, G., eJ., (1993). SAR geocoding: data and systems. Wichmann.

Schytt, V., (1964). Scientific results of the Swedish glaciological expedition to Nordaustlandet, Spitsbergen, 1957 and 1958. Parts I and II. Geografiska Annaler, 46, 3, 243 -281.

Schytt, V., (1969). Some comments on glacier surges in eastern Svalbard. Can. J. Earth ScL, 6 , 867 - 873.

Shabtaie, S. and C. R. Bentley, (1987). West Antarctic ice streams draining into the Ross ice shelf: configuration and mass balance. J. Geophys. Res., 92, 1311 - 1336.

Stephenson, S. N. and R. A. Bindschadler, (1988). Observed velocity fluctuations on a major Antarctic ice stream. Nature, 334, 695 - 697.

Solaas, G. A., (1994). ERS-I interferometric baseline algorithm verification. ESA publication ES-TN-DPE-OM-GS02.

Tarayre, H. and Massonnet, D., (1996). Atmospheric propagation heterogeneities revealed by ERS-1 interferometry. Geophys. Res. Lett., 23, 9, 989 - 992.

Unwin, B. and Wingham, D., (1996). Topography and dynamics of Austfonna, Nordaustlandet, Svalbard, from SAR interferometry. Ann. GlacioL, 24, 403 - 408.

Warrick, R. A., C. L. Provost, M. F. Meier, J. Oerlemans and M. Woodworth, (1995). Changes in sea level. In Climate change 1995: The science of climate change, Cambridge University Press.

Watts, L. G., J. A. Dowdeswell and T. Murray, (1997). The dynamics of Austfonna, Svalbard: two dimensional modelling of ice motion over a deformable substrate. Mat. Glyatsiologicheskikh Issled. Khronica Obsuzhdeniya, 83, 10 - 22.

Weertman, J., (1964). Theory of glacier sliding. J. GlacioL, 5, 39, 287 - 303.

Wegmüller, U. and C. Werner, (1997). Gamma SAR processor and interferometry software. Proceedings of the third ERS scientific symposium. ESA SP-414.

114 Whillans, I. M., J. Bolzan and S. Shabtaie, (1987). Velocity of ice streams B and C, Antarctica. J. Geophys. Res., 92, B9.

Willis, I. C., (1995). Intra-annual variations in glacier motion: a review. Progress in , 19, 1, 61 - 106.

Winebrenner, D.P., I.R. Joughin and M.A. Fahnestock, (1997). Interferometric SAR for observation of glacier motion and fim penetration. Proceedings of the third ERS scientific symposium. ESA SP-414.

Zebker, H. A. and R. M. Goldstein, (1986). Topographic mapping from interferometric synthetic aperture radar observations. J. Geophys. Res., 91, B5, 4993 - 4999.

Zebker, H. A. and J. Villasenor, (1992). Decorrelation in interferometric radar echoes. IEEE Trans. Geosci. Rem. Sen., 30, 5, 950 - 959.

Zebker, H. A., C. L. Werner, P.A. Rosen and S. Hensley, (1994). Accuracy of topographic maps derived from ERS-1 interferometric radar. IEEE Trans. Geosci. Rem. Sen., 32, 4, 823 - 836.

115 Appendix 1 : Justification of use of spherical co-ordinate system

The coordinate system used to formulate the equations used throughout this thesis is that of a sphere. The value of the sphere is obtained by computing the radius of curvature of ellipsoid WGS-84 at the central latitude of the area of interest. In order to validate the use of this system, I will here show that across the distance spanned by one SAR frame, terrain height above the reference sphere does not vary significantly from that above the ellipsoid.

y axis is into page

R tf' ►

’c / i

Figure A l. 1 Relationship between spherical and ellipsoidal coordinate systems.

In Figure ATI, the coordinate system is that of an ellipsoid, centred at E, with a semi­ major axis length a, and semi-minor axis length b. The point C, at geodetic latitude 0c and longitude Ac, is the position of a resolution cell at SAR scene centre-range. Point Tp, at geodetic latitude 0pp and longitude App, represents a resolution cell at the far-range edge of the same image. R^ is the geodetic radius at C, and hence also the radius of our reference sphere, the centre of which is at O. R jf is the geodetic radius at Tp, and R jf is the distance between Tp and O.

116 If terrain height is calculated for this image according to equation (2.1), then the resulting error in the height calculated at Tp will be Azc, where :

— ^TF ~ ^TF (A l.l)

From Schreier (1993), the radff of curvature of the ellipsoid at positions C and Tp, are, respectively, given by : n - sin ^ ÿ j

Rtf — { l-e ^ sin^ (I>tt) (A1.2) where : 2 a " - 6 " e =

(A1.3)

If we define a Cartesian coordinate system (%,y,z) centred at E, the co-ordinates of point O are (xq , yo, Zo), and those at Tp are (xtf , yrf, Zrr), where :

X q = 0

7o = 0

and : Xtf — R^f co s fj^fF cos ^ tf

yjF = Rjf cos Tf sin

Ztf = Rtf{^~ sin (j)TF

The distance between Tp and O is given by

Rtf ~ \^TF yrf ^o) (A1.4)

The distance g, between C and Tp, is never more than 50km, and therefore a "worst- case" value of <{)tf can be taken as (f>c+ 0.008 radians. Using equations A1.2 and A 1.4, equation A l.l was solved for the height error Az^ that would arise in this case.

117 and the results were plotted against (j)c in Figure A 1.2. It can be seen that the height errors at the far-range edge of a SAR image will never be more than about 1.3 metres, and in most cases the error will be much less than this. For the high latitude scenes used in this research, the errors introduced by the use of a spherical co-ordinate system are of order 10 ^ metres, and are insignificant compared to other errors in the system.

Azc (m)

0.0

- 0.5

- 1 .0

- 1.5 0 2040 60 80 100 Latitude (j)c in degrees

Figure A1.2 Plot of coordinate-system dependent height error at far-range against latitude at image centre.

118 Appendix 2 : Baseline constraint using tie-points

As discussed in section 4.2.3, large height errors can be introduced into interferometrically derived DEMs if the differential baseline parameters ^pu3 are not accurately known. These parameters are best obtained by the use of tie-points, and this section outlines the procedure by which this is done. The same procedure solves for the constant «^23 equation (3.14), and compensates linear sources of height error. The method is a slight variation on that of Joughin (1995).

The baseline components B„^^^(y) and may be expressed in terms of their values, B^hi23 ^pH2 3 ^ ^1 the scene's mid-azimuth position plus linear changes in those values according to relative azimuth position :

r \ y-yh ^«123 ^«*123 ^^^«123 \ J

y - y h ^P\23 ^Ph\23 ^^P\23 V 4 y (A2.1) where and are the changes in 4 i23 across a distance Ly, which is the total azimuth length of the scene in question.

Combining equations (A2.1), (2.23) and (3.14), we can obtain the following expression for the unwrapped differential phase difference ^tui 23 •

r \ y-yh sin0 ^ ^ T ui23 ^ ^ c i 23 “ 2 r. V 4 /

y-yh A ^ - ® p,23 cos 6 4. - 4 y 2r,

(A2.2)

With the exception of the two rj terms, which are comparatively small, equation (A2.2) is a linear expression containing five unknowns; and the unwrapping constant «^ 23- However, 0^^ varies by only a few degrees across the

119 swath and, as a result, the term is virtually constant. The problem of having two unknown constants is that any two constants whose sum equals ‘ will yield a solution (Zebker et al., 1994). Consequently, we cannot uniquely determine both and «^ 123' Instead we must fix the value of one of the constants, Bp^^^^, to the value Bp^o^^^ that was obtained from the best available orbit information. B 123 and /lr ,23 also substituted by their equivalents, Bo ,23 and using the best available orbits. However, as the terms containing these variables are small, this will not significantly affect the results. Equation (A2.2) can now be written :

f \ f \ y - y h y - y h c o s 0 ^ j - ^ ^ ci23 s i n ^ 4 ~ ® " I 23 L L \ y J \ y J (A2.3)

If the target heightZt is known, we can calculate Ato^23 using equations (2.1) and (2.28). The other terms on the left hand side are also known. In such circumstances, (A2.3) is a linear equation with four unknowns. If at least four tie-points within an image are available then the equation can be solved using a standard linear least-squares algorithm. This exercise will have the effect of fixing the interferometric height solution into the coordinate system of the tie-points used. Any bias in the tie-point heights will be transferred to the interferometric height results. Similarly,the process will tend to compensate for any constant or linear bias in the interferometric phase or imaging geometry.

If solving for the baseline parameters of an interferogram containing both motion and topography, as in Section 3.4, a similar analysis yields the following equivalent to equation (A2.3) :

c o se ,+ 4 2r,

( \ f \ ■ y - y h COS 0 ^ J - ^ n h n L L \ y ) \ y J (A2.4) where :

120 / \ y-yh 4 ; r \

\ ^y J (A2.5)

We now need tie-points of both height and velocity, so that may be calculated using equation 2.7. In the work presented here, so called "zero velocity" tie-points were selected from bedrock regions and ice divides, so that \ could be set to zero.

For interferograms containing only displacement effects, such as those discussed in section 2.3.2, the baseline terms are zero, and a minimum of just one velocity tie-point is needed in order to solve equation 3.22 for the unwrapping constant «vc-

121