Studies of Bagley Icefield during surge and Black Rapids Glacier, Alaska, using spaceborne SAR interferometry
Item Type Thesis
Authors Fatland, Dennis Robert
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STUDIES OF BAGLEY ICEFIELD DURING SURGE AND BLACK RAPIDS GLACIER, ALASKA, USING SPACEBORNE SAR INTERFEROMETRY
A
THESIS
Presented to the Faculty
of the University of Alaska Fairbanks
in partial Fulfillment of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY
By
Dennis R. Fatland, B.S.
. Fairbanks, Alaska
December 1998
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STUDIES OF BAGLEY ICEFIELD DURING SURGE AND BLACK RAPIDS GLACIER, ALASKA, USING SPACEBORNE SAR INTERFEROMETRY
By
Dennis R. Fatland
RECOMMENDED:
Department Head
APPROVED: F J lc ^ u c S C Dean, College of Science, Engineering and Mathematics
Dean/if the Graduate School /
Date
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT. This thesis presents studies of two temperate valley glaciers—
Bering Glacier in the Chugach-St.Elias Mountains. South Central Alaska, and
Black Rapids Glacier in the Alaska Range. Interior Alaska—using differential space-
borne radar interferometry. The first study was centered on the 1993-95 surge of
Bering Glacier and the resultant ice dynamics on its accumulation area, the Bagley
Icefield. The second study site was chosen for purposes of comparison of the inter
ferometry results with conventional field measurements, particularly camera survey
data and airborne laser altimetry. A comprehensive suite of software was written to
interferometrically process synthetic aperture radar (SAR) data in order to derive
estimates of surface elevation and surface velocity on these subject glaciers. In ad
dition to these results, the data revealed unexpected but fairly common concentric
rings called phase bull's-eyes', image features typically 0.5 to 4 km in diameter
located over the central part of various glaciers. These bull’s-eyes led to a hypo
thetical model in which they were interpreted to indicate transitory instances of
high subglacial water pressure that locally lift the glacier from its bed by several
centimeters. This model is associated with previous findings about the nature of
glacier bed hydrology and glacier surging. In addition to the dynamical analysis
presented herein, this work is submitted as a contribution to the ongoing develop
ment of spaceborne radar interferometry as a glaciological tool.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS
Signatures ...... i
T itle ...... ii
Abstract ...... iii
Table of Contents ...... iv
List of Figures ...... vi
List of Tables ...... viii
Preface and Acknowledgements ...... ix
Chapter I. Introduction ...... I
Chapter 2. Analysis of the L993-95 Bering Glacier Surge Using Differential SAR Interferometry .6
Introduction ...... 7
Processing Overview ...... 11
Conversion of Radial Distance Change to Surface Velocity Vector Field ...... 28
West Bagley Icefield Results ...... 34
Failure of the Constant Velocity Assumption ...... 37
Resolving Surge Drawdown ...... 40
S u m m a ry ...... 40
Acknowledgements ...... 42
Appendices ...... 42
Chapter 3. Acceleration of Bagley Icefield During the 1993-95 Surge of Bering Glacier. Alaska.
Observed With Spaceborne SAR Interferometry ...... 45
Introduction ...... 46
M e th o d s ...... 47
Pre-Surge to Surge-State Velocity Change ...... 50
Shear Margin Widths and Maximum Principal Strain Rates ...... 52
Phase Bull’s-Eyes ...... 55
During-surge Acceleration ...... 58
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After-Surge Return to Quiescence ...... 61
Discussion ...... 64
S u m m a ry ...... 65
Chapter 4. An Interferometric Study of Black Rapids Glacier Alaska ...... 67
Introduction ...... 68
Field D a t a ...... 70
Topography ...... 71
Velocity ...... 78
Strain Rates ...... 84
Bull’s-Eyes ...... 86
Summary and Discussion ...... 90
References ...... 92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES
Figure I. Bering Glacier. Alaska ...... 8
Figure 2. 1993-1995 Bering Glacier Surge Event Sequence ...... 10
Figure 3. Multi-Pass SAR Interferometry Imaging Geometry ...... 13
Figure 4. SRI Processing Algorithm Flowchart ...... 14
Figure 5. Non-Glacier SRI 'Topography-Only' Phase ...... 15
Figure 6. Comparison of Non-Resampled Versus Sub-Pixel Resampled Interferogram Data ...... 16
Figure 7. Surface Motion Resulting in Radial Distance Changes ...... 18
Figure 8. Phase Unwrapping...... 21
Figure 9. DSRI Processing Algorithm Flowchart ...... 25
Figure 10. DSRI Schem atic ...... 26
Figure 11. DSRI Interferograms: Various Processing Stages ...... 27
Figure 12. Velocity Projection Geometry ...... 31
Figure 13. Determination of Two-Dimensional Flow-Direction Unit Vectors ...... 32
Figure 14. Velocity Error as a Function of Flow-Direction Error ...... 33
Figure 15. Comparison of Velocity Transects from 1992 and 1994 ...... 35
Figure 16. West Bagley Icefield Longitudinal Velocity Comparison. 1992 to 1994 ...... 36
Figure 17. Phase Bull’s-Eye Features. East Bagley Icefield 1994 ...... 39
Figure 18. East Bagley Icefield...... 49
Figure 19. East Bagley Icefield Comparison of 1992 to 1994 Longitudinal Velocity Profiles ...... 51
Figure ‘20. Lateral Transect Sites: Widths and Strain Rates, 1992 versus 1994 ...... 54
Figure 21. Multiple Differential Interferogram Time Sequence ...... 56
Figure 22. Acceleration Profile Time Sequence ...... 59
Figure 23. Bering Glacier, October 28. 1995. After Surge...... 62
Figure 24. Bering Glacier Terminus, October ‘28, 1995. After Surge...... 63
Figure 25. Black Rapids Glacier ...... 69
Figure ‘26. Comparison of Airborne Laser Altimetry Data with a SAR DEM ...... 73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vii
Figure 27. Medial Moraine Elevation Profiles ...... 75
Figure 28. Loket Medial Moraine Migration. 1992-1994 ...... 77
Figure 29. Surface Velocity Vector Field ...... 79
Figure 30. Comparison of 1992 Day 22 and 1995 Day 351 Transect Velocity Profiles ...... 81
Figure 31. Principle Strain Rate Field ...... 85
Figure 32. Black Rapids Bull's-Eye Events. 1992 ...... 87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii
LIST OF TABLES
Table L. Field camera velocities. Black Rapids Glacier. 10-day averages ...... 70
Table ‘2. BulFs-eye Data. Black Rapids Glacier 199*2 ...... 89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PREFACE
The first chapter of this thesis consists of an introduction to some of the ideas behind SAR inter
ferometry as applied to valley glaciers. The remaining three chapters are papers either in press or
in preparation for submission to Journal of Glaciology. The first paper (Chapter 2) is intended to
be an algorithm overview or ‘methods’ paper that presents some of the complicated and (for now)
unavoidable processing details necessary to get to the glaciological results. This paper also intro
duces the subject of the Bering Glacier surge and the analysis of its impact on West Bagley Icefield
using interferometry. This large network of glaciers is located in South Central Alaska. The second
paper. Chapter 3. is a sequel to the first, giving an analysis of the surge impact on the much larger
East Bagley Icefield. Finally Chapter 4 presents a comparison of interferometric results to field data
acquired on Black Rapids Glacier in Interior Alaska.
ACKNOWLEGEMENTS
The author wishes to acknowledge financial support from several grants to C. Lingle. These in
clude an NSF Small Grant for Exploratory Research OPP 93-19873. NASA grants NAGW-4930
and NAGo-4068. a grant from Cray Research. Inc., University Research and Development Grant
Program, and support via a research assistantship from the Alaska SAR Facility. The Arctic Re
gion Supercomputing Center is acknowledged for providing computational support. The European
Space Agency is acknowledged for approving ERS data proposal A02.USA163 (to C. Lingle). and
acquiring the SAR data over Bagley Icefield and other Alaskan glaciers and icefields which form the
basis of this work.
Continuing with a few personal observations. I would like to thank my advisor Dr. Craig Lingle for
his guidance, support, and patience throughout my tenure as a graduate student. Without Craig's
encouragement to ‘get to the glaciology’ I would have languished in a morass of interferometric
computer code, never to be seen again except at GI Christmas parties. As it was I believe I barely
escaped from the ARSC Visualization Lab with my life (and my bag of chips, still unconfiscated).
I owe debts of gratitude also to many of the UAF Geophysics faculty, particularly to David Stone,
Will Harrison, Keith Echelmeyer, Roland Gangloff, Carl Benson, Shusun Li, and Keith Runcorn.
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I would also like to express my appreciation to the extended family made up of the Geophysics
graduate students at UAF. and particularly to Ms. Laura Peticolas. who engendered the Graduate
Student Organization and led us to the realization that problems faced by graduate students and
by the University can be addressed and often solved, given the time and energy to make the effort.
I am hopeful that the consequences of her initiative to think beyond just taking classes and doing
research will resonate throughout our lives.
I was not clear, six or seven years ago. about what I would do in graduate school: I only knew
that I wanted to make something of a transition from engineering to science, an idea placed in my
head originally by my father and re-awakened by John Villasenor. When I was getting ready to
leave JPL around 1993, Dick Goldstein took a moment to show me a 4-meter-baseline interferogram
he had just generated of Rutford Ice Stream in Antractica. I had very little idea why he was so
excited about it at the time, but finally at this stage, six years later, I am happy to report that I
have some idea, and that I have managed to locate some of the science that I set out to find.
Finally. I note that the process of my life is made worthwhile by the friends who have helped me
along the way, and I must particularly acknowledge my friend Donna Anger for lending me a helpful
ear and a big dog now and again, and my friend Martin Truffer for innumerable games of chess,
buckets of coffee, and for saving my bacon when the pressures of life and deadlines got the heaviest.
I consider myself a very fortunate individual.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1
Chapter 1. Introduction
This thesis presents a study of two temperate valley glaciers (Bering Glacier in the Chugach-St.Elias
Mountains, South Central Alaska, and Black Rapids Glacier in the Alaska Range. Interior Alaska)
using Synthetic Aperture Radar (SAR) data and particularly using the technique of SAR interferom
etry. This technique, when proceeding from spaceborne SAR data and using multiple differencing to
distinguish surface motion from topography, is termed differential spaceborne radar interferometry'
(DSRI). (A more generalized acronym in common usage now is IFSAR. for 'interferometric SAR’).
DSRI is fairly simple in principle but encompasses a complexity of details and image processing
algorithms necessary to produce high-spatial-resolution mesoscale glaciological data. As a starting
point, the general problem of applying DSRI to glaciers can be broken down into two sub-problems:
First, the problem of extracting a useful signal from SAR images, and second, the problem of inter
preting this signal in a glaciological context. This introduction elaborates some of the ideas inherent
in DSRI signal processing and data interpretation. These themes are further developed in the en
suing three chapters, which consist of papers either in press or in preparation for submission to the
Journal of Glaciology.
The core idea of interferometry is the comparison by superposition of two or more signals. In
the case of DSRI. these signals are images produced by spaceborne SAR. This work uses data from
the European Space Agency (ESA) SAR instruments ERS-1 and ERS-2 downlinked to the Alaska
SAR Facility (ASF) from 1991 to 1995. The images produced from this data are two-dimensional
complex-valued fields in which each pixel has both an amplitude and a phase. SAR interferometry
compares superimposed pixel phases from two or more images. These phase values are the sum
contribution of both stationary and non-stationary random processes overlain by a range signal
coupling the SAR to surface scatterers through the radar carrier wavelength (here 5.7cm). It is the
fortunate correspondence between this wavelength and the typically small distance a glacier moves
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. over the course of a few days that permits the use of DSRI for observing glacier motion.
Two interferometric ‘comparison’ source images are produced by SAR overflights which have a
small variability in their flight paths with respect to the fixed earth. Typically two flight paths vary
by 10 to 100 meters or more, such that during each overflight the side-looking SAR observes the
surface terrain from a slightly different perspective. The precise determination of this separation is
necessary for processing, and was achieved in this work using an iterative least squares solution to
a parameterized relationship between the unknown flight path variations and the known elevations
and data values at a small set of ground control points. Once this orbital separation is determined,
the two source images can be processed to produce a single image synthesized from the two orbital
perspectives. The resulting stereo’ image of the surface contains information about its topography
in addition to information about surface motion. The first problem of DSRI can therefore be restated
more specifically as the problem of recovering and separating these two superimposed signals, motion
and topography.
The comparison of two images is achieved by subtraction of the phase of one image from that of
another on a pixel-by-pixel basis to produce a third image called an interferogram’. This subtraction
eliminates the stationary component of the random phase signal under good observing conditions,
leaving the residual superimposed surface topography and surface motion signals. These must be
differentiated using multiple comparisons (further phase subtractions) between several images. This
technique is described in more detail in chapter two. Once the two signals are separated, there
remains the second problem of interpreting them. All motion is observed by the SAR along a
one-dimensional line-of-sight ray from the SAR to the surface, hence all SAR motion data reduce
to measurements of radial distance change. However, the true glacier surface motion is a three
dimensional vector that tends to lie close to the glacier surface tangent plane. The resolution of
the true surface motion vector from the radial distance change measurement with respect to the
SAR requires either assumptions about the glacier motion (as presented in this thesis) or more
than one set of SAR imaging perspectives. The latter approach is more rigorous but tends to be
limited by operational constraints on SAR data acquisition. An important limitation to using a
single spacecraft flight path stems from side-looking nature of synthetic aperture radars. Since the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3
SAR is only sensitive to radial distance changes, glacier surface motion parallel to the SAR flight
path can not be resolved as such motion produces comparatively little change in radial distance.
Conversely, the technique works best for glaciers that flow perpendicular to the SAR flight path, as
this motion results in the maximum relative radial distance change in the data.
In considering the usefulness and validity of DSRI for glaciology on temperate glaciers, questions
arise concerning other influences on the phase signal. For example, could the phase signal be
influenced by precipitation, e.g. due to changes in dielectric constant, a decrease in surface elevation
due to a snow overload or melting, etcetera? Could the phase signal be influenced by atmospheric
or ionospheric effects? Such influences would undermine measurements of radial distance change
presumed to be represented by interferogram motion phase.
In broadest terms, interferogram phase patterns are in excellent agreement with the way glaciers
are known to move. Furthermore, a drop in surface elevation due to melting over some observation
time interval will result in a severe change in the scattering geometry of the surface layer. This
means that the SAR return phase at the second of two interferometric observations will not be
correlated to the phase at the first observation, as the ’scattering antenna' intrinsic to the surface
layer of snow and ice was perturbed. That is, the random phase signal is no longer stationary.
As a result, the interferogram phase at some pixel (the difference of the two source observation
phases) will be decorrelated relative to nearby pixels, i.e. the phase signal will consist of noise.
Conversely, the absence of noise in an interferogram necessarily indicates that the structure of the
scattering layer was stable over the observation interval. In practice, this coherence-stability varies
from one observation pair to another and even within a scene, indicating that surface changes due
to precipitation, wind and temperature do affect the interferogram phase signal, but in such a way
as to tend to make the data unusable. Only in stable circumstances are coherent data processed
further to obtain glaciological results.
The principle results presented in this work are surface velocities derived from longitudinal flow
patterns. In addition to derived two-dimensional vector fields, these velocities are presented as
centerline speed profiles and lateral transects. The data have an approximate spatial resolution of 40
meters with speed resolution of less than five centimeters per day. Of particular interest are velocity
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characterizations before, during, and after the Bering Glacier surge from 1993-1995 (chapters two
and three). Topographic results are noted on Black Rapids Glacier relative to airborne laser altimeter
data, showing good general agreement but with DSRI errors in excess of a necessary tolerance for
good mass balance estimation (chapter four). This high uncertainty is attributed to small variations
in surface speed that introduce considerable topographic errors, as the motion signal is typically an
order of magnitude stronger than the topographic signal.
In addition to longitudinal flow patterns, an important characteristic motion-phase pattern ob
served repeatedly in the interferograms of the glaciers in this study is a phase bull's-eye. a series
of concentric rings in the phase signal. These bull’s-eyes are invariably localized over the center of
an ice mass, either in a tributary or bay or more commonly at the center of a main glacier chan
nel. which argues against atmosphere or precipation as a cause. In one case, a time series overlay
of bull’s-eyes observed during the 1993-1995 Bering Glacier surge covers most of the East Bagley
Icefield centerline over a distance of 60 km. On Black Rapids Glacier, a bull’s-eye is observed which
persists for several weeks, with its center gradually drifting down glacier at a rate of 30 meters per
day (chapter four).
The cause of a phase bull's-eye is an open question. A model is presented here that takes as its
initial premise a hypothetical influx of liquid water at some low point of the glacier bed. The source
of this water may be some combination of basal friction, geothermal melting, and surface water
travelling to the bed through the subglacial conduit system. Support for this idea is apparent in one
instance of a bull’s-eye on a Bering Glacier tributary bay which is directly down-glacier from a surface
lake. If an influx of water were to raise the basal water pressure above the overburden pressure,
it would create a large, localized jacking force that could lift the entire glacier at that point. This
model contains a latent mechanism for negative feedback, as the change in the subglacial cavity after
an uplift would permit changes in the conduit system, for example permitting drainage of trapped
pockets of water and corresponding surface drop events. In fact bull’s-eyes are observed with both
positive and negative phase curvature, which would indicate both surface rise and drop events. The
necessary water volume represented by a bull’s-eye event is of the order of a million cubic meters.
The model also allows the data to suggest time and distance scales over which such processes would
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act. with bull's-eye event time scales from less than a day up to several weeks. The data consistently
suggest surface elevation changes on a scale of a several centimeters, acting over an area of several
square kilometers. Thus the model accounts for bull’s-eye recurrence, the location of bull’s-eyes
exclusively over the center of the ice channel, and the radial structure and size of the bull’s-eye.
It also suggests ongoing subglacial conduit flow blockage and release events consistent with current
models of channel reworking.
In the context of this speculative interpretation, a time sequence of interferograms prior to and
during a glacier surge onset would be of considerable interest. Also of interest would be a search for
bull’s-eyes on cold glaciers with frozen beds. Bull's-eye events and other DSRI-derived measurements
of temperate glacier motion have yet to be properly confirmed by simultaneous field observations,
particularly observations that make use of GPS systems. Such confirmation would help resolve
ambiguities in the DSRI technique and refine DSRI as a useful glacological tool.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6
Chapter 2. Analysis of the 1993—95
Bering Glacier Surge Using
Differential SAR Interferometry
D e n n is R . F a t l a n d. C r a ig S. L in g l e
Geophysical Institute. University of Alaska Fairbanks. Fairbanks. Alaska 99775. U.S.A.
ABSTRACT. Differential spaceborne radar interferometry observations of the
West Bagley Icefield are used to measure surface velocity and topography. The
Bagley Icefield is the accumulation area for the Bering Glacier which surged in two
phases from spring 1993 through summer 1995. The observations presented are
based on data collected during the winter of 1992. prior to the surge, and during
winter 1994 while the surge was in full progress. Both observation intervals corre
spond to three-day repeat orbit phases of the ERS-1 C-band SAR. This paper gives
an overview of the algorithms used to derive surface velocity vector fields and topo
graphy for valley glaciers from SAR images. The resulting high-resolution velocity
data clearly show West Bagley Icefield accelerating from its quiescent pre-surge
velocity by a factor of 2.7 in response to the Bering Glacier surge. Persistence of
interferometric phase coherence and the relatively moderate degree of acceleration
on the western arm of Bagley Icefield suggest that the velocity increase may have
been caused by increased longitudinal stress gradients resulting from coupling to
the surging main trunk of Bering Glacier.*
* This chapter is in press under this title and authorship in Journal of Glaciology as of December
1998.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTRODUCTION
This paper presents an overview of the concepts and methods of differential radar interferometry
applied to valley glaciers. This is done from an algorithm point of view, as the theory is well
established (e.g. Joughin. 1995: Joughin and others. 1996a: Joughin and others. I996d) with the
intent of showing the progression from SAR images to a surface velocity vector field. We also show
how the constrained motion of a valley glacier can be used to resolve an inherently ambiguous
component of this velocity and we discuss sources of error. In the context of this discussion of
methods, this paper presents the results of an interferometric study of the Bagley Icefield, showing
the acceleration of the ice subsequent to the surge onset of the Bering Glacier in 1993 (Figure l-see
also Molnia, 1993: Lingle and others. 1993).
The 1991 launch of the first European Remote Sensing satellite (ERS-1) was followed by
R.M.Goldstein's recognition that repeat-pass spaceborne radar interferometry (SRI) could be used
to measure the movement of polar ice sheets (Goldstein and others. 1993). SRI makes use of the
comparison of the phase of complex-valued SAR images from repeat orbits. The spatial separation
between two satellite orbits functions like a stereo-vision optical baseline for resolving topography
on a scale of meters. A separate aspect of complex image phase records surface translations, such as
ice motion, as fractions of the radar carrier wavelength on a scale of centimeters. Goldstein's original
innovation made use of fortuitous satellite passes which were spatially coincident, with separations of
only a few meters. These gave poor topographic resolution and so emphasized the ice motion signal.
The technique has subsequently been generalized to obtain results from more typical orbit pairs
with larger baselines (hundreds of meters), giving both surface motion and topography (Gabriel and
others. 1989; Rignot and others. 1995: Joughin. 1995). The generalized technique, referred to as
differential SRI (herein DSRI), has advanced the measurement of surface movement, deformation
and topography of ice sheets and glaciers (Joughin and others, 1996b: Joughin and others, 1996c:
Kwok and Fahnestock, 1996: Rignot. 1996: Rignot and others, 1996: Mohr and others, in press).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1. Bering Glacier. Alaska
Bering Glacier. Bagley Icefield, and associated glaciers, South-Central Alaska.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 00
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9
The launch of ERS-L was also followed by a major surge of the Bering Glacier in the Chugach-
St.Elias mountains of Southcentral Alaska. The Bering Glacier together with its accumulation
area, the Bagley Icefield, and associated glaciers (notably Jefferies Glacier) are shown with arrows
indicating flow directions in Figure 1. With an area of 5200 km 2. the Bering is the largest glacier
system in continental North America (Molnia and Post, 1995). A full description of the ice dynamics
of the 1993-95 Bering surge is incomplete, but much of what is known has been derived from ERS-1
SAR images. As shown by the timeline in Figure 2. the first evidence of the surge visible in a
SAR image became apparent in an ERS-1 scene from April 1993 that shows surface disruptions
approximately 22 km up-glacier from the Bering Glacier terminus within the lower ablation area
(Roush, 1996). The surge front subsequently propagated down the glacier with speeds of up to
100 m d~l. reaching the terminus in August 1993. Typical ice velocities varied from 10 to 20 m d~l
(Fatland and Lingle. 1994). The surge also propagated upstream to the East/West Bagley Icefield
confluence and farther up-glacier into the East Bagley Icefield (Figure 1). The first stage of the
surge ended in August 1994 with an outburst flood at the eastern edge of the terminus. The second
stage of the surge began at an indeterminate time after this, with terminus advance observed in
April of 1995. A second outburst flood in September 1995 marked the end of the surge.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. t Bering _ -(-BERING GLACIER SURGE-) Quiescent STAGE 1 STAGE 2
^ TOF TOF i f I I r I I 11 [ 1 111111 111 i 11 111 1111 mini mill ...... i t / 3 5 D A Y REPEAT/ Hill -'168/35DAYREPEAT.
— 3 Day Repeat Orbits-----: i 992 | 1993 1i 9 9 4 19 9 5 TOF = Terminus Outburst Flood
Figure 2. 1993-1995 Bering Glacier Surge Event Sequence Timeline showing the progression of the Bering Glacier surge (above horizontal bar) and ERS-1 observation phases (below bar). SRI data were obtained from 3-day repat orbit periods only. 11
From 1992 through 1995 the Bering Glacier system was periodically imaged in the 100 km-
wide swath of the ERS-l C’-band (5.7 cm wavelength) SAR. For most of this period the repeat-
orbit interval was either 35 or 168 days and the Bering system was observed from several different
orbital tracks. The 35+ day repeat interval is too long for useful SRI because surface changes
introduce decorrelation noise (Zebker and Villasenor. 1992). but SAR amplitude images are useful
for tracking the progress of the surge through changes in large features such as crevasse fields and
medial moraines. From January through April in both 1992 and 1994. ERS-l was placed in an orbit
(Ice I and Ice II mission phases-Figure 2) which repeated itself to generally better than 250 meters
every three days, imaging a 100 km length of Bagley Icefield. Ice velocities and surface stability
on Bagley Icefield were suitable for DSRI. opening the possibility of highly detailed and spatially-
continuous measurements of How and topography both prior to the surge onset in the winter of 1992
and while the surge was in full progress during the winter of 1993/1994. By contrast. DSRI has
proven unfeasible farther downstream on the rapidly moving ice of the Bering Glacier, both before
and during the surge. The next section provides a DSRI processing overview, starting with the
synthesis of interferograms from SAR image pairs and continuing to the generation of topography
and velocity. These are first presented in the simple cases of (i) fixed topography and a moderate
satellite baseline (for ERS-1. < 300 m), and (ii) a moving surface with zero-length interferometric
baseline. DSRI is then described in the algorithm sense for the general problem of a continuously
moving glacier surface imaged with a moderate interferometric baseline. The algorithm is used to
measure the pre-surge to surge velocity increase on West Bagley Icefield and the sources of error are
discussed.
PROCESSING OVERVIEW
This section describes the main SRI and DSRI processing steps, summarized in Figures 3-10. An
excellent resource on the derivation of the equations given here and further details of DSRI imple
mentation in practice can be found in Joughin (1995). This algorithm overview presents a general
description of DSRI processing in order to provide a basis for evaluating the glaciological utility of
the results. SAR interferometry is a relatively simple image processing concept made complex in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12
practice by the exigencies of the data. Figure 3 shows the interferometric imaging geometry in a
plane approximately perpendicular to the instrument flight direction. Figure 4 is a flowchart for the
generation of a Digital Elevation Model (DEM) from two SAR images as in the case of an unglaciated
region in which the interferometric phase signal represents topography only. An example scene near
Bagley Icefield, used later to determine the interferometric baseline, is shown in Figure 5.
The first step in forming an interferogram is the coregistration of two images to a fraction of
a resolution cell (Figure 6). Resolution cells are interchangeably thought of as small blocks of
pixels defined by the resolution of the SAR and the corresponding surface region in the physical
scene. A resolution cell is generally several pixels in size, but it is often convenient to blur the
distinctions between pixels, resolution cells, and corresponding patches of ground. Once two images
are coregistered, the complex phases are differenced while the amplitudes are retained to form a
new complex-valued image called an interferogram. The spatial separation between the two imaging
passes in the plane perpendicular to the spacecraft flight path is described in terms of a line-of-sight
parallel component Bp and a line-of-sight perpendicular component Bn (Figure 3). The latter is
called the interferometric baseline and it is analogous to an optical baseline in stereo imaging. For
ERS-1 both Bp and Bn are frequently less than 250 meters for repeat-orbits separated by three days,
which represents good orbit control from the point of view of satellite orbital mechanics and glacier
DSRI.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3. Multi-Pass SAR Interferometry Imaging Geometry
Interferometric imaging geometry. Bn and Bp are defined in the plane of the SAR look direction,
perpendicular to the satellite flight track. Bn is norm al to. and Bp is parallel to the line from Si to
the center point of the image swath C.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 3. Multi-Pass SAR Interferometry Imaging Geometry
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4. SRI Processing Algorithm Flowchart
SRI processing flowchart showing the generation of a digital elevation model (DEM) under circum
stances in which no glaciers are present to introduce additional translation phase into the topographic
phase signal.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14
SRI
1 1. Acquire two coregistered images
I 2. Make interferogram
3. Obtain baseline estimate
4. Remove geometric phase
j i 5. Unwrap residual topographic phase
rBaseline ^ i 7.Refine baseline .accurate.
t8. Rectify image to ground range i ( 9. Determine elevation uncertainties I Products: SAR image and DEM
Figure 4. SRI Processing Algorithm Flowchart
Reproduced w»d p e n sio n C «de cop,rigd, owner Fodder reproduce prodded w»dou, p en sio n . 15
Figure 5. Non-Glacier SRI ‘Topography-Only’ Phase
Interferograms of a non-glacier-covered valley near Bagley Icefield. (a) Phase signal prior to removal of flat-earth phase (parallel bands). (b) Phase signal after removal of flat-earth phase. (c) Perspective rendering of (b) showing topographic relief with slant-range layover still present
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I .eft image (a) is a glacier (a) is surface .eft image from source two coregistered images I to within pixel. 1 Coherence improvementin interferometricphase onJefferies Glacier, atributary the of EastIcefield. Bagley signal gain Rightaftershows (b) image sub-pixel coregistration adjustment. Figure 6. Comparison of Non-Resampled Versus Sub-Pixel Resampled Interferogram Data Interferogram Sub-Pixel Resampled Versus ofNon-Resampled 6. Figure Comparison
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17
The intrinsic phase coherence of an interferogram is evaluated as a scalar field of autocorrelation
values p for a small cluster of .V pixels:
X m E . = 1 *iVi P ~ ( 1)
where x, and y, are (complex) signal values from source images I and 2. respectively, and y“ is the
complex conjugate of y,. Since an interferogram pixel phase is the difference of the source image pixel
phases, interferogram pixels can be represented as x,y". Interferogram coherence varies throughout
the image and is used as a quality guide in subsequent processing.
Having removed the random phase variation throughout the individual SAR images by making
an interferogram. the residual phase signal 'P is given by
total — 'I^noijc 4" 4 ^geom 4" topo 4* ^tram • " here (2) 2 kB nA R scene . g e o m ~ JTT------• R tan a _ 2kB„Ah ... * to p o a - 5 - = ----- : ( 4) ft sin a trans a 2kAR. (5)
and where k is the radar wavenumber 2ff/A. A is the radar carrier wavelength (5.7 cm for ERS-1),
R is the distance from the SAR to the scene center, and a is the image-center radar incidence angle
(Figure 3). A/?Jcens is the change in range across across the image relative to the center range R.
This distance is measured in kilometers, in contrast to DeltaR. which is the radial distance change of
a resolution cell due to its spatial translation between imaging passes (Figure 7). DeltaR drives the
translational phase signal 'Pjran* and is measured in terms of centimeters. The topographic elevation
of the resolution cell relative to a reference elevation is given by A h. and only the topographic phase
term 'I'to p o contains an explicit dependence on both the topography and the perpendicular baseline
p aram eter Bn. '8r„oije is related to the interferometric signal coherence p and is neglected for now.
leaving the three terms ^Sfgeom + 4'topo + ^iranj • These three phase signals must be separated in the
general case of a moving glacier with surface topography.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 7. Surface Motion Resulting in Radial Distance Changes
Two SAR data acquisitions, with resolution cells 1 and 2 moving during the intervening period
give radial distance changes A/?i and Afto-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 7 Figure 7. Surface Motion Resulting in Radial Distance Changes
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19
Case 1: Topography Without Surface Motion
We first consider the case of a fixed surface topography with no glaciers, a moderate interferometric
baseline. \Bn\ < 300 m. and no phase noise. The total phase is then
•r. '2k B * . u -I total ~ + - 5 — ------• 6 rttana nsma ( )
since 'f,tPonj = 0. Joughin (1995) gives a derivation of the topographic phase signal and the conver
sion from SAR slant range images to ground range. The steps for producing a ground- range DEM
are presented in outline in Figure 4 with some elaboration as follows:
1. Image acquisition is a matter of opportunity subject to restrictions of SAR orbital paths and
other flight agency operational issues. Suitable image pairs are coregistered to within a pixel using
immobile features. These image pairs are separated by a time interval A t which is generally short
(days) to minimize signal decorrelation. Sub-pixel resampling is a second order' process which can
significantly improve interferometric phase coherence as shown in Figure 6 (see also Appendix).
2. An interferogram is generated by subtracting the phases of the two images on a pixel-by-pixel
basis. In this case the resulting phase signal will consist of the two terms given in Equation 6 plus
a spatially varying noise contribution. Pixel phase is often represented visually using color scaled in
intensity by pixel amplitude. This shows the general phase characteristics of the interferogram as
well as identifiable features.
3. Both terms of Equation 6 are dependent on the normal baseline component S„. analogous to
a stereo vision interocular baseline. It is thus necessary to make an initial estimate of Bn by some
means in order to analyze the phase signal. Image misregistration can be used for this estimate but
it is generally simpler and more accurate to consult an appropriate flight agency online database
(e.g. for ERS-l. at ESRIN: http://gds.esrin.esa.it/). It is sometimes necessary to iteratively refine
the initial baseline estimate as shown in Figure 4 (see also Appendix).
4. The geometric phase contribution to the total phase is a regular, nearly linear ramp, modulo 2;r,
which covers the entire interferogram (apparent in Figure 5a). This is primarily due to a dependence
on the baseline B„ which typically varies nearly linearly by only a few meters along-track from one
end of an image to the other and by its dependence on the incidence angle a which varies across-track.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20
Wgeom is the phase signal due to the imaging geometry that would be present in the interferogram
if the scene were completely flat (no surface topography: only the earth's curvature). Consequently
Vgeom does not contain any useful information and can be subtracted from the interferogram phase
signal, leaving only residual topographic phase (Figure 5b).
Often ‘flat-earth ramp' phase subtraction is followed by low pass filtering that reduces signal noise
and produces pixels with near-unity aspect ratio. Filtering the phase signal is often necessary to
some degree and may be implemented with a locally adaptive scheme which uses phase coherence
and/or signal amplitude as a guide.
5. Phase unwrapping is shown in both one and two dimensions in Figure 8. It consists of the
addition or subtraction of integer multiples of 2;r to each pixel as necessary to eliminate phase
discontinuities and is described in more detail in the next section. In noisy areas phase unwrapping
is quite problematical: such regions are often cut from the final data product or interpolated between
regions of good signal (Goldstein and others. 1988: Pritt. 1996. see also Appendix).
6. An unwrapped phase signal will have a precise relationship between unwrapped phase values
and corresponding surface elevations. These can be compared to a suitably selected set of tie points
distributed as widely as possible throughout the scene. If the fit to the tiepoints is poor then we
conclude that the baseline used in step 4 is in error and must be refined, for example using the
linear least-squares approximation described by Joughin (1995). The baseline estimate is refined
iteratively to an acceptable tolerance before proceeding further.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 8. Phase Unwrapping
Phase unwrapping in one and two dimensions. The jagged nature of the centerline phase plot is
indicative of data noise rather than variations in velocity. In both the upper and lower plots, a
signal is shown in which the vertical coordinate is phase constrained to the interval [— ~. jt]. The
unwrapped phase is no longer subjected to this constraint: instead the interval between adjacent
unwrapped pixels must have an absolute value less than tt.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21
Glacier center line relative distance (km)
noise artifacts
Wrapped phase, two dimensions Unwrapped phase, two dimensions Figure 8. Phase Unwrapping
h, owner Furtherreproduction prohibited without permission. Reproduced with permission of the copyrightFurth P owner. •22
7. It is useful to transform SAR image products from their processed form to a ground range' map
projection in which each pixel represents the same size surface area. Normally single-look complex
(SLC) SAR images are processed to ’slant range' format, in which each successive pixel in the cross
track direction represents a quantization of some number of meters in radial distance from the SAR
antenna. For a flat earth surface, the increasing angle of incidence across the swath will result in
successively smaller ground-range projections of each slant-range pixel so that there is not a simple
constant relationship between slant range and ground range pixels. The problem of transforming
images to ground range is further complicated by layover distortion produced by scene topography.
Slant-to-ground-range rectification using interferometrically derived surface elevations produces a
ground-range image in which all pixels have the same map-projection dimensions (Joughin and
others, 1996d).
8. Elevation uncertainties can be estimated directly from phase variance try using Equation 6 to
give _ R s in a
The end result of the process outlined in Figure 4 is thus a DEM (herein designated where h is
the surface height at pixel (i.j)), consisting of an array of pixel elevations with respect to a reference
datum, with associated errors. The (rectified) SAR amplitude image can be draped over the DEM
to show feature correspondence. Typically the derived DEM has an accuracy of ~ 5 — 20 m (Zebker
and others. 1994), dependent on the availability of ground control.
Case 2: Surface M otion W ith Bn = 0
In this situation we consider a scene containing moving resolution cells imaged twice from the same
location over some time interval At so that Bn = 0. giving 'Pgeom = 0 and 'ftopo = 0. When a
particular region on a glacier undergoes a Tigid’ (locally non-deforming) translation Ax relative to
some other fixed region in the scene, there is generally a corresponding change in radial distance
A R from that resolution cell to the SAR as shown in Figure 7. Spaceborne SAR has a coarse-scale
two-dimensional (map view) resolution of the order of tens of meters, but at the same time for each
resolution cell the SAR measures radar echo phase as a fraction of the carrier wavelength. Thus it also
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23
acts as a range-sensitive instrument on a scale of centimeters, but with no angular spatial resolution
at this scale. As a result, surface translations result in a globally ambiguous fractional wavelength'
interferogram phase signal which indicates only small radial distance changes at each resolution
cell, relative to nearby resolution cells. For example, if over three days a resolution cell moves 9.1A
closer to the SAR. then the roundtrip distance change is 18.2A which would only be apparent in
the phase signal as a fractional shift of 0.2A or 0.2 x 2;r radians in terms of pixel phase. By itself
this would be indistinguishable from a radial distance change of 8.1A. 7.1A. etc.. so it is necessary to
have a gradually varying phase signal with locally small (< ~) phase increments between adjacent
pixels to allow unambiguous integration of A R. This process of integration, starting from a known-
value reference location (e.g. a fixed surface) and summing phase increments to keep track of total
accumulated phase is referred to as ‘phase unwrapping’ (Goldstein and others. 1988). Unwrapped'
phase is no longer constrained to [— tc, ~] and is related, in this example, to the radar line-of-sight
radial translation of surface resolution cells by the direct proportionality 'F,ranj = 2kAR.
Case 3: A Moving Surface W ith Topographic Relief and Non-Zero Baseline
Generalizing Figure 7 to a non-zero baseline will add geometric and topographic phase signals 'tgeom
and 'Ftopo- both dependent on the norm al baseline Bn. to the translational phase $ tranj- This
represents the general case for interferometric analysis of glaciers and ice sheets. It is of interest
to distinguish the scales of translational and topographic phase, as SRI systems generally give
topographic resolution on a scale of several meters (Zebker and others. 1994) whereas the fractional-
wavelength translation phase measurements give translation resolution on a scale of centimeters.
Furthermore only one of the three translation vector components is given by the translation phase:
that is. only the component of ground motion in the radar line of sight direction is obtained. The
remaining two components must be derived by other means, as discussed in the next section.
Assuming B„ has been adequately determined and the geometric phase removed from an inter
ferogram. the remaining phase is
^ to ta l ^ ^ to p o 4*
« ■ 2 k- Bn Ah + 2kAR. (8) r ts tn a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. •24
The separation of these two terms exploits the inherent differential scaling of the two types of
information using multiple image pairs: this is shown in the flowchart in Figure 9 and schematically
in Figure 10. The phase superposition and separation is shown in Figures lla-d on West Bagley
Icefield. The procedure is as follows.
I. Four source images are used to generate two interferograms with two respective 'normal'
baselines B\ and Bn. Since the random scattering phase is (ideally) eliminated in these source
interferograms. there is no restriction on the time interval between pairs. However, subsequent
interferogram comparisons must account for possible physical differences in the imaging conditions.
For example, a glacier interferogram from winter compared with another from a different season will
have phase signals reflecting seasonal differences in surface speed, violating the constant velocity
assum ption' (see below).
*2. It is assumed (for now) that the surface motion between images I and "2 is the same as between
images 3 and 4. i.e. we assume that the glacier moves with constant velocity so that A R i = A Rn =
AR. To maximize the probability of this, it is best for the two image pairs to be closely spaced
in time. The result of failure of this assumption is discussed below. Differencing the phases of
interferograms 'Ft and 'tn thus cancels the translation phase component to produce a differential
interferogram 'F12 in which the phase represents topography only, scaled by the differential baseline
By — Bn.
'ifi =2kARl +aBlAh: (9)
= 2kARn + aBnAh: (10)
«13 = «! - V3«a(Ri-£o)AA. (11)
where a = 2k/ Rsina. Topography-only phase ^ 1 2 is shown in Figure 11c.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 9. DSRI Processing Algorithm Flowchart
DSRI processing flowchart, showing the generation of glacier surface velocity field and. in passing,
a DEM. under the assumption of constant glacier velocity.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25
DSRI
I. Acquire two pairs of coregistered images, make two interferograms
2. Make double interferogram topography only
i 3. Use topography-only interferogram to remove topography from original interferograms I 4. Unwrap residual motion phase i i 5. Project line-of-sight motion into velocity vector field i 6. Determine uncertainties i Products: SAR image, DEM and Surface Velocities
Figure 9. DSRI Processing Algorithm Flowchart
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 10. DSRI Schematic
DSRI processing schematic illustrating the differentiation of topographic and translation phases. B\
and Bn are the interferometric baselines (normal component. B„) for the two source image pairs.
A R is the radial distance change to be derived from the translation phase signal 'I'tronj -
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AR only by base line ratios Unwrap phase, rescale Figure 10. DSRI Schematic Interferograms Differential Interferograms Images Base line Bj Base line 62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 11. DSRI Interferograms: Various Processing Stages
This set of interferograms correspond to various stages of Figure 10. (a) West Bagley Icefield
interferogram. January 19-22. 1992. prior to the 1993 Bering Glacier surge onset. Ice flows from left
to right, (b) Same site, data from February 4-7. 1994. with more central phase bands indicating
post-surge-onset velocity increase, (a) and (b) also have the moderate glacier surface topography
folded into the phase signal, (c) Differential interferogram in which translation phase is removed
leaving only topographic phase. Phase-color boundaries are analogous to topographic contour lines,
showing a typical accumulation area profile with glacier margins higher than the center, (d) Surface
translation phase only for 1994 interferogram. after removal of topographic phase. Comparison with
lib shows more central bands present.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27
Figure 11. DSRI Interferograms: Various Processing Stages
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28
3. The isolated topographic phase can be unwrapped into an unconstrained scalar field and
rescaled to any desired baseline, particularly to B\ and B->. T hat is. 't’ 12 is rescaled to match the
'J'topo component of interferograms 4 ' 1 and 'I’o. so that another phase difference can be used to
isolate the translational phase signal:
t f 12 % 2 kA R = 4?tranj * ( 12)
l2 % 2k AR = trans (13)
4. Either ^i_[2, ^ 2 _ i2. or some combination (such as their average) can be taken to represent
the isolated translational phase 'ttrana- Because the translation phase represents relative velocity, a
suitable fixed point must be chosen as the zero-velocity starting location for phase unwrapping, for
example a pixel on a mountain near the glacier margin. Because the topographic phase has been
removed, all pixels on fixed features should have constant phase, regardless of pixel elevation. This
distinction is apparent in a comparison of Figures 11a and lib (which include topographic phase)
with Figure lid from which the topographic phase has been removed.
5. The radial distance change A R given by 'iftrans can be converted to a surface velocity vector
by projection of the (unwrapped) 4 *trans phase into an appropriately chosen flow direction (next
section).
6 . As with the DEM generation process, local phase variance obtained from the data can be used
(E quation 5 ) to estimate uncertainties in A R which can be translated into velocity uncertainties.
CONVERSION OF RADIAL DISTANCE CHANGE TO SURFACE VELOCITY
VECTOR FIELD
Figure 12 shows a coordinate system with origin located at the center of a resolution cell, z axis
defined vertically upwards and x axis lying in the local horizontal plane (not the glacier surface
plane) pointing in the SAR cross-track direction, which in the case of Bagley Icefield is similar but
not identical to the glacier flow direction. When the side-looking SAR is imaging this resolution
cell, the SAR will have coordinates (A's,0, Zs). Between the two passes the resolution cell moves
a distance S along a flow unit vector u. The derivation of ti is problematical, but below it will be
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. *29
derived from a 2-dimensional flow unit vector / defined in the xy-plane. The ice-flow vector Sii
results in a change in radial distance of A R along a line-of-sight unit vector r = (rr .O. r:). where
rx/ r - = X s / Z s . In fact. Sii can be written as the sum of the vector A R ■ r and some vector .4
perpendicular to r:
Sii = A R r + A. .41 r. (14)
In lieu of fortuitous multiple-direction SAR data acquisitions (Joughin and others. 1996b: Mohr
and others. 1997) this method of velocity calculation necessitates some means of determining the
unit vector ti for surface-parallel flow in the longitudinal direction. Using the topographic gradient
(ti = Vh,j/|V/i,jj is inadequate because valley glacier topography is dynamically supported by
moving ice (Raymond. 1971: Echelmeyer. 1983). It is more feasible to calculate u by assuming
that the glacier flows parallel to the valley walls across most of its width. In this work, the two
relative components of it in the ry-plane are derived first, giving the map-plane flow unit vector
/ = { / i , / 2 . 0 }. The r-component of ti is then derived by taking the surface gradient of the glacier
topography in the / direction. The unit vector ti = {u t . u 2 , 113} is then normalized and the translation
vector A R ■ r is projected in the u direction to give 5. The correction from / to u is necessary to
avoid introducing a five per cent error in velocity. The difficult part of this process, determining
fi and / 2 at each glacier-pixel in the image, can be done 'by hand’ for a particular study site.
Particularly problematical is the determination of / for embayments. tributaries, and in representing
small transverse velocity components. A first order approach to deriving / at each pixel is to draw a
(smoothed) centerine through the image which approximates the glacier flow direction (Figure 13).
At a particular pixel along this line, f is given by the local centerline tangent. A perpendicular
transect line is extended from this centerline pixel across the glacier, and each pixel of this transect
is assigned the same value of /. If the centerline is curved, some pixels will be visited multiple
times by this technique and others will be missed entirely, necessitating some filtering to produce a
continuous and smoothly varying / vector field. A second-order improvement could model the map-
plane lateral convergence or divergence of this field (in accumulation and ablation areas respectively)
which empirically seems to approach 7° — 10° at the transition area from centerline flow to the glacier
shear margin on typical temperate valley glaciers. Errors in / and thus in velocity are discussed
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30
below.
Having determined / at a particular pixel and derived ti from the local surface gradient along /.
the projection geometry gives - A rt S = ------( lo) ui ■ ri + U3 ■ fj
where AR is determined from the unwrapped translation phase by A R = 'f?(?arl3/'2k. As a rule
of thumb, for a glacier moving at an azimuthal angle 9 with respect to the cross-track direction under
ERS-1 imaging conditions, one phase fringe (a complete color cycle) from an image pair separated
by three days corresponds to ~ 2.5/cos 9 cm d~l. (Here 9 is defined relative to the cross-track axis
such that it satisfies the constraint || 0 || < « /2 .)
Using the above technique, errors in flow-direction angle 9 and to a lesser extent the incidence
angle a are the biggest contributors to error in the calculation of surface velocity. Figure 14 shows
resultant velocity errors in percent for given flow direction and incidence angle errors using the
approximate relationship for surface speed 5 as a function of unwrapped phase 'P:
, * (16) '2k - At • sin a ■ cos 9
Errors in a. the local incidence angle, are caused by errors in the estimation of glacier surface
slope: these will be smaller than flow-direction errors but are also subject to greater local variability
with undulations in the glacier surface. Under good conditions DSRI will pick out such undulations
from the differential topographic interferogram. Using an upper limit for the flow-direction error
A 9 of 5° and a maximum acceptable velocity error of "20%. Figure 14 gives the restriction that the
glacier m ust flow in a direction 9 < 65° from the SAR cross-track image axis. That is. single-pass
DSRI velocity determination works poorly or not at all on glaciers which happen to flow close to
the along-track image axis (i.e. parallel to the SAR flight path).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 12. Velocity Projection Geometry
Observed radial translation = R f . ad hoc horizontal-plane flow direction = /. and derived velocity
vector = S ■ u.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 13. Determination of Two-Dimensional Flow-Direction Unit Vectors
Flow-direction unit vectors are determined from a centerline. The local tangent direction is extrap
olated laterally across the width of the glacier.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32
Figure 13. Determination of Two-Dimensional Flow-Direction Unit Vectors
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 14. Velocity Error as a Function of Flow-Direction Error
Velocity error as a function of flow-direction error. Inset plot: Corresponding errors for errors in
incidence angle estimation.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33
Flow direction 6 with respect to cross-track direction
Figure 14. Velocity Error as a Function of Flow-Direction Error
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WEST BAGLEY ICEFIELD RESULTS
Figures 15 and 16 show the acceleration of West Bagley Icefield between January 199*2 and February
1994. Figure 15 shows a comparison of transect velocity profiles approximately 10 km downstream
from the ice divide separating West Bagley Icefield from Steller Glacier. The 199*2 velocity transect
is plateau-like in the center of the glacier whereas the 1994 transect velocity is somewhat more
rounded. In the inset graph, both velocity curves from the centerline north to the margin have
been rescaled to compare curvature with a simple theoretical curve for deformational flow (flow law.
n = 3, no shape factors (Glen. 1955)):
(17) — f e1/2 ) 4
Here x is distance from centerline toward the margin and r i / 2 is the half-width of the icefield.
The 1992 profile is assumed to represent the non-surging character of the West Bagley Icefield
velocity. The departure of this profile from the curvature given by Equation 17 may be indicative of
the influence of the valley shape (Echelmeyer. 1983) and/or some degree of laterally-varying basal
m otion.
The second departure in velocity profile curvature, that from the 1992 profile to the 1994 profile,
shows that the acceleration induced by the surge was stronger at the center of the icefield than
at the margins. The mechanism for this acceleration is likely to be a separate lateral variation in
basal motion associated with the Bering surge (as opposed to an increase in flow due to internal
deformational). Such variations have been observed previously (e.g. Raymond. 1971) and in this case
are presumed to be due to the manner of coupling between the Bagley Icefield and the Bering Glacier.
One possible mechanism is a longitudinal stress impulse imparted by the removal of restraining ice
downstream as the Bering Glacier surged. Relative to the margins, the central part of West Bagley
Icefield is less susceptible to marginal shear stress. Another potential factor in causing lateral sliding
variations is a hypothetical increase in subglacial water pressure acting to reduce basal shear stress,
e.g. Robin and Weertman. 1973.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 15. Comparison of Velocity Transects from 1992 and 1994
Comparison of several overlain velocity transects from 1992 and 1994. The dissimilarity in these
profiles indicates variable sliding speed, probably in response to the Bering Glacier surge. The inset
plot shows both velocity curves from the centerline north to the margin, arbitrarily rescaled for
comparison of shape with the curvature of a theoretical (flow law. n = 3) velocity profile (solid line).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35
Transect distance (km) from south to north
Figure 15. Comparison of Velocity Transects from 1992 and 1994
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 16. West Bagley Icefield Longitudinal Velocity Comparison. 1992 to 1994
West Bagley Icefield longitudinal velocity comparison. 1992 to 1994. (a) Velocity-only phase signal
from 1992. with transect location and longitudinal profile shown in white, (b) Same location. 1994.
Areas which are black or solid color indicate signal dropout due to poor coherence, (c) Centerline
velocity profile comparison, (d), (e) Perspective rendering of surge-related acceleration of West
Bagley Icefield, looking west from the East/W est Bagley confluence. Vertical relief indicates surface
speed.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36
Figure 16. West Bagley Icefield Velocity Comparison, 1992 to 1994
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37
Figures L6a and L 6 b are translation-only differential interferograms from 1992 and 1994. respec
tively. Considerable changes in the phase signal in the central part of the glacier show the longitudinal
acceleration in the 1994 image associated with the Bering surge, also shown by the change in the
centerline velocity profile in Figure 16c. A remarkable aspect of this centerline comparison is that
the 1994 profile is very similar to the 1992 profile multiplied by an empirical factor of 2.7 (dotted
curve in Figure 16c).
Near the confluence where West and East Bagley Icefields flow together, the centerline velocity
has increased from 0.36 m d~l in 1992 to 0.95 m d~l in 1994. Differential interferom etry also showed
appreciable acceleration over the one month interval from January to February 1994. At the rate of
acceleration derived from this one month period, the influence of the surge on West Bagley Icefield
can be estimated to have lasted for four to five months by the time the February 1994 data were
acquired. With the uncertainty in surge onset location (symbol. Figure I. or possibly farther up-
glacier) and surge start time (apparently between late March and late April 1993. possibly earlier),
these data suggest that the speed of up-glacier propagation of the Bering surge to the Bagley Icefield
confluence was of the order of 200 to 500 m d~l. Subsequently, increased longitudinal stress gradients
caused the centerline velocity of West Bagley Icefield to increase by a factor of ~ 2.7 over a time
period that may have been as little as four months.
FAILURE OF THE CONSTANT VELOCITY ASSUMPTION
To claim that the differential interferogram shown in Figure lie contains only information about
topography it is necessary to assume that the glacier velocity field is time-invariant so that the
translation components of the source phase-signals cancel. This 'constant velocity assumption"
(herein CVA) is generally quite valid on ice sheets (with notable exceptions: see Joughin and others.
1996c). For temperate valley glaciers with sliding speeds highly coupled to subglacial hydrology, it
may be best to say that, if possible, the CVA assumption should be demonstrated to be valid, for
example by deriving consistent topographic phase from a time sequence of many image pairs. Most
valley glacier CVA failures are observed to be small in magnitude, usually a fractional part of a
fringe representing velocity differences of less than one centimeter per day. A more extreme example
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38
of CV'A failure is shown in the differential interferogram (nominally topography-only ) in Figure 17.
in which two concentric fringe patterns or bull's-eyes appear on East Bagley Icefield, each ~ 4 km
in diameter. The constituent observation intervals are January '2-5 and January 11-14. 1994 and
the differential baseline B\ — B? is ‘28 m. Such a phase pattern, if it were to indicate topography,
would represent two steep conical hills 1600 m high.
There are other possible causes for phase anomalies of this sort, most notably some manner of
atmospheric or ionospheric contamination of the propogating radar signal. The effects of atmospheric
water vapor on topographic phase described by Goldstein (1995) and by Zebker and others (1997)
are present at low latitudes but are unlikely to have such a strong influence during winter at 60°
N latitude. Furthermore the nature of these bull’s-eyes (and others seen in similar data) argues
against atmospheric causes in general as they are cleanly localized and rest symmetrically over the
hypothetical deepest part of East Bagley Icefield. In fact we suppose that the most likely explanation
for these bull's-eyes is not that they represent a variation in longitudinal sliding velocity, but that
they represent a local rise of the surface of ~ 20 cm over a three day time interval, from January 2 to
January 5. This value is consistent with observations on Black Rapids Glacier, a surge-type glacier
in central Alaska, where Heinrichs and others (1996) observed annual elevation cycles of ~ 1 m and,
more to the point, elevation changes on a scale of 10 — 20 cm have been observed over a matter
of hours in association with rapid lake drainage events (M. Nolan, personal communication). A
hydrological event of this sort, normally considered unlikely in winter, may be facilitated by the
dynamics of the Bering surge (for comparison see Kamb and others. 1985, regarding a surge-related
event in February 1983 on Variegated Glacier, Alaska). The volume represented by this hypothetical
surface uplift is 7 x 10” m3.
The hypothesis of a surface rise is only one possible type of surface translation (albeit the most
obvious one) which could account for the observed bull's-eyes. This emphasizes the importance
of recognizing that subtle aspects of glacier dynamics and associated CVA failures introduce local
errors into the DSRI technique for estimation of the velocity field.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 17. Phase Bull’s-Eye Features. East Bagley Icefield 1994
Differential Interferogram (nominally topography-cnly) of part of East Bagley Icefield with two
features indicating failure of constant velocity assumption, from January 1994. These features are
speculatively interpreted as surface uplift of more than 20 cm over a three-day interval. January 2-5.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 17. Phase Bulls-Eye Features, East Bagley Icefield 1994
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40
RESOLVING SURGE DRAWDOWN
We expect the acceleration of West Bagley Icefield to be accompanied by a drawdown of the surface,
but resolving this change in surface elevation using DSRI-derived DEMs is problematical. The
theoretical limit to ERS-I-based SRI elevation is ~ 5 m rm s (Zebker and others. 1994). However,
the effects of small baselines for this data, acting in conjunction with phase noise, scattering depth
uncertainty, and the potential for CV'A failure (West Bagley Icefield was accelerating in 1994) require
us to revise this limit upward to 20 m rms accuracy at best. At this limit of resolution, a comparison
of pre-surge (1992) and during-surge (1994) elevation interferograms failed to give conclusive evidence
of surface drawdown. Taking a pre-surge centerline surface velocity of 100 m a ~ 1 and a surface slope
of 0.95°. and using a conventional flow law calculation for temperate ice with sliding speed ranging
from 20 % to 80% of the total speed (no valley shape factors since the half-width is greater than
three times the probable depth (Patterson. 1994)). the inferred depth of West Bagley Icefield is
about 500 — 700 m. The time of exposure to surge influence at the West Bagley Icefield equilibrium
line is estimated at between 150 and 200 days. A continuity calculation for the observed speed-up
shown in Figure 16c gives a maximum theoretical drawdown of 5 — 10m. which accounts for the
difficulty in resolving such a drawdown using DSRI.
SUMMARY
The large-scale glaciological problem of characterizing the dynamic behavior of West Bagley Icefield
during the 1993-95 Bering Glacier surge is addressed by differential interferometric analysis of SAR
data (DSRI). DSRI is only applicable to the study of relatively slow flow, for example on Bagley
Icefield and Jeffries Glacier, as it is easily rendered ineffective by decorrelation noise from rapidly
moving and deforming (i.e. surging) ice. The limitations of DSRI including its considerable compu
tational complexities are compensated by the capacity of this technique to produce glacier DEMs
and surface velocity vector fields at high resolution.
Due to the abundance of stable ice-free topography, interferometric baselines for valley glacier
scenes are comparatively easy to determine and refine (compared to the relatively featureless polar
ice sheets) using tiepoint-iteration techniques. Baseline refinement is consequently limited by tie-
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point errors and decorrelation noise. The determination of precise baseline data by the various flight
agencies (e.g. European Space Agency) has reduced the problem of baseline refinement. Decorre
lation noise also makes the analysis of temperate valley glaciers difficult relative to ice sheet data.
This decorrelation is likely due to high temperatures and proximity to coastal weather systems in
the G ulf of Alaska.
Using only a single observation geometry, an assumption of flow parallel to the axis of the valley
(rather than flow down the surface gradient) should be used to obtain valley glacier surface velocity
fields. Flow-direction errors are minimized as the direction of glacier flow approaches the radar
cross-track look direction but are exacerbated in regions of complex flow, particularly at glacier
confluences. In addition to flow-direction errors. DSRI error sources (in the ERS-1 3-day repeat
context) can be summarized as follows: Errors in baseline estimation will give a systematic bias
to the entire scene which can easily be mistaken for real data (Joughin and others. 1996a). Phase
unwrapping from a non-zero-velocity starting location will introduce a small constant offset to all
data within a particular scene, in general less than (2/cos 9) cm d~l. A phase unwrapping error
(using the Goldstein technique (1988)) may introduce discontinuities in the unwrapped phase as
integer multiples of 2ir. If undetected during analysis, these will lead to errors in the derived surface
velocities by corresponding integer multiples of (2.5/cos 0) cm d~l. Such discontinuities are often
easily noticeable and may be remedied by filtering. Coherence-related phase noise introduces a high
frequency noise component in velocity or topography results. In this work, phase noise introduces a
speed uncertainty of about ±(3/cos0) m m d~l in regions of high coherence. Finally an important
case-dependent source of error is failure of the constant velocity assumption (C’VA). In subtle cases
the introduced errors will be less than one fringe (< (2.5/cos0) cm d~l). Drastic CVA failures can
invalidate velocity and topography results but can also provide insights into glacier dynamics and
subglacial hydrology.
Particular to the Bering Glacier surge, a three-fold acceleration of West Bagley Icefield is clearly
observed in the comparison of DSRI results from 1992 to 1994. This observation was possible because
phase coherence is maintained in 1994 scenes acquired while the surge was in progress, implying that
the surface of West Bagley was fairly stable over three-day periods during this time. Such stability,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42
combined with moderate acceleration relative to the Bering Glacier surge, may further imply that
the massive restructuring of the subglacial hydrological system associated with surging glaciers
(Kamb and others. 1985) did not extend up into West Bagley Icefield. If this is the case, the 20 km
longitudinal acceleration profile was probably caused by a simple reduction of downstream restraint
due to lowering of ice during the surge. This downstream surface lowering may have imparted
increased longitudinal stress gradients which had greatest effect along the centerline of West Bagley
Icefield where the resistance of marginal shear stress was minimal. The data also place a coarse
limit of 200 to 500 m d~l on the upstream surge propagation speed. This is considerably faster
than the observed downstream propagation of the surge front at ~ 100 m d ~ l (Roush. 1996). The
pre-surge velocity was used to estimate the depth of West Bagley Icefield at 500 — 700 m. The
surface drawdown implied by the acceleration event was not observed, possibly because it was not
within the resolution limits of topographic DSRI.
ACKNOWLEDGEMENTS
We thank the National Science Foundation for providing initial support for this work with Small
Grant for Exploratory Research OPP93-19873. NASA for providing support with grants NAGW-
4930 and NAG5-4068. CTay Research. Inc.. for providing additional support via their University
Research and Development Grant Program, and the Arctic Region Supercomputing Center for pro
viding computational support. We thank the Alaska SAR Facility. University of Alaska Fairbanks,
for a graduate research assistantship to D.R. Fatland. and we also thank Ian Joughin. Dick Goldstein.
Mark Fahnestock. Eric Rignot. Will Harrison. Keith Echelmeyer, Martin Truffer. Charles Raymond,
and Matt Nolan for valuable conversations and comments on this work.
APPENDICES
Image Coregistration
Images are misregistered due to scene topography, the spatial separation of the two spacecraft
orbital passes (the baseline), and other systemic errors. Image coregistration to within one pixel
is accomplished with a straightforward linear translation of one image. Sub-pixel coregistration
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43
is commonly applied to improve phase coherence. In a system of glaciers with a variety of flow
directions (Figure I) it is necessary to use a locally adaptive resampling technique to compensate
for misregistration incurred by the ice motion on top of the other effects. For this work, ‘20.000
local misregistrations measurements are calculated on a 1/3 km grid for each 40 km x 50 km scene.
This is done both from image I to image 2 and vice versa, with only reciprocating offset vectors
retained in order to eliminate spurious results. Each measurement is made using small correlation
chips oversampled by a factor of 4 in both directions. The resulting misregistration grid is low-pass
filtered to reduce noise, giving a self-consistent smoothly varying fractional-pixel offset grid which
is used to drive a local bilinear interpolation resampling of one of the two images. This technique
provides extremely useful signal recovery as shown in Figure 7.
Baseline Calculation
A linear approximation to the non-linear problem of refining the interferometric baseline is given
by Joughin (1995). The standard approach involves phase unwrapping an interferogram to deter
mine phase differences between several tiepoint locations in the scene. These phase differences are
compared to the theoretical phase differences given an assumed baseline, and the error between the
two is used to refine the baseline estimate. This process is iterated to give convergence to a working
baseline. The difficulty for valley glaciers is that ice covered regions with good phase signal coher
ence have surface velocity information folded into the unwrapped phase, and the areas which are not
moving are generally mountains which often have poor signal coherence and are difficult to phase
unwrap. A solution lies in performing the baseline estimation process further along the swath in an
area with moderate topographic relief and no moving ice. The baseline is then extrapolated back
to the scene of interest, as orbital separations vary slowly and fairly linearly over distance scales of
tens of kilometers.
Phase Unwrapping and Adaptive Phase Filtering
In general, interferograms of temperate valley glaciers contain a great deal of decorrelation noise
(for example, relative to polar ice sheets). This is due to such influences as surface rotation in
areas with curving flow lines, rapid marginal shearing between the constraining valley walls and the
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center of the glacier, surface deformation of rapidly moving (e.g. surging) ice. surface melting, and
in the case of the Bering system, wind and precipitation from mercurial coastal weather systems.
Decorrelation noise necessitates adaptive phase filtering prior to phase unwrapping in order to recover
lower frequency phase signals that are corrupted by high frequency noise. The tradeoff in this process
is a loss of resolution, so that the problem becomes one of performing the minimal amount of phase
filtering.
We used Goldstein's phase-unwrapping algorithm (Goldstein and others. 1988). Valley glaciers
often include large regions of mediocre to poor coherence, so the interferometric phase is adaptively
low-pass filtered using both amplitude and coherence weighting. Adaptive filtering selectively im
proves coherence in noisy areas and enables the algorithm to unwrap more of the scene while keeping
the full spatial resolution intact in areas with good coherence. Low-pass filtering only works in areas
where some coherence remains and where the phase signal is low frequency. There is a danger in
low-pass filtering areas with extremely poor coherence, as a coherent signal can 'emerge' with no
physical meaning. Unwrapping such a false signal using Goldstein's technique can lead to global
(multiple of 2 jt) phase errors elsewhere in the scene.
Manual assistance can be provided to the phase unwrapping process. In this work, sets of points
were chosen by hand such that they passed through regions of low coherence. These points were
connected by lines to the edge of the image so that the resulting pixel chains would guide the branch-
cutting part of the unwrapping algorithm, acting in effect like singularity grounding cables. Manual
assistance is not feasible for large-scale SRI applications, but for small scale research projects with
well-defined regions of interest it can prove useful in eliminating spurious data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45
Chapter 3. Acceleration of Bagley
Icefield During the 1993-95 Surge of
Bering Glacier, Alaska, Observed With
Spaceborne SAR Interferometry
D e n n is R . F a t l a n d
Geophysical Institute, University of Alaska Fairbanks, Fairbanks. Alaska 99775. U.S.A.
ABSTRACT. Time-varying accelerations were observed on Bagley Icefield dur
ing the 1993-95 surge of Bering Glacier. Alaska, using repeat-pass SAR interferom
etry. Observations were from datasets acquired during winter 1991/92 (pre-surge),
winter 1993/94 (surge-state), and winter 1995-96 (post-surge). The surge is shown
to have extended 110 km up the icefield to within 15 km or less of the flow di
vide. Acceleration and step-like velocity profiles are strongly associated with an
along-glacier series of central phase bull's-eyes with diameters of 0.5 to 4 km. These
bull's-eyes are hypothesized to represent glacier surface rise/fall events of 3 to 30 cm
during 1-3 day observation intervals and suggest migrating pockets of subglacial
water as an enabling mechanism. The resulting surface velocity gradients cause
both compressive and extensive stresses that produce patterns of orthogonal sur
face crevassing characteristic of the Bering and other glaciers during surge.*
* In preparation for submission to Journal of Glaciology.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46
INTRODUCTION
The Bering Glacier, together with Bagley Icefield (its associated accumulation area) and smaller
tributaries, covers an area of 5200 km 2 in the Chugach-St.Elias Mountains of South-Central Alaska,
USA. In spring 1993 a major surge began on the Bering Glacier ablation area which proceeded in
two phases through summer 1995. both of which ended with outburst floods at the terminus. An
overview of the Bagley Icefield/Bering Glacier system and the progression of the surge is given in
Fatland and Lingle (in press). While that work devoted particular attention to the dynamics of
the West Bagley Icefield, this study presents results from a subsequent analysis of the surge on the
considerably larger East Bagley Icefield. Further observations and studies of the 1993-95 Bering
Glacier surge can be found in Molnia (1993): Lingle and others (1993): Molnia (1994): Molnia and
Post (1995): Roush (1996): Herzfeld and Mayer (1997).
Surging glaciers have been recognized for several centuries, but serious scientific study of the
problem of how and where surges happen began only as recently as the 1960s. A major symposium
on the subject was held in Quebec. Canada in 1968. at which Hoinkes (1969) showed that periodic
catastrophic glacier advances were recorded in 1678 and L772. Research into the phenomenon
over the last three decades has focused on the complex relationship between surges and subglacial
hydrology. Robin and W'eertman (1973) described the backward propagation of surge motion up-
glacier from the initiation or trigger" zone, hypothesizing that this was due to the damming of
subglacial water. Subsequent theoretical work by Bindschadler (1983) described a parameterized
relationship between subglacial water pressure and glacier surging. An important and detailed
study of glacier surges was presented by Kamb and others (1985). Surge cessation was observed to
coincide with floods of sediment-laden water at the glacier terminus on Variegated and West Fork
Glaciers (Harrison and others. 1986 and 1994: Raymond. L987). This work led to the understanding
that water is trapped under the glacier during the surge by a large-scale disruption of the basal
drainage system, resulting in a large volume of stored water and bed separation. The resultant high
subglacial water pressure is thought to lead to rapid surge motion through some combination of
ice-bed decoupling (i.e. flotation above and sliding over a hard bed) and/or shear failure of non
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47
consolidated material at the base of the glacier (i.e. plastic failure of a deformable, soft bed). In
both cases, the shear stress at the glacier margins exerts the dominant restraining force as the basal
shear stress is reduced. The work presented here makes use of high-resolution spaceborne radar data
to contribute to the analysis of this complex problem.
The Bagley Icefield and the upper part of Bering Glacier were observed from winter 1991/92
through winter 1995/96 by European Space Agency (ESA) synthetic aperture radars (SAR) onboard
ERS-I and ERS-2 in short-repeat (1-3 day) orbits. Data downlinked to the Alaska SAR Facility
from these satellites were interferometrically processed into three datasets showing the nature of ice
flow on Bagley Icefield before, during, and after the surge. The first dataset, acquired in winter
1991/92 by ERS-1 (3-day repeat orbit) shows the quiescent pre-surge surface velocity field on most
of Bagley Icefield, which is the primary accumulation area of Bering Glacier. The second dataset,
acquired by the same means during winter 1993/94. is a time-series of images showing the surface
velocity field and surface acceleration over two months on Bagley Icefield during the dominant first
stage of the surge, slightly less than one year after the probable time of onset. The third dataset,
acquired by ERS-1 and ERS-2 during tandem 1 -day repeat orbits, winter 1995/1996. shows the
return to quiescence after the surge on both Bagley Icefield and along the entire Bering Glacier
ablation area to the terminus.
An important feature of the present study is the discovery and interpretation of consistently
recurring anomalies in the data which are referred to as phase bull's-eyes’.
METHODS
The use of SAR interferometry for glacier measurements has been described elsewhere, including
Gabriel and Goldstein (1989): Goldstein and others (1993): Joughin (1995); Rignot and others
(1995); Joughin and others (I996abc): Kwok and Fahnestock (1996): Rignot (1996): Rignot and
others (1996); Mohr and others (1997); and Fatland and Lingle (in press). The basic technique is
a comparison of two coregistered SAR images, both of which have phase angle values assigned to
each pixel. By subtracting these phases on a pixel-by-pixel basis, a new image is generated called
an interferogram in which (under good conditions) the stationary random component of the phase
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48
has been removed, leaving a residual signal containing information about the surface topography
and surface motion. The surface topography phase arises from the slightly different orbital tracks,
separated by a ‘baseline' of a few hundred meters or less, followed by the SAR during the two source
data acquisitions. This topographic phase signal typically resolves vertical relief with a resolution of
less than ‘20 meters. The surface motion phase is due to small relative displacements of the surface
of the moving ice on the scale of the radar carrier wavelength. 5.7 centimeters.
The surface motion phase signal, which is typically an order of magnitude larger than the surface
topography phase signal, can be separated from the latter using multiple differencing of more than
one interferogram in circumstances where the surface is moving at a constant velocity. This technique
and other technical details of SAR interferometry are further described in the references given above.
In this work, the differentiation of these two phase signals using multiple differencing techniques was
not feasible due to the constantly-changing surface velocities on Bagley Icefield during the surge.
Instead, surface motion was obtained for small-baseline pairs by first performing two-dimensional
phase unwrapping and then extracting one-dimensional transect datasets, either laterally across the
glacier or longitudinally along the glacier centerline. The topographic signal was ignored along the
lateral transects, which traversed a region with very little vertical relief. Along the glacier centerline,
which has a modest and fairly constant slope, the effect of the phase signal due to surface topography
could be approximately compensated using a precise estimate of the orbital baseline, determined
during processing. These two approaches allowed for the isolation of the surface motion phase signal
and hence estimation of surface velocities on East Bagley Icefield during the surge.
Figure 18 shows the East Bagley Icefield and associated tributaries. Two datasets are indicated:
A series of lateral transects and a longitudinal profile. The lateral transects are labelled A-N:
transects A-K follow the course of Bagley Icefield and transects L-N traverse tributary glaciers.
The longitudinal profile is indicated by the dark centerline passing through markers F l-F ll.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 18. East Bagley Icefield
This figure is taken from the USGS 1:250000 Bering Glacier topographic map. Transverse profile
areas are indicated with boxes and letter labels A-N. Arrows indicate profile direction, corresponding
to left-to-right in profile plots in Figures 19 and 22. The central longitudinal profile through the
fastest-moving ice is indicated by the solid line running east to west from the east edge of East Bagley
Icefield. This line, marked by feature diamonds FI—FI 1. begins about 15 km east of the flow divide
and runs 100 km to the Bering Glacier. Phase bull's-eyes that are apparent on at least one occasion
in the L994 time sequence are indicated by concentric dotted-line circles. A timeline is inset at the
lower left that shows the progression of the Bering Glacier surge, above the horizontal bar, and ERS
observation phases, below the bar (adapted from Fatland and Lingle, in press). ERS-1 spaceborne
radar interferometry (SRI) data were obtained from 3-day repat orbit periods before and during the
surge, as shown in the first two 'SRT boxes. After the surge. ERS-1/2 1 -day repeat tandem mission
(TM) data were acquired in late October. 1995. indicated in the "TM SRI' box.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1994 TOF = Terminus Outburst Flood
1993 | 1993-1995 tiering GlacierSurge Kvcnt Sequence 1992 ^ - 13 Day Repeal Orbits
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50
Transect data were extracted from the unwrapped phase signal and converted directly to velocity
profiles, ignoring elevation. The main 1993-94 data sequence consisted of normal interferometric
baselines of 98. 54. 19. 4. 30. 139. and 63 m. Assuming a worst-case transverse elevation variation
across the glacier as large as 200 m. this would result in corresponding velocity errors of 5. 3. 1.
0.2. 2. 7. and 3cm d_1. These errors are comparable to other errors in velocity estimation resulting
from assumptions about flow direction and are much smaller than the typical centerline velocities
of about 5 m d-1.
For the longitudinal transects, the gross elevation signal was subtracted from the data prior to
conversion to surface motion. This signal arises from the 880 m elevation difference between the
transect starting point. 15 km down-glacier from the East Bagley Icefield flow divide, and the end
point, another 90 km down-glacier at the East/West Bagley confluence. In each case the baseline-
dependent topographic signal was subtracted linearly, introducing self-consistent small-order errors
due to neglect of actual variations in the glacier surface slope. Note that phase bull's-eyes, inter
ferogram anomalies discussed in detail below, also introduce surface velocity errors of comparable
magnitude. In this study, velocity errors are estimated to be generally less than 20cm d-1.
PRE-SURGE TO SURGE-STATE VELOCITY CHANGE
O bservat ions
Figure 19 shows centerline velocity along the longitudinal profile F l-F ll (Figure 18) for Jan 19-22.
1992. before surge onset, and January 11-14. 1994. during the surge. The sequence of transect
locations A-J are also indicated in Figure 19 for reference. The Bering Glacier surge was first
observed during spring 1993 in the ablation area below Bagley Icefield (Molnia. 1993: Lingle and
others. 1993. 1994: Roush, 1996). The surge subsequently propagated up-glacier (as well as down-
glacier) toward the Bagley Icefield flow divide. This is apparent in the 1994 longitudinal velocity
profile, which shows higher velocities and more variability than the pre-surge profile. On West Bagley
Icefield the surge-state velocity profile was very close to the pre-surge velocity profile multiplied by
a constant factor of 2.7 (Fatland and Lingle. 1998). On East Bagley Icefield the correspondence is
not as clear but the velocity profiles before and during the surge have similar structure.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 19. East Bagley Icefield Comparison of 1992 to 1994 Longitudinal Velocity
P rofiles
Centerline markers F l-F ll and transects A-J correspond to locations marked on Figure 18. Areas
with signal loss are interpolated with dotted lines. The horizontal axis from left to right corresponds
to distance down-glacier from the flow divide on East Bagley Icefield, which increases from east to
west.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 19. East Bagley Icefield Comparison of 1992 to 1994 Longitudinal Velocity Profiles Velocity Longitudinal 1994 to 1992 of Comparison Icefield Bagley East 19. Figure
Surface speed, m d~ 20
40 Centerline distance from flow divide (km) divide flow from distance Centerline
60
80
100 52
Profile segments with longitudinally increasing velocity along the upper reach of Bagley Icefield—
west of marker FI. between markers F2 and F3. and between markers F4 and F5—all occur directly
downstream from tributary confluences. Along the lower reach of Bagley Icefield from markers F 6-
F 10 there is relatively little confluence of ice (only contributions from embayments in the confining
valley walls) but the profile segments of increasing velocity—-markers F 6 to FT and FS to F9— are
more pronounced. The sharpest velocity increase occurs at the confluence of East and West Bagley
Icefield between markers F10 and FI I. Interferogram phase bull’s-eyes, discussed below, occur more
frequently in this downstream region.
Interpretation
The velocity profiles in the upper reach of East Bagley Icefield (transect A through marker F4) are
similar in structure. This contrasts with the strong 9‘2-versus-94 velocity divergence further west
(downstream), showing how the surge influence diminishes with distance from the Bering Glacier.
Because of this diminished influence in the upper reach, the surge-state velocity profile retains the
expression of local modulating influences. In particular, the velocity profile suggests that there is a
correlation between the locations of tributary confluences and extensional flow, which is in agreement
with theoretical and observational results presented by Gudmundsson (1997) and Gudmundsson and
others (1997).
The region from markers F4 to F6 marks a transition to much stronger surge influence, with
steeper velocity-increase segments from F 6 through F10 in the 1994 profile, but comparatively
little tributary input. Finally, as the east and west branches of Bagley Icefield flow together into
Bering Glacier, the segment between FIO and F ll exhibits the strongest velocity increase. Here
the velocity reaches 5m d-1, still less than half the maximum velocities observed by Roush (1996)
farther downstream on the Bering Glacier. In general the step-like nature of the velocity profile
strongly suggests localized phenomena modulating the surge of Bagley Icefield.
SHEAR MARGIN WIDTHS AND MAXIMUM PRINCIPAL STRAIN RATES
An important consequence of the high resolution of SAR images is that the volume of data can
become overwhelming. The East Bagley Icefield shear-margin widths and maximum strain rates
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53
are presented as a means of characterizing the ice deformation in a manageable fashion at a small
number of sites. The large initial data volume is an asset, however, as particular sites need not be
chosen a priori as in the case of a field campaign.
Observations
Figure 20 shows a comparison of 1992. 1994. and 1995 shear-margin widths and maximum principal
strain rates across both the northern and southern shear margins of East Bagley Icefield (sites A-K.
Figure 18). Also included are data for the three tributary transects, labelled L. M. and N. The
widths of the shear margins were estimated from interferograms. In some cases, this estimation was
inferred from bands of incoherent interferogram phase, with the incoherence due to some combination
of high surface deformation combined with the limitations of the SAR resolution. Maximum extensile
strain rates in the range 1 to 7 x l0- 4 d - 1 were estimated from the steepest lateral velocity gradients,
assuming flow parallel to the valley walls. This gives a principal extensive strain-rate axis oriented 45
degrees down-glacier from the valley walls relative to the transverse direction, causing corresponding
shear crevasses to point 45 degrees up-glacier. In some cases where interferogram shear margins were
obscured by incoherence, the velocity gradient could still be estimated from the velocity at the center
and the assumed zero-velocity condition at the valley wall.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 20. Lateral Transect Sites A—N: Characteristic Widths and Strain Rates. 1992
versus 1994
The horizontal axes are indexed by site letters A-N. as labelled in Figure 18. Indicated maximum
sheer margin strain rates and glacier widths were determined either by interpolation or direct mea
surement from interferogram data. Most velocity transects show a nearly linear steepest gradient'
region across the shear margin which was used to calculate maximum principle strain rates using the
assumption of parallel flow in two dimensions (i.e. no vertical component, after Vaughan (1995)).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54
North Shear Margin Width L. M, N: Tributary Transect Sites
ABCDEFGHIJK$ L M N North Shear Margin Maximum Strain Rate
South Shear Margin Width * 3 0 0 0 a •o£ 2300 + 1992 8 2000A 1994 T? g09 1 soo j ABCDEFGHIJK$ L M N
tQ ,2 ^ S 2 1 5 §" in 1
Figure 20. Lateral Transect Sites: Widths and Strain Rates, 1992 versus 1994
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Interpretation
The primary down-glacier trends shown in Figure 20 are the increases in shear-margin width and
shear strain during the surge, as would be expected. The tributary sites L and M appear to be
essentially unaffected by the surge, whereas site N. in closer proximity to the down-glacier region of
East Bagley Icefield, shows a decrease in shear-margin strain rate during the surge and an apparent
shift in the location of the central flow channel relative to 1992. This may be due to a dynamic
restraint imposed on the tributary by the surge.
PHASE BULL S-EYES
Observations
Before proceeding to surge-state observations of East Bagley Icefield, it is relevant to establish the
common occurrence of phase bull 's-eyes in interferograms of glaciers, as shown for example in Figure
21. These bull’s-eyes are radially symmetric phase patterns with varying degrees of elongation and/or
distortion. They occur both in isolation as well as in conjunction with other bull’s-eyes, and are
consistently located over the deeper parts of a channel of ice. Phase bull’s-eyes are typically 0.5 to
4 km in diameter and. due to their size and magnitude, cannot represent topography. Consequently
phase bull’s-eyes on glaciers must necessarily represent motion along the one-dimensional SAR line-
of-sight vector to the ice surface. This motion, herein referred to as a bull's-eye event', must take
place during the 1-3 day observation interval between two SAR imaging passes. Bull’s-eye events are
therefore time- and space-localized variations in the normal movement of the glacier surface. Figure
18 indicates a distribution of bull's-eye events from the 1994 surge-state data, in which bull's-eyes
are apparent on East Bagley Icefield, the non-surging Yahtse Glacier to the south, and elsewhere.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56
(a) 1994, Jan (2-5) - Jan (11-14) (b) 1994, Jan (2-5) - Jan (17-20) (c) 1994, Jan (11-14) - Jan (17-20)
(a), (b), (c): Three differential interferograms that resolve the ambiguity of the time of the doable bullseve. Any balLs-eye events mast occur daring either the first or second 3-day observation interval. Using the vertical motion model, this sequence demonstrates that the glader surface rose a t both boOs-eye centers by 18 cm between L'TM 7:19 Jan 2 and LTM 7:19 Jan 5,1994, The third image shows ongoing activity centered at slightly different locations; more pairs would be needed to discriminate the time ami direction of these later events..
(d) 1994, Jan (11-14) - Jan (20-23) (e) 1994, Jan (17-20) - Jan (20-23)
(d), (e): A later tim e-sequence showing continued bat less dramatic activity, with the locations of the two large Jan 2-5 bafiseyes indicated as before with white crosses. The dashed white circle in (d) indicates an intermediate region probably active both daring Jan 2-5 and Jan 11-14 bat not active from Jan 17-23. Figure 21. Multiple Differential Interferogram Time Sequence
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57
Phase bull's-eyes occur with both positive and negative phase curvature. Because they have
typical magnitudes of one to ten fringes, they are often obscured by the interferogram phase of
the normal downstream flow of the glacier. Thus they are generally more apparent in differential
interferograms in which two ice-flow phase signals are used to cancel one another. That is. for two
observation intervals A and B. a phase bull's-eye may not be apparent in corresponding interfero
gram s a and 3. but a differential interferogram (a — J) that removes most of the surface motion
phase will clearly reveal the phase bull's-eye on the glacier. In such a case, the time at which the
bull's-eye event occurred is ambiguous. For example, negative phase curvature in the differential
interferogram will represent either a toward the SAR’ motion during interval A. or ‘away from
the SAR' motion during interval B. This ambiguity can often be resolved using a third observation
interval C (interferogram 7 ). If the phase bull's-eye event occurred during A. then this event will
also be apparent in differential interferogram (0 — 7 ). but not in (3 — 7 ).
Interpretation
Without independent information, the interpretation of phase bull's-eyes must rely on a conceptual
transition from indicated motion along the radar line of sight to actual motion of the glacier surface
in three dimensions. The simplest idea invokes vertical rise or fall of the surface and is adopted
here as part of a hypothetical model of the principle mode of bull's-eye events. In this model,
subglacial water flows through a distributed subglacial drainage system to the deep central part of
the glacier channel creating a localized transient fluctuation in basal water pressure that exceeds
the overburden. Such localized transients, also thought to occur during surge-onset. would lift the
glacier upwards from the bed resulting in the observed phase bull's-eyes. Similarly when subglacial
channel conditions permit water drainage from a locally elevated region, the surface would drop
producing a phase bull's-eye of opposite sign.
Circumstantial support for water as a driving mechanism is apparent in one instance of a bull's-
eye on a Bering Glacier tributary bay directly down-glacier from a surface lake. Furthermore, data
acquired several months after the surge ended (October *27-28. 1995) show the ice near the terminus
to be stagnant across the entire Bering Glacier piedmont lobe, while at the same time II of 14 phase
bull's-eyes dotting the region indicate surface drop events of from 3 to 30 cm during a one-day time
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58
interval. This one-day observation is consistent with the notion that after a surge ends, previously
trapped basal water drains out through open channels. The change in water volume indicated by the
data is on the order of 10-30 million cubic meters per day. Phase bull's-eyes are commonly distorted
from circular shape in a manner that appears consistent with downstream ice flow, particularly
around bends or at channel confluences. This suggests that the simple vertical motion model is only
a starting point and that asymmetrical bull's-eye events may also indicate variations in horizontal
velocity.
DURING-SURGE ACCELERATION
Observations
Seven sequential interferograms from 1994 were used to generate a time sequence of centerline ve
locity profiles. The reference points F l-F ll are indicated in Figure 18. The three-day interferogram
observations intervals were: Jan ‘2-5. Jan 11-14. Jan 17-20. Jan 20-23. Feb 7-10. Feb 13-16. and
Feb 25-28. Each profile was adjusted by the gross topographic gradient based on the interfer-
ometric baseline as described above. Profile pairs were then subtracted and normalized by the
inter-observation time interval to produce a sequence of longitudinal acceleration profiles, shown
in Figure 22. with vertical axis representing acceleration in cm d - 2 and horizontal axis indicating
distance down-glacier from the East Bagley Icefield flow divide in kilometers
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 22. Acceleration Profiles
Time-interval dates are indicated in the upper left interior of each plot, with J = January and F =
February, 1994. The horizontal axis indicates the distance down-glacier from the East Bagley Icefield
flow divide. From left to right on the horizontal axis corresponds to east to west (i.e. right to left)
on Figure 18. As an example, the plot at the upper left shows acceleration along the longitudinal
centerline between two observations: The first observation was during the January 2-5 time period,
and the second during the January 11-14 time period. The acceleration becomes more pronounced
from left to right, i.e. with increasing proximity to the Bering Glacier.
The left-hand column plots: (a), (b), (c). (d), (e). and concluding with (j). comprise a sequential
time series that begins with the interval given in the example above and concludes with the February
13-16 to February 25-28 time interval acceleration measurement.
Plot (b) also begins a second sequence of increasingly longer-duration acceleration measurements,
continuing with plots (f). (g). (h). and (i). Here the first (reference) observation interval is always
that from January 11-14. while the second observation interval varies from January 17-20 (plot b)
to February 25-28 (plot i). The latter shows that time averaging over longer intervals produces a
more uniform longitudinal acceleration profile.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59
(J2—5)—(J11—14) (a) 2L (J1I-I4HJ20-23) (0 s \ / y r 2
F=~ 2 0 "ST
- i : J -itL Horizontal Axis: Distance Do wn-G lacier From East Bagley Flow Divide (Ian) « -cc 1 i 22 (J11-I4MJ17-20) (b) (Jll-14)—(F7-10) (g)
- I F '« ■ P : I 2 3 4 5 6 7 8 9 lfl! -2t—.— ...... SC ’
i 2F- (J11—14)—(F13—16) , 2 (J17-20MJ20—23) (C) 2 (h)
1u 1 e '■V 2 OS I 0 -lr •Ju 1 < -1
—2 - i i ,L (J1I-I4MF25-28) (i) ,2 (J20—23)-(F7-10) (d)
-i:
: L (F13-t6MF25-28) a J ? ^
i o— e : u — J - i :
- 2 : Figure 22. Acceleration Profile Time Sequences
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The graphs in the left-hand column of Figure 22 (concluded in the graph at the bottom-right)
comprise the consecutive series of acceleration profiles from January 2-5 through February 25
28. The second image includes a key to the horizontal markers Fl-Fll. In the first graph, the
dip/dropout between markers F 6 and F7 is due to the January 2-5 bull's-eye uplift event (Figure
21). Without recognition of the bull’s-eye. this would be misinterpreted as rapid downstream flow
(in the direction of the SAR). Other bull’s-eye events also contribute localized bumps in the profiles,
apparent in the second and third plots.
The graphs in the right-hand column are progressively longer time-interval acceleration profiles
from the January 11-14 data to later datasets. Longer time intervals show a reduction in the
smaller-scale structure and the emergence of a gradual acceleration profile of constant slope, seen
for example in the final plot. (January 11-14)—(February 25-28).
Interpretation
The sequential series in the left-hand column has two important characteristics. The first is the long
term trend of gradually increasing acceleration with distance from the flow divide toward the Bering
Glacier ablation area, at a slope of ~ 10- 4 cm d - 2 k m '1. The second characteristic is the short
time-interval acceleration changes along the lower reach of East Bagley Icefield, down-glacier from
approximately the 70 km location (between markers F 6 and F7). This location, which corresponds
to the two bull’s-eyes shown in Figure 21. seems to behave like a hinge from which acceleration
pulses emanate. This is particularly apparent in plots 2. 3. 4. and 5 in the left-hand column time
sequence. The bottom-left plot also suggests a transition region from roughly 45-70 km which tends
to act as a consolidated unit. This regional characterization of East Bagley Icefield in terms of an
‘upper-transition-Iower’ sequence based on acceleration profiles is consistent with the velocity profile
analysis presented above.
Also of note in Figure 22 is the recurrence of positive acceleration values at the eastward limit
of the SAR scene (km 15). This implies that the surge influence continues up to the flow divide,
possibly displacing it eastward.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61
AFTER-SURGE RETURN TO QUIESCENCE
The first phase of the Bering Glacier surge ended in August 1994 with an outburst flood at the
terminus, followed by about 9-10 months of quiescence (Roush. 1996). The second phase of the
surge began in spring 1995 and ended in late summer. Later in 1995 the Bering Glacier was imaged
by both ERS-l and ERS-2 in one-day repeat tandem mission' (TM) orbits. The interferogram from
an ERS-1/2 small-baseline image pair acquired October 27-28. 1995 shows the first observed phase
coherence on the Bering Glacier ablation area from the Bagley Icefield to the terminus in Vitus
Lake near the Gulf of Alaska coast, as shown in Figures 23 and 24. (Earlier attempts failed due to
signal noise presumably caused by the longer 3-day interferometric observation interval.) Because
the interferometric baseline is less than 20 meters, the contribution of topography to the phase of
this single interferogram is small (one color fringe per 500 meters elevation change) so that most of
the detailed phase structure visible in Figures 23 and 24 may be interpreted as being due to surface
m otion.
Figure 23 shows the interferometric phase from the confluence of East and West Bagley Icefields
down the Bering Glacier to the up-glacier limit of the terminus piedmont lobe. On East Bagley
Icefield at the eastern limit of the TM SAR scene the post-surge velocity is about 45cm d-1. This
increases to a region of maximum velocity labelled in Figure 23 on the upper part of Bering Glacier
that corresponds to site J on Figure 18. The velocity here varies from 100-I30cmd_1. which is
comparable to the pre-surge velocity of ~ 130 cm d-1. Downstream from site J there are three
distinct regions where tightly spaced fringes indicate that the surface velocity is decreasing.
Further downstream on the Bering Glacier the 1995 data show the ice flow essentially ceases about
40 km above the terminus. leaving the entire piedmont lobe stagnant but for a scattering of phase
bull’s-eye events (Figure 24). The surface relief from the terminus on Vitus Lake to the eastern limit
of the stagnant ice is about 700 meters or about 1.4 phase fringes. The bull’s-eye patterns observed
across the piedmont lobe strongly suggest continued drainage of subglacial pockets of water resulting
in localized surface drops, as discussed above.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 23. Bering Glacier. October 28, 1995. After Surge
Tandem Mission interferogram of the reach of Bering Glacier from the Bagley Icefield confluence to
the piedmont lobe. The small interferometric baseline (20 m) means that most of the observed phase
structure is due to variations in surface motion, as indicated by labels. The surrounding mountains
have been rendered as greyscale SAR image amplitude to emphasize the moving glacier ice. in color.
Arrows on the glacier indicate flow direction.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 24. Bering Glacier Terminus. October 28. 1995. After Surge
Tandem Mission interferogram of the Bering Glacier terminus piedmont lobe. This image is a
continuation of Figure ‘23 (note overlap in upper right corner with the middle-left part of Figure 23).
The piedmont lobe shows little of the phase structure associated with longitudinal flow, indicating
that the ice is fairly stagnant. A number of phase bull's-eyes are accentuated with white arcs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
DISCUSSION
The relatively quiet Bagley Icefield surge response—in contrast to more widespread and dynamic
fracturing and chaotic motion within the Bering Glacier ablation area—was accompanied by the
surface stability and hence stationary-phase signal coherence necessary to obtain results from SAR
interferometry. Near the East-West Bagley Icefield confluence. West Bagley Icefield accelerated from
January through March. 1994. at an average rate of O.ocmd - 2 to about lm d '1. On East Bagley
Icefield, the corresponding acceleration was considerably higher at 1.3 cm d-2. with a maximum
observed velocity of about 5m d-1. For both East and West Bagley Icefield these accelerations
attenuated fairly linearly to near zero with distance up-glacier toward their respective flow divides.
Both flow divides may have been displaced away from Bering Glacier by the surge, but this was not
directly observed in the SAR data. These observations are consistent with those given by Herzfeld
and Mayer (1997). who observed surge-related crevassing as far east as marker FI on Figure 18. The
segmented structure in both the velocity and acceleration profiles observed on East Bagley Icefield
indicates locally varying influences from longitudinal stress, bed conditions, and lateral shear stress
from converging tributaries. In particular it is likely that the lateral shear-stress coupling of East
and West Bagley Icefield at their confluence plays an important role in modulating the velocities
of each. The acceleration of East Bagley Icefield may also have constrained the flow of one of its
tributaries as shown in the pre-surge to surge-state marginal shear zone analysis.
It is suggested here that water moving through subglacial conduits may reach and locally exceed
the overburden pressure, lifting the entire ice mass several-to-tens of centimeters and producing
frequently-observed interferogram phase bull's-eyes. It is of interest to note, in light of the strong
versus weak similarity of pre-surge to surge-state velocity profiles on West and East Bagley Icefields
respectively. that while there is a high spatial and temporal density of bull's-eye events on East
Bagley Icefield, there is practically no clear evidence of phase bull’s-eyes on West Bagley Icefield.
The data indicate that up to 5% of East Bagley Icefield may have been influenced by bull's-eye
events at any given time during the surge in winter 1994. Phase bull’s-eyes with both positive
and negative signs are observed, indicating surface rise and drop events in the proposed model. A
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65
large number of bull's-eyes were also observed on the post-surge stagnant ice of the Bering Glacier
piedmont lobe, most of which indicate a surface drop that can be attributed to ongoing post-surge
drainage of subglacial water. A similar phenomenon may have been observed in a 10 cm drop
observed by Kamb and others (1985) at the end of the 1982-83 surge of Variegated Glacier. On
non-surging glaciers, bull’s-eyes are commonly (but less frequently) apparent.
The phase bull’s-eye model, in which pressurization/depressurization events occur continuously
along the line of maximum glacier depth, should be tested in the field by accurately monitoring
surface elevations over short intervals of several days using a GPS network and by measuring glacier
depth profiles (seismics. ice penetrating radar).
SUMMARY
SAR images used in this study typically yielded valid data over areas of 1000 — 2000 km 2 with a
horizontal resolution of 40 — 80 m. While this is a positive development in glaciological remote
sensing, there is an accompanying problem in the management of extremely large data volumes. A
data management technique presented here is the reduction of the data to a small set of characteristic
parameters, for example shear-margin widths, maximum principal strain rates, and velocity and
acceleration profiles that characterize the flow and serve as an historical benchmark.
The results presented here show the extent and manner in which the Bering Glacier surge prop
agated up into the Bagley Icefield. Consistently recurring anomalies in the data, referred to as
phase bull’s-eyes, are interpreted to represent local raising or lowering of the glacier surface by 3 to
30 cm during 1-3 day observations intervals. In some cases, non-radial irregularities in the bull’s-eyes
suggest that this vertical motion is also coupled to variations in horizontal velocity. The general
nature of these phase bull’s-eyes suggest that they are expressions of migrating pockets of subglacial
water that cause localized variations in subglacial water pressure, in turn modulating (and perhaps
enabling) the acceleration response of East Bagley Icefield to the Bering Glacier surge. The accom
panying positive and negative velocity gradients, while not sufficient to cause heavy fracturing along
most of the reach of East Bagley Icefield, are nevertheless consistent with the extreme orthogonal
crevassing observed downstream on Bering Glacier as well as on other glaciers during surge. This
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66
open-ended hypothesis could possibly prove relevant to the general problem of the bed morphology
of surging glaciers as well as to the longitudinal transmission of pulses of acceleration during a surge.
The less frequent but still remarkable presence of bull's-eyes on non-surging glaciers (notably the
Yahtse. Tana, and Jefferies Glaciers near Bagley Icefield and on Black Rapids Glacier in the Alaska
Interior (Fatland and Truffer. in preparation)) suggest that the apparent discrete regions of stored,
pressurized subglacial water are ubiquitous, becoming more extensive and dominant during surges.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67
Chapter 4. An Interferometric Study of
Black Rapids Glacier Alaska
D e n n is R . F a t l a n d . M a r t i n T r u f f e r
Geophysical Institute. University of Alaska Fairbanks. Fairbanks. Alaska 99775. U.S.A.
ABSTRACT. Surface velocities, strain rates and elevations are measured on
Black Rapids Glacier, Alaska, a surge-type temperate valley glacier, using differ
ential spaceborne radar interferometry from a single satellite orbital track imaging
geometry. These results are compared to field camera data and airborne laser al
timetry. Error analysis indicates that errors are primarily due to longitudinal and
vertical variations in glacier motion on a time scale of tens of days. A phase bull's-
eye anomaly that persists for two months in 1992 is described in the speculative
context of the basal hydrology associated with glacier surges.*
* In preparation for submission to Journal of Glaciology.
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INTRODUCTION
Black Rapids Glacier is a surge-type temperate valley glacier located along the Denali fault in the
Alaska Range of interior Alaska. It is 42 km long with an average width of 2.3 km and a mean
grade of 2° (Figure 25). Black Rapids Glacier last surged in 1936/37 and has been the subject of
intensive field study from 1970 to the present. An important reference on field work on Black Rapids
Glacier through 1995 is Heinrichs and others, 1996. The main glacier makes a hairpin turn near the
equilibrium line, but aside from this bend, it flows obliquely away from and later directly towards
the ERS-1/2 SAR look direction, in the accumulation and ablation areas respectively, making it an
excellent subject for study using differential spaceborne radar interferometry (DSRI). This technique
involves differentiation of superimposed signals in interferometric SAR data, where the two signals
of interest indicate surface topography on a vertical scale of meters and surface motion on a scale
of centimeters per day (Gabriel and Goldstein. 1989: Goldstein and others. 1993: Joughin. 1995:
Rignot and others. 1995: Joughin and others. I996abc: Kwok and Fahnestock. 1996: Rignot. 1996:
Rignot and others. 1996: Mohr and others. 1997; Fatland and Lingle. in press). An earlier study
on Black Rapids Glacier (Rabus and Fatland. in preparation) used a simplified approach to SAR
interferometry which correlated one-dimensional surface velocity transects to existing survey and
seasonal trend data.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 25. Black Rapids Glacier
Outline of Black Rapids Glacier. Alaska Range. Interior Alaska. Two flight altimeter tracks are
shown, one running along the main branch of the glacier, and one running along the major
tributary—the Loket—into the main branch. The moraine pushed out by the Loket tributary is
indicated by a bold line. Dotted circles are plotted every 5 km along a centerline coordinate system.
The diamonds at the W ills Ear' site and the Lake' site show the positions of stakes that are sur
veyed by automated cameras. L'nits on the axes are meters in a local coordinate system with the
ordinate axis pointing north. The main glacier flow is from west to east.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CO Oi i i i i i i i— i i i i i i ( I i i i r Figure 25 Figure 25 Black Rapids Glacier 5000 10000 15000 20000 25000 30000 35000 40000 I I | I I I I | I I I I | I I I 1 [“ Main glacieraltimeter track Loket tributaryaltimeter track 1 i i | i i i i | i i i i | i i i—i | i i i i | i—i—i i—|—i i—i i | i—i—i—r ~1 0 - j - r
- - 0 5000 - 15000 15000 - 10000 25000 -r-r 20000
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70
We present here a study of Digital Elevation Models (DEMs). surface velocity vector fields,
and strain rate fields produced by DSRI in comparison with field measurements. DSRI uses the
assumption that the velocity fields remain constant between two sequential observation periods, an
assumption that is more valid on polar ice sheets than on temperate valley glaciers. Failure of this
assumption introduces errors and can highlight interesting dynamical behavior, as described below.
The principle SAR observations are from winter 1991-92 (3-day repeat orbits using ERS-l) and from
winter 1995-96 (1-day repeat orbits using ERS-l/ERS-2 Tandem Mission pairs). Data accuracy and
errors are discussed throughout, with emphasis on the recurring theme of high local relative accuracy
combined with lower absolute accuracy.
FIE L D DATA
Two primary sources of field data are used for comparison with SAR-derived results.
1. Camera Survey Data at two locations. 'Will’s Ear' (14 km) and Lake’ (20 km). (Both in the
ablation area; see Figure 25). Photography period: Winter 1995-1996. coincident with SAR
Tandem Mission data.
2. Airborne Laser A ltim etry data: Acquired 1995 Days 138. 139 (June 28. 29).
Table 1. Field camera velocities. Black Rapids Glacier. 10-day averages
Location Velocity 1995 Day 351 1996 Day 56 1996 Day 91
Will’s Ear Horizontal 9-3 ± 0.8 cm /day 11.0 ± 1 .0 cm /day 13.0 ± 1.2cm /day
Lake Horizontal 10.8 ± 2.4 cm /day 13.7 ± 4.1 cm /d ay 13.3 ± 4.1 cm /day
Camera Survey Data
Camera data show that the horizontal glacier speed varies during the winter to within ~ 30% of
the mean. Positive flow direction angles (i.e. above horizontal) were reported by Heinrichs over
winter 1992/93 of +0.4° near Will's Ear and +2.0° at Lake. This is presumably due to seasonal and
long-term thickening of the glacier during the quiescent period between surges. The implications
of the vertical velocity component on SAR-derived DEMs and velocity determination are discussed
below.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71
Airborne Laser Altimetry
A SAR DEM is compared with two airborne laser altimeter tracks acquired on 1995 Days 138/139.
The Day 138 track begins at the upper end of Loket Tributary and follows the Black Rapids centerline
to the terminus. The Day 139 track does the same starting from the top of the main accumulation
area. The nominal altimeter accuracy is about 0.3 m with a beam footprint of about 0.18 m in
diameter when the aircraft is 100 m above the glacier surface (Echelmeyer et al. 1996).
TOPOGRAPHY
M e th o d s
A differential SAR interferogram—i.e.. an interferogram in which the surface motion signal has been
removed by differencing two source interferograms—was rectified to UTM projection using three
different ground control point schemes outlined below. Ground control points are reference values
that guide the transformation of SAR image data into a geographical coordinate system. The data
were acquired by the ERS-1/2 Tandem Mission on 1995 Day 351 and 1996 Day 91. The resultant
map-plane DEM was then compared with airborne laser altimetry profile data (1995 Day 138. Day
139).
- Case 1 (Worst): Ground control points were taken from L’SGS 1:250000 scale map. 61 m (200 ft)
contours, made from aerial photographs acquired in 1958 (ellipsoid NAD 27).
Result: The SAR DEM was consistently more than 100 m below the laser altimeter profiles.
- Case 2 (Best): Ground control points taken directly from the altimeter flight track. 1995 Day
138.
Result: The SAR DEM was much closer to the altimetry data.
SAR DEM - altimetry for Day 138: difference = 5 ± 26 m.
SAR DEM - altimetry for Day 139: difference = —36 ± 85 m.
- Case 3 (Intermediate): Ground control points same as Case 2 but with three additional ground
control points taken from the second altimeter track. 1995 Day 139.
Result: The SAR DEM varied further from the altimetry than in Case 2.
SAR DEM - altimetry for Day 138: difference = 1 ± 32 m.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72
SAR DEM - altimetry for Day 139: difference = — 29 ± 96 m.
A n alysis
This error discussion, as well as that for velocity determination, ignores potential atmospheric in
terference with the SAR signal discussed by Goldstein (1995) and by Zebker and others (1997).
primarily due to the high latitude of the study site and lack of evidence for such interference. The
SAR image pixel spacing is 20 m with low-pass filtering reducing the horizontal resolution to 40-50
m. This filtering is necessary to reduce high-frequency noise intrinsic to the SAR data. For com
parison purposes, sub-sampled airborne altimeter data was used with along-track sample spacing
similar to the SAR DEM resolution.
Figure 26 shows a best-fit comparison of altimeter data (1995 Day 138) with corresponding
differential SAR DEM data (source observations from 1995 Day 351/352 and 1996 Day 91/92).
Here we wish to account for elevation differences of up to 70 m and a standard deviation of 26 m.
The seasonal time lag gives an elevation change of less than 8 m. Map plane coregistration of the
two data sets is accurate to 80 m. giving less than 4 m vertical error. Penetration depth of the
C-Band (5.7cm wavelength) radar is at most a few meters (Eric Rignot. personal communication.
1998). While dry snow can permit significant microwave penetration, this shallow penetration depth
is particularly constrained by the typical winter snow depth on the Black Rapids Glacier ablation
area of two meters, as seasonal melt cycles introduce significant firn and ice lensing which scatter
the incident radar signal. Comparing these relatively small error sources (less than 10 m) with the
much larger errors given above we conclude that the errors are primarily intrinsic to the SAR DEM.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 26. Comparison of Airborne Laser Altimetry Data with a SAR DEM
Comparison of an Airborne Laser altimeter track dataset with a SAR DEM. The altimeter data
runs from the upper accumulation area of Loket tributary down the center of Black Rapids to
the terminus, (a) indicates the full dataset, (b) is a sub-range (indicated in (c)) over which the
altimetry elevation is subtracted from the SAR DEM elevation. The curve in (b) can be evaluated as
a potential observation of surface motion variations between the two SAR interferogram observations
(1995 Day 351 and 1996 Day 91). This variability would include both longitudinal velocity changes
and vertical motion.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright of the permission with Reproduced
Figure Comparison of SAR 26. DEM with Airborne Laser Altimeter Elevation (meters) 11 ' i Black K:i|>i Field camera data strongly suggest that the SAR DEM errors are due to relative changes in glacier surface motion during the two source observation intervals. Camera data given in Table 1 indicate spot horizontal speed increases of ~ 3.1 ±3.1 cm/day ( ~ 30%) during this time. Taking an approximate average SAR DEM error of 50 m (Case ‘2. above) and a differential baseline of 90 m we calculate a comparable velocity change of 3.3cm/day. Thus errors in the SAR DEM are consistent with field measurements of horizontal surface motion variations. These errors should taper to zero at the fixed glacier margins, but this idea could not be confirmed due to SAR coverage limitations and the restriction of the altimeter track to the glacier centerline. A similar comparison, made using SAR Tandem Mission data from 1995 Day 351 and 1996 Day 56. gave consistent (and slightly better) results, due in part to a larger differential baseline (‘224 m). The elevation difference from the laser altimeter track (Loket-Black Rapids, Day 138) improved from 5 ± 26 m to —‘2 ± 19 m error. Bumps in the SAR DEM profile correspond precisely to altimeter track crossings of the current and previous Loket tributary medial moraines shown in Figure ‘27. Both moraines, crossed obliquely by the altimeter track, are about 150 m wide and ‘20 m high. The structure of the Loket moraine is shown in more detail by a series of SAR DEM transects, indicating localized relative' data quality despite limitations on absolute data validity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 27. Medial Moraine Elevation Profiles The existing copy of the figure contains the caption. Further notes to include: The scene is in UTM projection with 20 m x 20 m pixels. In plots (a), (b). and (d), the horizontal axis is given in terms of sample index (pixel number). A line of .V pixels will represent from .V • 20 to .V • 20 ■ \/2m . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright of the permission with Reproduced Klevation (m) Worth* uni Wurttontm) 1360 a T (at Sample Index Sample Sample Index Sample Figure 27. Medial Moraine Elevation Profiles Elevation Moraine Medial Figure 27. Sample index Sample series of eleven alternating solid/da shed-line moraine moraine solid/da eleven of shed-line alternating series (e): Overlay of moraine crossings Indicated in (d) in crossings Indicatedshowing of moraine Overlay (e): locations. crossing track (moraine crossing between a is two crossing and dots) white (moraine track flight imageSAR showingfrom altimeter Sub-scene (d): surge). Glacier increasing relief and width of of moraine. the width and relief increasing glacier (old Loket moraine prior to last Black Rapids Rapids Black last to prior moraine Loket (old glacier down- crossing further moraine DEM SAR Second (c): (a).to crossing corresponding moraine DEM SAR (b): signal showing laser altimeter airborne Full-resolution (a): Data were acquired 1995 Day 1996351 Day and 91.acquired were Data on acquired Datawere crossing. moraine tributary Loket 1995138.Day 75 76 Figure 28 is a comparison of the 1992 Day 22 and 1993 Day 361 Loket tributary moraine positions from SAR amplitude images. The moraine bulge moves downstream into the main glacier channel by about 70 m over this time interval giving a speed of 10cm/day. In comparison. 1995 interferogram data gives 10.4 cm d-1. The current position of the Loket moraine resembles that of the moraine cut off and transported down-glacier by the 1936/37 surge. This led Heinrichs and others (1996) to speculate that Black Rapids Glacier may again be approaching its surge geometry. The geometrical argument for an imminent surge is valid only if the moraine continues to intrude laterally across the main valley (i.e. the two merging flows are not in steady state) as demonstrated by the above SAR-derived results. However, current mass balance and surface evolution data (unpublished data, not presented here) argue against the likelikhood of an imminent surge. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28. Loket Medial Moraine Migration. 1992-1994 This plot shows the relative positions of the leading edge of the Loket medial moraine from 1992 Day 22 to L994 Day 35 with an aspect ration close to 1:1. The outward bulge in 1994 indicates that the moraine is not yet in equilibrium. The upstream (straight) leg of the moraine is fairly fixed and so may be taken as a good approximation to a flowline. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28. Loket Tributary Relative Medial Moraine Positions, 1992 and 1994. and 1992 Positions, Moraine Medial Relative Tributary Loket 28. Figure kilometers 78 A comparison analysis of SAR DEM data from 1992 (ERS-1 Ice Phase I) proved inconclusive. Heinrichs and others (1996) indicate an elevation increase of less than 5 m over this time interval in the accumulation zone and up to 25 m of surface drop near the terminus, well within the signal variations introduced by motion changes. While DSRI analysis gave a qualitatively similar result, our failure to obtain quantifiable results in this case re-emphasizes the contingent difficulties associated with transforming radar data to calibrated absolute values. VELOCITY M e th o d s Several assumptions are necessary to derive surface velocity vector fields from a single orbit-trajectory imaging geometry. The principle assumption is one of flow along the surface taken in the direction parallel to the glacier's constraining valley walls (Fatland and Lingle, in press). Flow direction for tributaries and confluences are determined by a compartmentalized best guess technique, with some guidance from field data and from comparison of images separated by two years in which pothole features and medial moraines are observed to move, as in Figure 28. Once an estimated surface flow-direction field is established, the radial distance phase is projected into surface tangent velocity vectors and divided by the observation interval to produce a velocity vector field (Figure 29). As noted above, variations in glacier speed are the primary contributor to errors in the estimated velocities. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 29. Surface Velocity Vector Field Velocity vector field plots, (a) is a series of transects with flow directions and relative amplitudes overlain on top of a darkened amplitude image, (b) indicates velocity contours, (c) is a three dimensional perspective in which vertical relief indicates speed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ______(pixel Index) liK~ullnn liK~ullnn Centerline 400 ooo aoo QUO I ’*00 Figure 29. Velocity Vector Field, 1995 Day 351 ^ . i 3 0 >. >. ___ 2 5 , , I , ...« ___ , ___ 2 0 , , I , ______, ___ perim posed on a S \R ima^e kilometers 1 5 sii 1 0 5 i a i a i i S m lari' H\ u n tie s 0 I— ,— I— ,— .— ,— ,— I— ,— ,— ,— , i , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Observations Figures 29 and 30 show graphical representations of the Black Rapids Glacier surface velocity field. Data gaps at both the main Black Rapids Glacier bend near the equilibrium line and in the Loket tributary are due to orientation of the ice flow parallel to the SAR flight track. The longitudinal velocity profile in Figure 29(b) shows the expected extensional and compressional flows in the accu mulation and ablation areas respectively. Superimposed on this trend is a 50% (8 cm d_I) slowdown of the main glacier above the Loket tributary confluence. Continuing down-glacier, the velocity re covers' immediately after the confluence. The distance over which this slowdown occurs corresponds to 3-4 ice thicknesses, in good agreement with the longitudinal coupling scale suggested by Kamb and Echelmeyer (1986). A high-resolution longitudinal velocity profile such as that presented here can be used to infer rates of basal motion using inverse theory (Echelmeyer. in preparation). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 30. Comparison of 1992 Day 22 and 1995 Day 351 Transect Velocity Profiles These plots are overlays of early 199*2 (dashed) and late 1995 (solid) lateral glacier speed profiles. The corresponding locations are shown on the image at the bottom. The direction-sense of each profile is indicated by the compass labels at the extreme left and right interiors of four of the plots (S = South. N'W = Northwest, etcetera). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 1995 Day 351 120 Pixel index Figure 30: Comparison of 1992 Day 22 and 1995 Day 351 Transect Velocity Profiles Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 Figure 30 shows 17 transverse velocity profiles from the accumulation area (8 km) down-glacier to 10 km above the terminus (32 km). The southern margin profiles undergo a transition from parabolic shape, indicative of deform ational flow (8 km group), to steep-gradient plug-flow shape (14-20 km), indicative of more rapid basal motion. Further down glacier they transition again, back to parabolic shape (above Loket tributary). In contrast, the heavily debris-covered northern margin are consistently parabolic with an outer inflection indicative of stagnant ice. From survey camera data, the Will's Ear site speed changes from 9.3 ± 0.8 to L 1.0 ± 1.0 cm d-1. an increase of 18% over the DSRI 67 day observation interval from 1995 Day 351 to 1996 Day 56. The corresponding DSRI velocity is 10.5 ± 0.9cmd_1. The Lake survey site speed changes from 10.8 ±2.4 to 13.7 ±4.1cm d_l. an increase of 27%. while the corresponding DSRI velocity is 14.8 ± 0.3cm d-1. Using the Heinrichs (1994) flow directions (i.e. positive emergence velocities) in place of surface-tangent flow the DSRI velocities were recalculated at 11.9cmd - 1 at Will’s Ear and 9.8 cm d - 1 at Lake. Error Analysis This analysis begins with the flow direction model discussed in Fatland and Lingle. in press, with the objective of quantifying errors in velocity magnitude, i.e. glacier surface speed. High-frequency signal noise and baseline estimation error contributions are reduced in processing to be small relative to the other error sources discussed here. Surface Velocity Variation Errors We consider two constitutive interferograms with a slight relative variation in surface velocity. These variations are small in contrast to common phase bull’s-eye patterns and are therefore not readily noticeable in an image. In terms of the radial motion change A R. later to be projected into a velocity error, we take relative interferogram phases to be Ac., = C' • B x - A/i - 2k • A R. (18) Aoo = C ■ So • A/i — 2k ■ ( A R + SR). (19) Here C is a function of incidence angle a and slant range R ,C = -2k/(R-sin.a). k is the wavenumber. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 27r/A. about L L l.lm - 1 for ERS-1/2. 6R is a range motion change due to a ice velocity variation during observation interval 2. B i and B n are the respective interferometric baselines perpendicular to the radar line of sight. Taking the second as a scaling of the first. Bn = F-B\. we find a differential motion-only phase ♦motion = ~ 2 k • (A/? + . (2 0) As expected for two identical baselines (F = 1). the motion signal can not be distinguished. As B n varies from B i the influence of the velocity variation driving SR decreases. Taking the velocity change SV as a proportion of the mean velocity I'. 6V = E ■ V. the velocity calculated from the SAR data will be in error by an amount f error = ■ (21) For example, taking B i = —156 m and B n = 67 m. with a velocity change of 30%. the calculated velocity from the first observation interval (first interferogram) will be only 80% of the true velocity. This evaluation rather problematically relies on advance knowledge of the ice speed variability. In principle, the effects of surface velocity variability should be minimized by using SAR observations that are closely spaced in time. Zero- Velocity Reference Point Errors For 1995 (ERS-l/2 Tandem Mission) the zero-velocity phase at the glacier margin had uncertainty ±0.12 rad. This constant value was projected into the flow-direction vector field to give errors of 0.14 — 0.52 cm/day. dependent on the azimuth flow-direction angle 9 in the range 0 — 75° relative to the SAR cross-track axis (where 9 is chosen to be an acute angle). Flow Direction and Incidence Angle Estimation Errors Azimuthal (map projection) flow direction angle 9 and incidence angle a are related to speed 5 by , A R s = ---7— ---- r=, (22) cos 9 ■sm a ■ A l where A R = —Ae>/2A* and AT is the repeat-pass time interval. Glaciers flow parallel to their con straining valley walls with slight divergence in ablation areas and convergence in accumulation areas Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 as one traverses from the center to the glacier margin. Flow directions are further complicated by variations in the constraining rock and. more significantly, by the influences of tributaries (Ray mond. 1971. Echelmeyer. 1983). We take an 'average' flow direction error of 8° in consideration of errors in estimating flow direction combined with divergent/convergent flow. This gives velocity errors of about 15% in the Black Rapids accumulation area. 5% in the plug-flow area above the Loket moraine, and 2% below the Loket moraine where the glacier flows directly along the SAR look direction (Fatland and Lingle. in press). The slope of the SAR DEM profile in comparison with the slope of the airborne laser altimeter tends to vary by about 0.4°. giving a velocity error contribution of about 2% for ERS-l/2. Note that this error is less than related uncertainties due to non-surface-tangent flow of the glacier ice as described above. Error Summary Consideration of all the error sources gives an absolute velocity uncertainty of ~ *21% on the Black Rapids Glacier accumulation area and ~ 14% on the ablation area. STRAIN RATES L'sing surface velocity vector fields discussed above, it is straightforward to produce a two dimensional principle strain rate field as shown in Figure 31 in which vertical strain is neglected (Vaughan, 1995). On Black Rapids Glacier the maximum observed principle strain rate, found in the shear margins, was about 2.5 x 10- 4 d-1 . Strain rates determined from local velocity gradients are not subject to absolute velocity errors. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. oc t Scale Scale 2 \ III (I I irtm e 3 I. I’t ineiple Strain ineiple ield Kate I’t I I. 3 e irtm I t blur is i. <1111111 rssn r strain. blur <1111111 is i. H lute is r\(rn si\ rain, c s| Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 6 BULL'S-EYES Observations A differential interferogram from 1992. generated by differencing two interferograms with similar baselines, exhibited an unusual localized fringe pattern which suggested further investigation. Figure 32(a) shows the normal' situation, a subscene from an ERS-L/2 Tandem Mission interferogram acquired four years later (1995 Days 351/352. baseline 156m). This subscene (indicated in Figure 25) includes the ice divide between Black Rapids Glacier and the Susitna Glacier where the ice is moving very slowly. Here the interference fringes primarily indicate topography. The same area is shown in Figures 32(b) and (c), the suspect passes during the ERS-1 Ice Phase I Mission. The acquisition dates were 1992 Days 22/25 and Days 37/40. with interferometric baselines of 27.4 m and 37.9 m respectively. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (a) ERS-1/2 Tandem Mission data, 1995 (b) ERS-1 3-day repeat, 1992 Day 22-25 Tandem Mission data (a) has no bullseye phase, whereas both 1992 subscenes (b) and (c) do. In subscenes (b), (c), and (d) the mountains are (c) ERS-13-day repeat, 1992 Day 37-40 masked out in Mack. In subscene (b) the tributary associated with the bullseyes is labelled *T’. The pothole area is labelled ‘P’. Black Raplds/Susitna Glacier ice divide (approximate) is shown as a dashed line in (a) and (b). The •+’ indicates 780 meter downstream migration of the bullseye center over 27 days. The differential interferogram (d) shows little topography due to the small differentia! baseline (-10 m) but the difference in bullseye amplitudes from (a) to (b) is dearly apparent. The bullseye in (d) is interpreted as a difference in magnitude between two events, each occurring over separate 3-dav intervals. Plot (e) shows inferred surface rise rates at the siowiv migrating bullseye centers for (b) and (c) plus three additional scenes from early 1992. (d) differential interferogram, (b) — (c) (e) 1992 Inferred rise rates Julian day Figure 32. Black Rapids Bullseye Events, 1992. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 In both I99‘2 subscenes, a very distinct concentric phase 'bull's-eye' pattern is apparent in contrast with the 1995 data. It is more pronounced in the second image, and the differential interferogram in Figure 32(d) shows that the difference between the two source interferograms is itself a teardrop shaped bull's-eye. The differential baseline for this subscene is 10.5 m. small enough to almost completely remove topographic sensitivity, evidenced by the near-constant phase on the ice apart from the bulFs-eye. The bull's-eye in (d) is clearly a result of the failure of the assumption of constant ice velocity, rather than evidence for the existence of a 15.714 m — high hill protruding from the center of the glacier (FAA. personal communication. 1998). The 3-day observation interval in 1992 (in contrast with only l-day intervals in 1995) does not account for these patterns, which are furthermore not evident in 3-day repeat data from early 1994 (ERS-1 Ice Mission II). The tear-drop shaped phase bull's-eye is about 3.5 km long, ending with its wide end in the ■potholes' area, a group of semi-permanent depressions which may be relics associated with past surges of Black Rapids Glacier. The bull’s-eye is 1.7 km wide and is centered slightly to the north of the glacier centerline. Its apex favors the tributary coming into the ice divide from the north, a bias even more apparent in the constitutive interferograms (b) and (c). Interpretation Our interpretation of these bull’s-eyes invokes a vertical motion model in which bull's-eyes represent changes in surface elevation over three day time intervals. For ERS-l data from 1992. one fringe corresponds to about 3.1 cm of vertical motion per three days. The bull's-eyes here indicate that the surface is moving upwards by about 3cm/day. Three additional scenes from 1992 were processed, and although the signal was noisier, the bull's-eye patterns persisted with two distinct trends. The first is shown in Figure 32(e) in which the hypothetical surface rise rate at the center of each bull's- eye is plotted with time. The second trend is the progressive movement of the bull’s-eye centers downstream at about 30 meters per day. Table 2 shows relevant factors from the 5-element 1992 dataset. The consistent appearance of these bull’s-eyes over several weeks eliminates the possibility that they are atmospheric effects. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 Table 2. Bull’s-eye Data. Black Rapids Glacier 1992 data acquisition baseline rise rate bull's-eye distance 1992 days (meters) (cm /day) downstream (meters) '22-25 24 2.6 ± 0.5 0 28-31 -209 3.1 ± 0 .5 0 ± 40 37-40 35 3.6 ± 0.5 510 ± 6 0 46-49 127 2.6 ± 0.5 460 ± 160 49-52 -181 •2.3 ± 0.5 780 ± 70 These observations suggest a model in which the subglacial water pressure is close to the overbur den pressure. Additional water input from some source causes the pressure to exceed the overburden. Water sources include melting from geothermal and frictional heat (~ 1—‘2 cm/year (Paterson. 1994)) as well as possible channel flow of stored meltwater from the south-facing tributary. The basal water pressure jacks the glacier upward at the bull's-eye at a rate of about 3cm/day. comparable to rates reported elsewhere (Iken and others. 1983: Kamb and others. 1985). As the water cavity grows it also migrates downstream at about 30 m/day. The data in Table 2 indicates that this migration may be somewhat episodic rather than continuous. An extrapolated integration of the rise rates, taking into account their areal extent and the downstream bull's-eye migration, gives a total uplift over 85 days of 1.0 ± 0.2 m. corresponding to a volume of about three million cubic meters. An incident related to this implicit water storage capacity occurred during a field campaign on Black Rapids Glacier in April 1996 (well before the onset of surface melt). Water was pumped from a 600 m — deep borehole with a water level 80 m below the surface (an hydraulic head at 96% of the overburden pressure). 3000 liters of water, the approximate equivalent of the total borehole volume, were removed from the borehole in ‘20 m inutes with no noticeable change in this water level. Furthermore. 1000 liters were subsequently pumped back into the borehole in the same amount of time with the same result, indicating that the borehole was connected to a considerable subglacial aquifer. The frequent initiation of surges in early winter seems to imply that a surging glacier must be capable of storing a substantial amount of water Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 subglacially. after the end of the melt season. In conjunction with the hypothesis of vertical motion due to basal water pressure, we suppose that sliding anomalies might also introduce horizontal motion and vertical strains, making a further contribution to the observed phase patterns. From continuity arguments, an upward strain should necessarily be accompanied by a corresponding downward strain which would show as a bull's-eye of opposite sign, yet none are observed. Observations on Gornergletscher in the Swiss Alps show hydraulic uplift to be the dominant component of vertical surface motion (Iken and others. 1997). If subglacial water pressure is taken to be the principle source, however, there is still the problematical issue of "where did the water come from?’ i.e. where are the signs of surface lowering? It is possible that a combination of water storage, vertical straining, and the exigencies of data processing combine to account for the anomaly. SUMMARY AND DISCUSSION For this work the ratio of available to usable interferograms was found to be about 7:1. Of those usable, a smaller subset still were of adequately high signal-to-noise ratio to give quantifiable absolute elevation results, particularly due to large time separations over which seasonal velocity variation would introduce errors in the data. While qualitative and smaller-scale local-relative' results are of interest, as seen in the discussion of the Loket moraine tributary structure, improvements in DSRI methods combined with better data availability are necessary to address topography-related issues such as mass balance. Towards this end. this work demonstrates the usefulness of altimetry data as ground control for SRI-derived DEMs of glacier surfaces. SAR instruments carrying two cross track interferometry antennas, such as the NASA AIRSAR system or the proposed shuttle radar topographic mission, record no motion signal and are therefore optimal for topographic mapping of glaciers. Combined with a high-precision laser altimeter Velocity vector fields are generated from DSRI data with intrinsic uncertainties deriving from glacier velocity variability, as shown in survey camera data, and requisite assumptions about flow direction. The resulting vector fields can be thought of as first approximations with absolute errors on the order of 25%, but with very high local relative fidelity. Field point-measurements of velocity Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 could be used in a manner analogous to the use of altimetry data for topographic ground control points to constrain these uncertainties and improve the absolute accuracy of the results. Mult-pass DSRI is a more rigorous method of resolving flow directions (Mohr and others. 1997) but in practice data availability is limited due to operational coverage constraints. The phase bull's-eye sequence plotted in 30(e) shows a slowly varying phenomenon of several weeks duration. Phase bull's-eyes are ambiguous in nature: that is. they can not be attributed to typical glacier flow, and they can not be fully resolved because they represent ice motion observed only along the axis of the SAR look-direction. In this work they were interpreted as vertical motion as the simplest and most consistent interpretation. In interpreting ice-penetrating radar studies. Gades (L998) suggests localized bed changes as an important factor in large scale changes in glacier speed. Both SAR data and camera data show large scale speed variations, and at the same time the phase bull's-eyes indicate spatially localized hydrological events. Since DSRI bull's-eyes are associated with surging (Fatland. in preparation), the 199'2 migrating bull's-eye sequence may be speculatively interpreted as a nascent surge-initiation event (glacier-bed decoupling) which dispersed before reaching a necessary critical instability. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 REFERENCES Echelmeyer. K.A. 1983. Response of Blue Glacier to a perturbation in ice thickness: Theory and Observation. (Ph.D. thesis. California Institute of Technology.) Echelmeyer. K.A.. VV.D. Harrison. C .F. Larsen. J. Sapiano. J.E . Mithcell. J. De.VIallie. B. Rabus. G. Adalgeirsdottir. L. Sombardier. 1996. Airborne surface profiling of glaciers: a case-study in Alaska. I. Glaciol.. 42(142). 538-547. Fatland, D.R. and C.S. Lingle. 1994. The surface velocity field on Bagley Icefield. Alaska, before and during the 1993- 94 surge of Bering Glacier, from ERS-1 SAR Interferometry. [Abstract.] EOS. 75(44). Supplement. 62. Fatland. D.R. and C.S. Lingle. in press. Analysis of the 1993-95 Bering Glacier Surge Using Differ ential SAR Interferometry. ./. Glaciol.. in press. Gabriel. A.K.. R.M. Goldstein. H.A. Zebker. 1989. Mapping small elevation changes over large areas: differential radar interferometry. J. Geophys. Res.. 94(B7). 9183-9191. Gades. A.M. 1998. Spatial and Temporal Variations of Basal Conditions Beneath Glaciers and Ice Sheets Inferred From Radio Echo-Sounding Measurements. (Ph.D. thesis. University of Washing ton.) Glen, J.VV. 1955. The creep of polycrystalline ice. Proc. Roy. Soc. London. Ser. .1. 228, 519-538. Goldstein. R.M., H.A. Zebker. C.L. Werner. 1988. Satellite radar interferometry: Two-dimensional phase unwrapping. Radio Science. 23(4), 713-720. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 Goldstein. R. M.. H. Engeihardt. B. Kamb. R..VI. Frolich. 1993. Satellite radar interferometry for monitoring ice sheet motion: application to an Antarctic ice stream. Science. 262(5139). 1525 1530. Goldstein. R.M. 1995. Atmospheric limitations to repeat-track radar interferometry. Geophys. Res. Lett.. 22(18). 2517-2520. Gudmundsson. G.H. 1997. Ice deformation at the confluence of two glaciers investigated with con ceptual map-plane and flowline models. ./. Glaciol.. 43(145). 537-547. Gudmundsson. G.H.. A.Iken. and M. Funk. 1997. Measurements of ice deformation at the confluence area of Unteraargletscher. Bernese Alps. Switzerland. Glaciol.. 43(145). 548-556. Harrison. A.E. 1964. Ice surges on the Muldrow Glacier. Alaska. .J. Glaciol.. 5(39). 365-368. Harrison. W.D.. C.F. Raymond, and P. MacKeith. 1986. Short period motion events on Variegated Glacier as observed by automatic photography and seismic methods. Ann. Glaciol.. S. 82-89. Harrison. W.D.. K.A. Echelmeyer. E.F. Chacho, C.F. Raymond, and R.J. Benedict. 1994. The 1987 88 surge of West Fork Glacier. Susitna Basin. Alaska. U.S.A. J.Glaciol.. 40(135). 241-254. Heinrichs. T.A. 1994. Quiescent phase evolution of a surge-type glacier: Black Rapids Glacier, Alaska. USA. (Masters thesis. University of Alaska Fairbanks.) Heinrichs, T.A.. L.R. Mayo, K.E. Echelmeyer, YV.D. Harrison. 1996. Quiescent-phase evolution of a surge-type glacier: Black Rapids Glacier, Alaska, U.S.A. J. Glaciol.. 42(140), 110-122. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 Herzfeld. U.C.. H. Mayer. L997. Surge of Bering Glacier and Bagley Ice Field. Alaska: an update to August L995 and an interpretation of brittle-deformation patterns. ./. Glaciol.. 43(145). 427-434. Hoinkes. H.C. L969. Surges of the Vernagtfemer in the Otzal Alps since 1599. Canadian Journal of Earth 5ciences. 6(4) part 2. 853-861. (Proceedings from ‘Seminar on the causes and mechanics of glacier surges'. St. Hilaire. Quebec, Canada. September 10-11, 1968.) Iken. A.. H. Rothlisberger. A. Flotron and W. Haeberli. 1983. Unteraargletscher at the beginning of the melt season-a consequence of water storage at the bed? J. Glaciol.. 29. ‘28-47. Iken. A.. K. Fabri and M. Funk. 1997. Water storage and subglacial drainage conditions inferred from borehole measurements on Gornergletscher. Valais. Switzerbungenwendlischheisenimmer- bahnfahrtwagen. J. Glaciol.. 29(141). ‘233-248. Lingle. C.S.. A. Post. U.C. Herzfeld. B.F. Molnia. R.M. Krimmel. and J.J. Roush. 1993. Bering Glacier surge and iceberg-calving mechanism at Vitus Lake. Alaska. U.S.A. (Correspondence.) J. Glaciol.. 39(133). 722-727. Lingle. C.S.. J.J. Roush, and D.R. Fatland. 1994. Time of onset of the Bering Glacier Surge. Eos. 75(44). 64. Lingle. C.S.. D.R. Fatland. V.A. Veronina. K. Ahlnas. and E.N. Troshina. 1997. Dynamic behavior of the Bering Glacier-Bagley Icefield system during a surge, and other measurements of Alaskan glaciers with ERS SAR imagery. Proc. 3rd ERS Symp. on Space at the service of our Envi ro n m e n t Florence. Italy, 17-21 March 1997{ESA SP-414), 995-1000. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 Joughin. l.R. 1995. Estimation of ice-sheet topography and motion using interferometric synthetic aperture radar. (Ph.D. thesis. University of Washington.) Joughin. I.R., R. Kwok. M. Fahnestock. 1996a. Estimation of ice-sheet motion using satellite radar interferometry: method and error analysis with application to Humboldt Glacier. Greenland. Glaciol., 42(142). 564-575. Joughin. I.R.. R. Kwok. M. Fahnestock. 1996b. Interferometric estimation of the three-dimensional ice-flow velocity vector using ascending and descending passes. Submitted to IEEE Trans. Geosct. Remote Sensing. Joughin. I.R.. S. Tulaczvk. M. Fahnestock. R. Kwok. 1996c. A mini-surge on the Ryder Glacier. Greenland, observed by satellite radar interferometry. Science. 274. 229-230. Joughin. I.R.. D. VV’inebrenner. VI. Fahnestock. R. Kwok. W. Krabill. I996d. Measurement of ice- sheet topography using satellite-radar interferometry. Glaciol.. 42(140). 10-22. Kamb. B. and 7 others. 1985. Glacier surge mechanism: 1982-1983 surge of Variegated Glacier. Alaska. Science. 227(4686). 469-479. Kwok. R. and M.A. Fahnestock. 1996. Ice sheet motion and topography from radar interferometry. IEEE Trans. Geosct. Remote Sensing, 34(1). 189-200. Mohr. J.J., X. Reeh. S.X.Madsen. 1997. Three Dimensional Glacial Flow and Surface Elevation Measured With Radar Interferometry. In press. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 Molnia. B. 1993. Major surge of the Bering Glacier. Eos. 74(29). 321-322. Molnia. B.F. and A. Post. 1995. Holocene history of Bering Glacier. Alaska: A prelude to the 1993— 1994 surge. Phys. Geog.. 16(2). 87-117. Patterson. YV.S.B. 1994. The Physics of Glaciers. Third edition. N'ew York. Pergamon Press. Pritt. M.D. 1996. Phase unwrapping by means of multigrid techniques for interferometric SAR. IEEE Trans. Geosct. Remote Sensing, 34(3). 728-738. Rabus, B.T.. D.R. Fatland. 1998. Comparison of SAR-interferometric and surveyed velocities on a mountain glacier: Black Rapids Glacier. Alaska. U.S.A. submitted to ./. Glaciol.. Raymond. C.F. 1971. Flow in a Transverse Section of Athabasca Glacier. Alberta. Canada. J. Glaciol.. 10(58). 55-84. Rignot. E.. K.C. Jezek. H.G. Sohn. 1995. Ice Flow Dynamics of the Greenland Ice Sheet from SAR Interferometry. Geophys. Res. Lett.. 22(5). 575-578. Rignot, E. 1996. Tidal motion, ice velocity and melt rate of Petermann Gletscher. Greenland, mea sured from radar interferometry. J. Glaciol.. 42(142). 476-485. Rignot, E.. R. Forster. B. Isacks. 1996. Interferometric radar observations of Glacier San Rafael, Chile. J. Glaciol.. 42(141). 279-291. Robin. G. de Q. and J. YYeertman. 1973. Cyclic surging of glaciers. J. Glaciol.. 12(64). 3-18. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 Roush. J.J. 1996. The 1993-"94 surge of Bering Glacier. Alaska observed with satellite synthetic aperture radar. (Masters thesis. University of Alaska Fairbanks.) Vaughan. D.G. 1995. Relating the occurrence of crevasses to surface strain rates. ./. Glaciol.. 43( 132). 255-266. Zebker. H.A. and J. Villasenor. 1992. Decorrelation in Interferometric Radar Echoes. IEEE Trans. Geosct. Remote Sensing. GE-30(5). 950-959. Zebker. H.A.. C.L. Werner. P.A. Rosen. S. Hensley. 1994. Accuracy of topographic maps derived from ERS-1 interferometric radar. IEEE Trans. Geosci. Remote Sensing. 32(4). 823-836. Zebker. H.A.. P.A. Rosen. S. Hensley. 1997. Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps. J. Geophys. Res.. 102(B4). 7547-7563. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IMAGE EVALUATION Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.