Changes in ice flow regime due toproglacial lake formation in an
alpine glacier

TSUTAKI Shun
Ph. D. Dissertation
Division of Earth System Science
Graduate School of Environmental Science
Hokkaido University

March 2011

Abstract
This thesis carries out ﬁeld measurements of glacier ﬂow velocity and subglacial water pressure
with 100 m of spatial distribution and shows the change in ice ﬂow regime caused by proglaciallake formation in an alpine glacier. Proglacial lakes are dammed by bedrock bump or debris.
Alpine glaciers in the world have been retreating signiﬁcantly under the inﬂuence of recent
climate change. In some of these glaciers, new proglacial lakes have formed. If a lake forms
at the glacier terminus, three processes occur and might accelerate the glacier retreat: (1)ice ﬂow acceleration due to increase in subglacial water pressure; (2) thinning of ice due tothe acceleration of ice ﬂow at the terminus; (3) surface uplift and ice disintegration due toincrease in subglacial water pressure and further glacier thinning. By revealing these three
processes based on the ﬁeld observation, it is possible to provide new insights into a evolutionof the proglacial lake. However, only a few observational studies have been conducted toglacier ﬂow change immediately after the lake formation over long periods with high spatial
resolution. Thus, understanding the mechanisms and quantitative evaluation of such ﬂow
change are not suﬃcient.
Previous studies investigated that melt water activates basal sliding and have discussed theimportance of the contribution of a subglacial drainage system for the glacier ﬂow. Temporaland spatial changes in subglacial drainage system have been explained by the observations
for subglacial water pressure by using hot water drilling technique and drilled borehole. It
is expected that subglacial water pressure at the glacier terminus adjacent to proglacial lake
is inﬂuenced by lake water. However, only a few measurement for distribution of subglacial
water pressure with high spatial resolution have been conducted and we have little understanding of impact of lake water on basal sliding.
The objective of this study is to investigate the changes in ice ﬂow regime at the glacierterminus due to proglacial lake formation. Field measurement were carried out in spatial
resolutions of 100 m at Rhonegletscher in the Swiss Alps during the summer seasons of 2007–2009. At this glacier, two proglacial lakes have formed since late 1990s as a result of glacierretreat. The measurements and subsequent data analyses focus on the spatial distribution ofhorizontal ﬂow velocity, surface vertical movement (uplift) and water level in borehole in eachmeasurement year. A three-dimensional ﬂow model is developed to reproduce observed ﬂow
ﬁelds and is used to interpret the inﬂuence of changes in basal lubrication due to proglacialiABSTRACT

lake formation on ice ﬂow regime.
Digital Elevation Models (DEMs) for surface and bed elevation were interpolated from GPS
survey for glacier surface and borehole drilling. Ice thickness near the terminus is thinningin a rate of −3.44 m a−1 from 2008 to 2009. This thinning rate has increased in the 21st
century.
Horizontal ﬂow velocity at the glacier terminus increased twofold from 2006 to 2007. Water
level in borehole was approximately equal to lake level and it approached 90% of ice thickness
in the range of 200 m up-glacier from the terminus, suggesting that a subglacial drainage
system in this region was well developed. It is suggested that high water pressure enhanced
basal sliding and caused the acceleration of glacier ﬂow. Acceleration of ice ﬂow at theterminus changed the ﬂow regime in the longitudinal direction from compressive to tensile.
This change was responsible for a part of the glacier thinning.
A crevasse began to form along Lake A margin toward Lake B. At the south western areafrom the crevasse, huge surface uplift was observed. Subglacial water pressure exceeded to ice
overburden pressure in the lake shore. This area coincided with the region where signiﬁcantsurface upward motion was observed. These observations suggest that if the glacier continues
to thin, the entire part of the terminus may get aﬂoat and disintegrate over the next few
years.
The observed ﬂow regime was reproduced by introducing pressure load of lake water andlocally enhanced basal sliding at the lake shore. It was shown that basal sliding is accelerated
signiﬁcantly by reduction of eﬀective pressure in the range of 200 m from the terminus.
This study revealed changes in ice ﬂow regime before and after the proglacial lake formationfrom the ﬁeld measurement with high spatial resolution and presents new insight for prediction of glacier evolution. Furthermore, the results of this study contributes for prediction of
glacier lake evolution and for prevention of glacial disaster such as Glacier Lake Outburst
Flood (GLOF).

ii

Contents

Abstracti

List of figuresvi

List of tablesvii

1 General introduction
1.1 Proglacial lake in an alpine glacier . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Inﬂuence of lake formation on the glacier ﬂow ﬁeld . . . . . . . . . . . . . . .
1.3 Hot water drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Field measurements
2.1 Study site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 A hot water drilling system . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Borehole drilling and ice thickness . . . . . . . . . . . . . . . . . . . .
2.2.3 Ice ﬂow speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Lake level and subglacial water pressure . . . . . . . . . . . . . . . . .
2.2.5 Surface elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.6 Meteorological observation . . . . . . . . . . . . . . . . . . . . . . . .

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3 Field data results
3.1 Surface and bed geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Time series of glacier motion and borehole water level . . . . . . . . . . . . .
3.3 Glacier ﬂow ﬁelds in 2008 and 2009 . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Borehole water level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Field data interpretations
4.1 Ice ﬂow acceleration in the terminus . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Changes in ice ﬂow speed before and after the lake formation . . . . .

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iii

CONTENTS

4.1.2 Mechanisms of ﬂow acceleration . . . . . . . . . . . . . . . . . . . . .
Dynamic thinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface uplift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Uplift and crevasse formation in the terminus . . . . . . . . . . . . . .
4.3.2 Interpretations of the uplifts . . . . . . . . . . . . . . . . . . . . . . .
Future evolution of Rhonegletscher . . . . . . . . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Numerical model of Rhonegletscher
5.1 Field equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Constitutive equations . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Finite element mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Basal sliding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 2D cross-section ﬂow models . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Lake water pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Sensitivity tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Modeling experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Experiment A: Non or uniform sliding . . . . . . . . . . . . . . . . . .
5.5.2 Experiment B: Locally enhanced sliding . . . . . . . . . . . . . . . . .
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Conclusion
6.1 Field observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Numerical modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Future prospects of the study . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Bibliography

77

Appendix84

A Performance test of the hot water drilling system
A.1 Test setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Performance test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Ice block drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.4 Borehole drilling in Rhonegletscher . . . . . . . . . . . . . . . . . . . . . . . .

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89

Acknowledgements

90

4.2
4.3

4.4
4.5

iv

List of figures

2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8

Map of the glacier and the measurement sites . . . . . . . . . . . . . . . . . .
Photographs showing the glacier terminus . . . . . . . . . . . . . . . . . . . .
Block diagram showing the conﬁguration of the hot water drilling system . .
The instruments of the hot water drilling system . . . . . . . . . . . . . . . .
Locations of surface elevation measurements . . . . . . . . . . . . . . . . . . .
The accuracy tests of GPS measurement . . . . . . . . . . . . . . . . . . . . .
Schematic diagram showing stake motion . . . . . . . . . . . . . . . . . . . .
Schematic diagram of the ﬁeld measurements . . . . . . . . . . . . . . . . . .

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3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8

Surface and bed geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diﬀerences in the bed elevation between 2009 and 2000 . . . . . . . . . . . .
Changes in surface elevation from 2008 to 2009 . . . . . . . . . . . . . . . . .
Time series of data taken in 2007 . . . . . . . . . . . . . . . . . . . . . . . . .
Time series of data taken in 2008 . . . . . . . . . . . . . . . . . . . . . . . . .
Time series of data taken in 2009 . . . . . . . . . . . . . . . . . . . . . . . . .
Horizontal and vertical ﬂow velocities in 2008 and 2009 . . . . . . . . . . . .
Borehole water levels in 2008 and 2009 . . . . . . . . . . . . . . . . . . . . . .

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4.1 Horizontal ﬂow velocity from 2000 to 2009 . . . . . . . . . . . . . . . . . . . .
4.2 Eﬀective pressure at boreholes in 2008 and 2009 . . . . . . . . . . . . . . . .
4.3 Horizontal ﬂow velocity and strain rate . . . . . . . . . . . . . . . . . . . . . .
4.4 Spatial distribution of horizontal strain rate in 2009 . . . . . . . . . . . . . .
4.5 Vertical displacement, borehole water level and ﬂotation level . . . . . . . . .
4.6 Spatial distribution of eﬀective pressure in 2008 and 2009 . . . . . . . . . . .
4.7 Photographs showing formation of a crevasse . . . . . . . . . . . . . . . . . .
4.8 Temporal variation of vertical displacement . . . . . . . . . . . . . . . . . . .
4.9 Schematic diagrams of uplift mechanisms . . . . . . . . . . . . . . . . . . . .
4.10 Photographs showing disintegration of the terminus . . . . . . . . . . . . . .
4.11 Flow diagram of inﬂuence of proglacial lake formation on glacier retreat . . .

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5.1

53

Surface nodes used for ﬁnite element mesh generation . . . . . . . . . . . . .

v

LIST OF FIGURES

5.2 Oblique view of the 3D ﬁnite element mesh of Rhonegletscher . . . . . . . .
5.3 A ﬁnite element mesh on the upper boundary . . . . . . . . . . . . . . . . . .
5.4 Scheme of simple shearing of one element . . . . . . . . . . . . . . . . . . . .
5.5 Plane view of the upper boundary of the model . . . . . . . . . . . . . . . . .
5.6 Computation of ﬂow velocities without basal sliding . . . . . . . . . . . . . .
5.7 Computation of ﬂow velocities with basal sliding . . . . . . . . . . . . . . . .
5.8 Sketch of the model boundary against to the lake . . . . . . . . . . . . . . . .
5.9 Model boundaries on which lake water pressure was applied . . . . . . . . . .
5.10 Vector components of lake pressure load . . . . . . . . . . . . . . . . . . . . .
5.11 Computed surface ﬂow vectors without sliding in Test 1 . . . . . . . . . . . .
5.12 Computed surface ﬂow vectors with basal sliding in Test 1 . . . . . . . . . . .
5.13 Computed surface ﬂow vectors with basal sliding in Test 2 . . . . . . . . . . .
5.14 Computed ﬂow velocities without sliding . . . . . . . . . . . . . . . . . . . . .
5.15 Computed ﬂow velocities with uniform sliding . . . . . . . . . . . . . . . . . .
5.16 The best ﬁt of computed velocity with uniform sliding . . . . . . . . . . . . .
5.17 Deﬁned sliding area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.18 The computed ﬂow vectors with locally enhanced basal sliding . . . . . . . .

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A.1
A.2
A.3
A.4

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Water jet temperature vs. time . . . . . . . . . . . . . . . . . . . . . . . . . .
Drilling nozzle and water jet in the ice block . . . . . . . . . . . . . . . . . . .
Map of the borehole locations drilled in 2007 . . . . . . . . . . . . . . . . . .
Drilling depth as a function of drilling time . . . . . . . . . . . . . . . . . . .

vi

List of tables

2.1
2.2

The locations and lengths of borehole . . . . . . . . . . . . . . . . . . . . . .
Dates of GPS measurement at Stake 1–20 . . . . . . . . . . . . . . . . . . . .

12
14

3.1

Horizontal and vertical velocities . . . . . . . . . . . . . . . . . . . . . . . . .

28

5.1
5.2

Summary of conducted sensitivity tests in Test 1 . . . . . . . . . . . . . . . .
Summary of conducted modeling experiment A . . . . . . . . . . . . . . . . .

6267

A.1 Time required for drilling through ice blocks . . . . . . . . . . . . . . . . . . .
A.2 Depth and mean drilling rate of the boreholes in 2007 . . . . . . . . . . . . .

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vii

Chapter 1
General introduction
1.1

Proglacial lake in an alpine glacierProglacial lakes are dammed by bedrock bumps pose a potential threat to communities inhigh mountain regions. These lakes form between the frontal margins of retreating glaciersand bedrock bumps or debris. A number of proglacial lakes formed and expanded during
the 20th century as a result of glacier thinning linked to climate change in the world: New
Zealand (e.g. Kirkbride and Warren, 1999; Purdie and Fitzharris, 1999; Quincey and Glasser,2009), Alaska, USA (e.g. Motyka and others, 2002; Boyce and others, 2007), Patagonia (e.g.
Warren and Aniya, 1999; Warren and others, 1995; 2001; Rott and others, 1998; Skvarca andothers, 2002; 2003).
Funk and Röthlisberger (1989) simulated the retreat rate of the terminus of Unteraargletscher,
Switzerland by numerical modelling. The results suggested that the glacier retreats rapidly
as soon as a calving process began at the terminus. In Triftgletscher, Switzerland, the glacierhas retreated signiﬁcantly since 1990. The retreat rate increased after 2000 as a result ofinteraction with a newly formed proglacial lake (Müller, 2004). These studies suggested thatlake formation increases the rate of glacier retreat. Similar phenomenon has been reported
in Patagonia (e.g. Naruse and Skvarca, 2000; Raymond and others, 2005), Alaska, USA (e.g.
Motyka and others, 2002) and New Zealand (e.g. Purdie and Fitzharris, 1999; Quincey andGlasser, 2009). Formation and expansion of proglacial lakes also pose a threat to humanactivity due to the possibility of ﬂooding caused by large ice avalanches (e.g. Haeberli, 1983;
Huggel and others, 2004; Salzmann and others, 2004).

1.2

Influence of lake formation on the glacier flow field

There are two mechanisms of glacier ﬂow, internal ice deformation and basal motion. In
a temperate glacier, basal motion takes a dominant role in intra-annual ﬂow variations.
Because basal ﬂow velocity ﬂuctuates as a result of the changes in the conditions at the1

CHAPTER 1. GENERAL INTRODUCTION

glacier bed such as, water pressure variations and evolution of the hydraulic drainage system. The relationship between subglacial water pressure and surface ﬂow velocity is studiedin several temperate glaciers. Iken and Bindschadler (1986) measured surface velocity with
subglacial water pressure at Findelengletscher in Switzerland. They plotted surface ﬂow
velocities against subglacial water pressure, and found that the velocity increases as the pressure rises up. In their plot, surface velocity appears to have an asymptote at the waterpressure equal to the ice overburden pressure. Jansson (1995) made similar measurements
at Storglaciären in Sweden. Measurements at Varigated Glacier in Alaska by Kamb andEngelhardt (1987) were conducted on a-surging glacier. These two studies also found surface ﬂow velocity increases under high subglacial water pressure condition as measured in
Findelengletscher. The eﬀective pressure is often used instead of subglacial water pressure
to discuss the relationship with surface velocity observed in temperate valley glaciers and ice
sheets (e.g. Bindschadler, 1983; Sugiyama and Gudmundsson, 2004). The eﬀective pressure
is deﬁned as Pe = Pi − Pw , where Pi and Pw are the ice overburden and subglacial waterpressures, respectively. Formation of a proglacial lake is expected to result in a high waterpressure condition and to enhance the basal motion at the glacier terminus. Investigations
at fresh-water calving glaciers have shown a linear relationship between ice ﬂow speed andlake water depth (e.g. Funk and Röthlisberger, 1989; Van der Veen, 2002).
Both acceleration of ice ﬂow and calving cause to decrease in ice thickness at the terminus.
In Tasman Glacier, Kirkbride and Warren (1999) observed acceleration and rapid thinningfollowed by an increase in the calving rate. Boyce and others (2007) calculated horizontal
strain rates from surface velocities near the glacier terminus. Results showed extending ﬂow
ﬁeld, and magnitude of dynamic thinning corresponded to thinning rates of about 4 cm−1 .
Here, the term dynamic thinning is used to represent eﬀect of ice thinning due to ice ﬂow
regime. Assuming that the subglacial water pressure is constant near a lake, the eﬀective
pressure decreases as the ice thins. Benn and others (2007) suggested that there are positive
feedbacks between glacier thinning and ﬂow acceleration on a lake calving glacier in a phaseof retreat. An initial thinning resulting from increased surface melting will lead to ﬂow
acceleration and dynamic thinning. Change in ice ﬂow dynamics will lead to further thinning,and so on. This feedback will trigger terminus retreat when increased calving losses outweighthe eﬀects of ﬂow acceleration.
Another important mechanism at the lake front is break-up of glacier terminus caused by thebuoyancy force of lake water. It may occur when the subglacial water pressure exceeds theice overburden pressure. Observation at Triftgletscher, Switzerland by Müller (2004) showedthat glacier terminus disintegrated and retreated by approximately 200 m from August 2002
to August 2003 after proglacial lake forming in 2000. Sudden uplift and break-oﬀ events havebeen observed during an outburst ﬂood events, which were caused by collapse of ice-dammedlake (e.g. Roberts and others, 2005; Walder and others, 2005, 2006; Sugiyama and others,
2008b; Riesen and others, 2011).

2

1.3. HOT WATER DRILLING

Field studies on ﬂow speed at the terminus of lake-calving glaciers have been conductedin Patagonia (e.g. Rott and others, 1998; Warren and others, 2001; Skvarca and others,2003), New Zealand (e.g. Kirkbride and Warren, 1999; Quincey and Glasser, 2009) and theHimalayas (Luckman and others, 2007; Bolch and others, 2008). However, to gain deeper
insights into the mechanisms controlling the dynamics of lake-calving glaciers, it is importantto carry out high-resolution measurements of surface ﬂow speed and subglacial water pressurein the process of lake formation. The marginal lakes forming in Rhonegletscher, Switzerland
provide such an opportunity. These lakes began forming when the glacier retreated behind abump in the bedrock, and the ice has been thinning at an increasing rate ever since (Sugiyama
and others, 2008a). Because the glacier is located near paved roadways, the retreat of theglacier and formation of the lake have drawn not only many glaciologist’s but also many
tourist’s and considerable public attentions.

1.3

Hot water drilling

Subglacial and englacial measurements can provide a wealth of information on glacier sliding(e.g. Fischer and Clarke, 1997; Engelhardt and Kamb, 1998), basal sediments (e.g. Fischer
and Clarke, 1994; Tulaczyk and others, 2001), subglacial hydraulic conditions (e.g. Engelhardt and Kamb, 1997; Iken and Truﬀer, 1997; Fudge and others, 2008), ice temperature (e.g.
Lüthi and others, 2002) and internal deformations (e.g. Hooke and others, 1992; Harper andothers, 2001). To drill a borehole for such measurements, it is preferable to employ a fastermethod than mechanical drilling, which is normally used for ice coring.
A hot water drilling system generally consists of water basin, high-pressure water pump,heater, hose and jet nozzle. The nozzle, supported by tripod and pulley, emits a jet of water
heated on a glacier surface. Hot water drilling has been used for a wide variety of measurements, both within and underneath glaciers. The features of this method are as follows: (1)a much faster drilling speed than a mechanical drill with drilling rate of 50–100 m h−1 , (2)the ability to drill both temperate and cold ice (e.g. Humphrey and Echelmeyer, 1990), (3)relatively simple construction using commercially available devices, and (4) easy operation.
Hot water drilling systems have been developed and employed at mountain glaciers and ice
sheets: South Cascade Glacier in the USA (Taylor, 1984; Fountain, 1994), Findelengletscher
in Switzerland (Iken and Truﬀer, 1997), Storglaciären in Sweden (Hanson and others, 1998),
Jakobshavns Isbræ in Greenland (Iken and others, 1993), Ice Stream B (Engelhardt andothers, 1990), Amery Ice Shelf (Craven and others, 2004) and Dome C in Antarctica (Koci,
1984). No such system has ever been constructed in Japan, however.

3CHAPTER 1. GENERAL INTRODUCTION

1.4

Objectives

Rhonegletscher is a temperate valley glacier in Swiss Alps. The changes in the terminus
position have been recorded in photographs and maps since the 18th century, from which adrastic retreat can be seen over the last 150 years (Sugiyama and others, 2008a). As a resultof retreat, a proglacial lake has formed between the glacier terminus and bedrock bump. The
lake formation draws glaciological interest because the ice calving process may accelerateglacier retreat as was observed at Triftgletscher, Switzerland (Müller, 2004).
The objective of this study is to investigate the impact of proglacial lake formation on ice
ﬂow regime. This objective is achieved by ﬁeld measurements and numerical investigation.
In the observation part, intensive ﬁeld measurements are carried out near the terminus ofRhonegletscher during the summer seasons of 2007–2009. Objectives of the measurements
are to obtain observational data for investigating the following phenomena expected at theglacier terminus;
1. acceleration of glacier ﬂow after the proglacial lake formation;
2. ice thinning due to extending ﬂow regime (dynamic thinning);
3. surface uplift and terminus disintegration;
We have developed a hot water drilling system for englacial and subglacial measurements,
which was able to drill up to 200-m thick temperate ice. The ﬂow speed and vertical ice
motion were measured with high spatial resolution in each year and compared with reported
data taken before the lake formed. Surface and bed elevations in the region were measured
by Global Positioning System (GPS) surveys and by drilling boreholes. The basal waterpressure was measured to obtain spatial distribution of subglacial hydraulic condition.
In the modelling part, ﬂow ﬁelds in a terminal part of the glacier are computed with a threedimensional (3D) numerical ﬂow model. The model is used to reproduce the ﬂow ﬁelds withthe basal motion and lake water pressure, which account for changes in recent ﬂow ﬁeld of
the terminus. Then, the measured ﬂow ﬁeld variations are simulated with the model in orderto test the hypothesis proposed for the ﬁeld data.

4

Chapter 2
Field measurements
The ﬁrst section of this chapter provides a brief introduction of Rhonegletscher, the ﬁeld
study site of this study. A summary of previously conducted important works related toRhonegletscher is presented. In the second section, the methods of borehole drilling, ice ﬂow
velocity and subglacial water pressure measurements are explained.

2.1

Study site

The ﬁeld measurements were carried out at Rhonegletscher, a temperate valley glacier in the
Urner Alps, Switzerland (Fig. 2.1a). It is the source of the Rhone river. The glacier has awide accumulation basin and a narrow tongue. The glacier is 7.85 km long with an area of
15.9 km2 (Bauder and others, 2007; Turi, 2009). It originates at 3600 m a.s.l., and terminates
at 2208 m a.s.l.. The orientation of both the accumulation and ablation areas is to the south.
The mean equilibrium line altitude (ELA) lies at 3035 m a.s.l. in 1981–82 (Chen and Funk,1990).
Rhonegletscher has drawn scientist’s attention since the 19th century. The Swiss GlacierCommission conducted the ﬁrst scientiﬁc ﬁeld measurements on Rhonegletscher from 1874
(Carlen, 2005). In this study, a trigonometric marker net was set up to survey and draw of
a complete map at 1:25,000 (Mercanton, 1916). Jost (1936) constructed a bedrock geometry
map after seismic measurements of the ice thickness in 1931. Digital elevation models (DEMs)of glacier surface were obtained in a 25 m resolution mesh by digitizing maps constructed forthe periods 1874–82 and 1928–30. These studies were carried out by Mercanton (1916) and
Jost (1936). DEMs were also obtained by maps constructed by photogrammetric analyses
of aerial photographs taken in 1959, 1980, 1991 and 2000 (Zahno, 2004; Bauder and others,2007). Zahno (2004) measured the ice thickness along 12 transverse proﬁles by radar echosoundings and constructed a bed elevation map by interpolation. In the region 500–800 m
from the current terminus, Sugiyama and others (2008a) founded that the ice thickness
obtained by borehole drilling in 2007 was up to 100 m thinner than the thickness reported

5CHAPTER 2. FIELD MEASUREMENTS

167

34

a

3200

166

30
0

165
Northing (km)

00

0

164
2800

163
162

260

0

161
00
24

160
159
671

672

673 674
Easting (km)

675

159.8

b

2320

Northing (km)

159.5

0
218

22

22
40
22
20

159.6

00

228
0
22
60

159.7

23

00

159.4

Lake A
22
80

159.3
226

159.2

0

22
40

159.1
Lake B
159
672

672.1

672.2

672.3

672.4

672.5 672.6 672.7
Easting (km)

672.8

672.9

673

673.1

673.2

Figure 2.1: (a) Map of Rhonegletscher with surface elevation. The surface elevations are
based on DEMs constructed from a photograph in 2000. The black square is the location of
the meteorological station. (b) The study area indicated by the box in (a). The black and grey
contours indicate surface in 2009 and bedrock elevations with intervals of 20 m, respectively.
These contours were obtained by GPS survey and borehole drilling conducted in this study.
The circles are locations of boreholes drilled in 2007–09. The two proglacial lakes are indicatedby the shaded areas. The coordinates correspond to the oﬃcial Swiss coordinate system.

6

2.1. STUDY SITE

Figure 2.2: Photographs showing (a) the study area and (b) the proglacial lakes viewed fromthe southeast. The photographs were taken on (a) 6 July 2009 and (b) 16 July 2009.

by Zahno (2004). Sugiyama and others (2008a) also indicated that the bedrock depression
exists at about 500 m from the terminus, and the lake depth along the valley centre will reachapproximately 50 m.
Rhonegletscher is one of the glaciers with the longest record of terminus ﬂuctuations in theworld (Chen and Funk, 1990). The glacier terminus retreated 1700 m from 1878 to 2000
(Sugiyama and others, 2011). The annual mass balance was measured for the periods of
1874–75 and 1885–1910 (Mercanton, 1916). According to these measurements, the volumeof the glacier ice reduced by 1.1×108 m3 between the years 1882 and 1912. The spatial
distribution of mass balance was examined in more detail by Funk (1985) and Chen and Funk
(1990), who investigated mass balance changes during the periods of 1882–83 and 1986–87 byin-situ measurements. Bauder and others (2007) measured the mass balance for the periodof 1874–2000 by comparing six DEMs. Huss and others (2008) reconstructed seasonal massbalance for the period of 1865–2007 for four Swiss glaciers, including Rhonegletscher. The
cumulative mean speciﬁc net balance over the years 1865–2006 is about −43 m w.e.a−1 .
The dynamics of Rhonegletscher has been measured since 19th century as well as mass balancemeasurements. The ﬁrst measurement of surface ﬂow speed has been carried out by tracking
stones distributed on the glacier during the period 1874–1915 (Mercanton, 1916). The ﬂow
speed ﬂuctuated little from year to year. The velocity was 230 m a−1 in the ice fall locateddownglacier from the bedrock bump. Nishimura (2008) reanalyzed the map showing thedisplacement of the stones and calculated the surface ﬂow velocity distribution. Nishimura(2008) also calculated the surface ﬂow ﬁelds for the periods 1970–71, 1881–82, 1999–2000 and
2005–06 by analyzing aerial photographs. Decreases in surface ﬂow velocity has accelerated
since 1970 over the range of 3.5 km from the current terminus. Turi (2009) made surface
ﬂow velocity and vertical displacement measurements by surveying stakes with a theodolite

7CHAPTER 2. FIELD MEASUREMENTS

Water supply fromsupraglacial stream
Water Basin
3000 L

FilterPump Engine

Pump / Heater
Kärcher
HDS 1000 BE

Honda GX390

PetrolDieselPulleyHose
Heater

Coupling

Snow / Ice

Drill Stem
1.5 m
2



Jet Nozzle

Coupling

Figure 2.3: Block diagram showing the conﬁguration of the hot water drilling system constructed for this study.

in the summer seasons of 2007 and 2008. A decreasing mean surface ﬂow velocity from theupglacier to the terminus can be noticed over the range of 3.0 km from the current terminus,
attributed to the compressive ﬂow regime in the ablation area.
Flowline models are commonly used to simulate the evolution of valley glaciers. One dimensional ﬂow line models have been applied to Rhonegletscher to simulate historical front
variations (Stroeven and others, 1989; Sugiyama and others, 2007). Flow line model also has
been applied to this glacier to study the sensitivity to climate change (Wallinga and Van deWal, 1998). Jouvet and others (2009) performed three dimensional numerical simulation of
the temporal and spatial changes of the glacier evolution over the period 1874–2007.
One of the recently formed proglacial lakes, referred to as Lake A in this paper, has existed
since the late 1990s. It is located at the northwestern margin of the glacier (Figs 2.1b and2.2). The other lake appeared in 2005 (Lake B) by ponding melt water in the depression
between the glacier front and the bedrock bump (Figs 2.1b and 2.2). The surface water levelof Lake B is nearly constant because excess water spills over the rock ridge. As shown in
Figure 2.2b, ice blocks broke into Lake B during the summer seasons of 2007–2009. All of
our ﬁeld activities were carried out in a region within 800 m from the glacier terminus, in thesummer seasons of 2007–2009 (Fig 2.1b).

8

2.2. METHODS

a

b

c

d

e

f

Figure 2.4: The instruments of the hot water drilling system. (a) The high-pressure hotwater machine (Kärcher HDS1000BE), (b) the 3000 l water basin, (c) the tripod with its
pulley, (d) a jet nozzle mounted at the tip of the drilling stem, (e) a water jet from a 3 mlong drilling stem with a straight nozzle, and (f ) a water jet from the conic spray nozzle.

9CHAPTER 2. FIELD MEASUREMENTS

2.2

Methods

2.2.1

A hot water drilling system

The conﬁguration of the drilling system used for this study is shown in Figure 2.3. Hot water isgenerated by a commercially available high-pressure hot water machine, Kärcher HDS1000BE(Fig. 2.4a), which is commonly used for cleaning vehicles and buildings. The same device has
been used by a British research team for drilling mountain glaciers (Hubbard and Glasser,2005). A petrol-driven water pump engine (Honda GX390) and diesel combustion heater
are combined to achieve ﬂow rates in a range of 450–900 l h−1 , pressures of 6–21 MPa,and temperatures of 30–140◦ C when they are used with a cleaning nozzle which is speciallydesigned to change the ﬂow rate for a cleaning purpose. The total weight of the machineis 165 kg. A safety device is installed between the pump and the heater, which turns oﬀ
the heater when the water pressure drops below an operating threshold. The pump draws
water from a 3000 l basin with a diameter of 2 m and a weight of 28 kg (National Marine
Plastic Inc. Type E) (Fig. 2.4b). On site, it can also draw water from supraglacial streams
and ponds. The drilling hoses, which individually are 50–100 m long and have an internal
diameter of 8 mm, are connected with couplings to obtain enough length. During drilling,
the hose is supported by a pulley hung on a tripod (Fig. 2.4c). The pulley is designed tomeasure the length of hose by counting rotations. An aluminum made tripod has a length of
2.2 m and a weight of 10 kg, and can be disassembled for transportation. The nozzle with
1.6, 2.0 and 2.5 mm diameters (Katorigumi Seisakusho Inc. Type K-18) produce a narrowand straight jet (Fig. 2.4d). Two 1.5 m long stainless steel pipes with internal and external
diameters of 19.6 and 27.2 mm were connected with a brass coupling (Fig. 2.4e). Two piecesof pipes were used in order to have enough length and weight to drill a straight borehole. Thisdrilling stem was constructed at the workshop of the Institute of Low Temperature Science,
Hokkaido University. A conic spray nozzle (Type K-20) is used to enlarge the diameter ofa borehole after drilling (Fig. 2.4f). The total weight of all equipment (hot water machine,
water basin, tripod, pulley and drilling stem) is approximately 220 kg, plus 30 kg per 100 mof hose.

2.2.2

Borehole drilling and ice thickness

In the summer seasons of 2007–2009, 51 boreholes were drilled to the glacier bed within theregion 800 m from the terminus (Fig. 2.1b). The pump and heater were always located near
GPS1, and the hose was extended to each drilling site (Tsutaki and Sugiyama, 2009). Before
drilling, required length of hose was piled up and insulated from ice surface with cotton cloth
and wooden poles. The hose extended to the drilling site would melt a groove into the ice
during operation, increasing its contact with the ice surface. To minimize heat loss, the hose
was often taken out of this groove. We normally pumped water into the hot water machine
directly from a supraglacial stream. The basin was used only when the amount of running102.2. METHODS

160

a
159.8

Northing (km)GPS fix
159.6

159.4

159.2

Lake A

GPS1

GPS3

GPS2

Lake B
159
672

672.2

672.4

672.6
Easting (km)

672.8

673

673.2

672.6
Easting (km)

672.8

673

673.2

160

b
159.8

Northing (km)GPS fix
159.6

159.4

159.2

159
672

Lake A
GPS3

Lake B
672.2

672.4

Figure 2.5: Locations of surface elevation, ﬂow speed and water level in borehole measurements in (a) 2008 and (b) 2009. The diamonds and white squares are locations of surface
elevation and margin survey. The black circles indicate the locations of continuous measurements of surface ﬂow and water pressure measurements. The hexagrams indicate surface ﬂow
and borehole water level measurements with 10–14 day intervals. The shaded squares are thelocations of borehole.

11CHAPTER 2. FIELD MEASUREMENTS

Table 2.1: The location and length of borehole drilled in 2007–09.
Borehole No.
BH701
BH702
BH703
BH704
BH705
BH706
BH707
BH708
BH801
BH802
BH803
BH804
BH805
BH806
BH807
BH808
BH809
BH810
BH811
BH812
BH813
BH814
BH815
BH816
BH817
BH818
BH819
BH820
BH821
BH822
BH823
BH824
BH901
BH902
BH903
BH904
BH905
BH906
BH907
BH908
BH909
BH910
BH911
BH912
BH913
BH914
BH915
BH916
BH917

Date
13 Jul. 2007
14 Jul. 2007
15 Jul. 2007
16 Jul. 2007
17 Jul. 2007
17 Jul. 2007
18 Jul. 2007
17 Jul. 2007
18 Jul. 200818 Jul. 200818 Jul. 200819 Jul. 200819 Jul. 2008
20 Jul. 2008
20 Jul. 2008
20 Jul. 2008
21 Jul. 2008
21 Jul. 2008
21 Jul. 2008
21 Jul. 2008
23 Jul. 2008
23 Jul. 2008
23 Jul. 2008
23 Jul. 2008
24 Jul. 2008
24 Jul. 2008
24 Jul. 2008
25 Jul. 2008
25 Jul. 2008
25 Jul. 2008
25 Jul. 2008
26 Jul. 2008
29 Jun. 200929 Jun. 200929 Jun. 200929 Jun. 200929 Jun. 200929 Jun. 200929 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 200930 Jun. 2009

Eastingm672698.03
672654.68
672616.75
672715.89
672812.51
672590.60
672720.24
672527.93
672533.28
672306.25
672305.15
672307.60
672308.65
672268.66
672289.87
672368.68
672327.49
672352.95
672337.08
672469.42
672593.02
672497.34
672460.29
672442.49
672389.90
672546.23
672665.12
672775.72
672438.80672406.07
672493.43
672546.16
672537.54672437.17
672409.58
672486.35
672544.44
672670.87
672783.90
672637.39
672596.26
672546.22
672382.06
672311.34
672334.68
672315.61
672247.12
672280.69
672418.37

Northingm159548.24
159463.21
159407.00
159648.79
159512.29
159584.72
159762.90
159360.07
159402.19
159168.95
159167.50
159168.53
159166.60
159162.57
159223.04
159226.98
159270.63
159185.67
159147.73
159258.93
159192.85
159176.66
159150.52
159210.14
159149.81
159148.21
159357.16
159325.47
159438.06
159326.33
159353.17
159321.58
159402.25
159440.59
159350.35
159343.39
159323.92
159354.55
159318.59
159256.58
159198.48
159148.67
159140.78
159171.16
159144.06
159232.67
159161.87
159144.72
159248.08

12

Surface elevationm
2304.632294.862287.722319.452309.422302.642339.46
2275.77
2272.542215.262215.222215.502215.732214.25
2213.33
2226.222214.04
2221.072217.972251.392255.75
2234.422227.272236.782223.282237.502283.892288.87
2273.542250.692265.622270.482267.482268.04
2249.112258.082265.102279.26
2283.532266.30
2252.67
2233.132218.25
2211.94
2213.75
2211.072211.04
2211.032235.76

Length
m
138.0
120.0
119.0
124.0
99.0
87.0
135.0
103.0
91.0
21.9
18.7
21.9
18.0
33.7
35.0
47.5
35.5
34.9
27.7
67.5
38.5
35.4
39.4
53.9
38.4
25.3
99.3
59.0
40.7
55.8
84.8
92.4
91.5
34.0
51.8
86.7
86.8
92.1
49.2
53.0
36.0
22.7
35.6
39.0
30.0
33.0
27.3
20.0
55.2

measurement
Pressure, GPS1

Stake 2Pressure, GPS3

Stake 10
Stake 8Pressure, GPS2
Stake 14
Stake 13
Stake 19
Stake 12
Stake 18
Stake 20
Stake 3
Stake 4
Stake 1
Stake 5
Stake 6
Stake 2
Stake 1
Stake 5Pressure
Stake 6
Stake 3
Stake 4
Stake 8
Stake 14
Stake 20
Stake 18
Pressure, GPS3
Stake 17
Stake 9Stake 15
Stake 16
Stake 11

2.2. METHODS

water was not suﬃcient for drilling. At times the heater would automatically shut down
due to the accumulation of black sediment from the glacier in a ﬁlter installed at the water
intake (Fig. 2.3). The drilling was carried out using either the 2.0 or 2.5 mm jet nozzle. For
some boreholes, the 2.0 mm conic spray nozzle was also used to enlarge the borehole. The
length of the hose in a borehole was recorded during drilling every 5–15 minutes to measure
the drilling speed. During the drilling, operator kept the nozzle slightly above the boreholebottom to drill a straight borehole. Drilling continued until the nozzle reached the glacierbed, a moment which could be recognized by the change in hose tension. The borehole depth
was determined by the length of the hose used for drilling. Borehole drilling in 2007 and 2008
were conducted with our hot water drilling system. In 2009, we loaned similar type of hot
water drilling system by Section of Glaciology, VAW, ETH Zurich.
The accuracy of the thickness is 1–2 m because of stretching of the hose during the drilling.
The ice thickness was also measured with a measuring tape lowered into some of the boreholes
with a weight on its end. The accuracy of this measurement is 20 mm. Bedrock elevation
was calculated from the ice thickness and the surface elevation measured by the kinematic
GPS survey. We constructed a bedrock elevation map with 25 m resolution by interpolating
the bed elevations obtained at the drilling sites (Fig. 2.1b).

2.2.3

Ice flow speed

We measured the surface motion of the glacier by surveying 23 stakes (aluminum poles 4.0–
6.0 m long) installed in the ice at the locations indicated in Figure 2.5a and b. These stakes
were named as Stake 1–20 and GPS1–3 (Table 2.1). We used dual-frequency GPS receivers
and antennae (Leica System 1200) to measure the three-dimensional (3-D) positions of the
stakes. One antenna was ﬁxed to solid rock on the western bank of the glacier as a reference
station (Fig. 2.5). Another antenna was mounted on the stakes and operated for 1 hour with
3 hour intervals at GPS1–3 and for 20–30 minutes every 10–14 days at Stake 1–20. These
data were processed in a static mode by GPS software (Leica Geo Oﬃce) to compute the 3-D
position of each stake. The displacement of a stake divided by the elapsed time of the two
measurements gives the ice ﬂow velocity. The GPS measurements at GPS1–3 were conductedfrom 14 July to 6 September in 2007, from 18 July to 7 September in 2008 and from 27 June
to 6 September in 2009. The measurements at Stake 1–20 were carried out in some periods
as listed in Table 2.2.
The distance between the rover and reference receivers was 208–634 m in the horizontal and
2–122 m in the vertical direction, and this relatively short distance was crucial to obtainthe necessary accuracy of the GPS measurement. The accuracy was evaluated after theﬁeld season by using the same survey method with two ﬁxed receivers standing apart 82 mhorizontally and 12 m vertically. Continuous test measurements for 6 days gave standard
deviations of 1.6 mm and 4.1 mm in horizontal and vertical directions, respectively (Fig. 2.6a).

13

CHAPTER 2. FIELD MEASUREMENTS

Measurement errors due to the tilting of the stake by ice melt or wind are about 10–20 mm.
This error is less than 3% of the total stake displacement over each survey interval in thethree seasons.
Surface ﬂow velocity at GPS1–3 was calculated every three hours in horizontal direction bysmoothing the horizontal displacement of the stake using Gaussian smoothing routine witha bandwidth of 4 hours. The data gaps due to the interruption of continuous survey were
removed from the data set.
For the correct measurement of the vertical velocity component, it was important to ﬁx thestakes into the ice during the measurements. our measurements provide the displacement of
a particle of ice near the glacier surface. Surface ablation does not inﬂuence on measured
vertical displacement in this study because the displacement means the movement of suchparticles in this study (Sugiyama and Gudmundsson, 2004). Figure 2.7 shows the componentsof measured ﬂow velocity in the ablation area of the glacier. Here, the x-axis has been taken
as horizontal and positive in the downglacier direction. The z-axis has been taken as positive
upward. The horizontal component of the ﬂow velocity u over a time period from t0 to t1
arises with the glacier surface slope α because the stake has moved downslope. The measured
surface elevation change w can be described as:
w = −utanα + w∗ ,(2.1)

where the quantity w∗ is the vertical component of ﬂow velocities. In the ablation area, w∗
is positive. Owing to the relative magnitude of the two terms on the right-hand side of theequation (see Fig. 2.7), the right-hand side is negative. The right-hand side is so-called theemergence velocity (Hooke, 2005). In the ablation area, the emergence velocity indicates the
upward of ice relative to the glacier surface at a point ﬁxed in space. In this study, thevertical velocity w∗ is calculated and descrived in Section 3.3.3.

Table 2.2: Dates of diﬀerential GPS measurement at Stake 1–20.
Measurement
1
2
3
4
5
6
7
8

Date 2008
24 Jul. – 1 Aug.
3–9 Aug.
26–30 Aug.
5–6 Sep.

14

Date 200926–29 Jun.
3 Jul.
16 Jul.
6 Aug.
11–12 Aug.
19 Aug.
30–31 Aug.
5 Sep.

2.2. METHODS

dh

35

Temperature

0.01

30

0

25

−0.01

20

−0.02

a
14

15

16
17
August 2010

10:30

11:00
August 19, 2010

18

19

20

o

dL

Temperature ( C)dL, dh (m)

0.02

15

dL, dh (m)

0.02
0.01
0
−0.01
−0.02
10:00

b
11:30

12:00

Figure 2.6: The accuracy tests of GPS measurement with (a) static and (b) kinematic mode.

2.2.4

Lake level and subglacial water pressure

The surface elevation of the two proglacial lakes was measured by using the some GPS static
survey as described in Section 2.2.2. As depicted in Figure 2.8, the antenna was ﬁxed at thelake shore. The measurements were taken on 29 August 2008 and 2 September 2009.
Vibrating-wire pressure sensors (Geokon Model 4500) were installed at the bottom of boreholes at GPS1 from 14 July 2007 to 6 September 2009, at GPS2 from 22 July to 7 September
2008 and at GPS3 from 18 July 2008 to 5 September 2009 to measure the subglacial waterpressure (Figs. 2.5 and 2.8). The pressure was recorded every 10 minutes using a data logger (Campbell Scientiﬁc CR-1000). The measured subglacial water pressure was converted
to water levels in boreholes. The accuracy of the pressure measurement was equivalent toa water level of 0.2 m. In other boreholes, which were not equipped with the sensor, wemeasured water levels with a measuring tape equipped with a ﬂoat sensor (Figs 2.5 and 2.8).
The measurement was conducted every 10–14 days with an accuracy of 0.1 m.

15

CHAPTER 2. FIELD MEASUREMENTS

u

P(t0)

Ice

z

P(t1)





w



w*

Ice

w’

u’



x

Figure 2.7: Schematic diagram showing stake motion over a time period from t0 to t1. P(t0)and P(t1) represent the positions of the stake at times t0 and t1. The horizontal componentof the surface ﬂow velocity is u and u0 . The measured surface elevation change is w. The
vertical component of ﬂow velocity is w∗ and w0 .

GPS antennadhdL

Glacier flowGPS antennadaWater pressuretransducer
Water gauge

Lake

Ice

Bedrock

Figure 2.8: Schematic diagram of the ﬁeld measurements.

16

2.2. METHODS

2.2.5

Surface elevation

The glacier surface elevation was surveyed on 27 and 31 July 2008 and on 12 and 29 July
2009. We used the same GPS devices, this time operating in kinematic mode, to measure
at more than 200 locations in the study area (Fig. 2.5a and b). According to accuracy tests
for 1.5 hours by using the same measurement settings described in previous paragraph, thestandard deviations were 3.3 mm in the horizontal and 9.1 mm in the vertical directions,
respectively (Fig. 2.6b). Errors due to the ice surface roughness are about 100 mm. We used
the same technique to survey the glacier and lake margins on 26 July, 27 July and 7 August
in 2008, and on 12 July and 29 July in 2009.

2.2.6

Meteorological observation

A meteorological station was established on the western side of the glacier at an altitude of
2531 m a.s.l (Fig. 2.1a). Air temperature and precipitation were measured at intervals of 5
minutes from 14 July to 7 September 2007, 17 July to 7 September 2008 and 28 June to 6
September 2009. A multi-weather sensor (Vaisala WXT510) was used for the air temperature and precipitation measurements. Data gaps occurred because of the failure of power
supply (battery drain), software problems (unknown reasons) and breakage of the sensor(thunderbolt).

17Chapter 3
Field data results
In this chapter, results of the ﬁeld measurements carried out in the summer seasons of 2007–2009 are presented. The presented data include (1) glacier surface and bedrock geometry
obtained from GPS survey and borehole drilling, (2) temporal change in surface verticalmovement, horizontal ﬂow velocity, borehole water level, air temperature and precipitation,(3) spatial distributions of horizontal and vertical velocities, and water level in borehole.

3.1

Surface and bed geometry

The length of the boreholes drilled in 2007–2009 are listed in Table 2.1. The total drilling
depths in 2007, 2008 and 2009 were 925 m, 1118 m and 1042 m, respectively. Figure 3.1aand b show the oblique perspective ﬁgure of Digital Elevation Models (DEMs) for glaciersurface and bed geometry for 2009, respectively. From these DEMs, surface and bed elevation
contour lines were drawn as Figure 2.1b. Surface elevation in the study region ranged from2208 to 2336 m a.s.l., and the bedrock geometry in the upper part of the study region showsa parabolic curve. In ﬁgure 2.1b, the maximum ice thickness in the region was about 130 m
near GPS1. A depression in the bedrock 30–40 m deep exists at 400–700 m from the terminus
beneath GPS1 and GPS2. In regions where the surface elevation is below 2250 m, the ice
thickness is less than 70 m. The glacier margins bordering Lake A and Lake B were about
26 m and 14 m thick, respectively.
Figure 3.2 shows the diﬀerence in bedrock elevation obtained in this study from that reportedby the ice radar survey in 2003 (Zahno, 2004). The bed elevation was 2188 m a.s.l. at GPS3,
which was 37 m lower than that calculated from the bedrock map in 2003. The discrepancy
decreases upglacier and they agree with each other within 10 m near GPS2. In contrast, at
GPS1, the bed elevation from this study was 2167 m a.s.l., which was 27 m higher than thatfrom the ice radar data. Accordingly, the ice radar data underestimate the bed elevation in
the upper reaches and overestimate in the current glacier tongue area. In previous study,
Sugiyama and others (2008) also pointed out the underestimation of the bed elevation in

19

CHAPTER 3. FIELD DATA RESULTSa

Altitude (m)

2350

2300

159.8
159.6

2250

159.4
2200
672.2

672.4

159.2
672.6

672.8

673

673.2

Northing (km)159

Easting (km)b

Altitude (m)

2350

2300

159.8
159.6

2250

159.4
2200
672.2

672.4

159.2
672.6

672.8

673

673.2

159

Northing (km)Easting (km)Figure 3.1: Oblique perspective ﬁgure of (a) glacier surface in 2009 and (b) bed geometry.
One mesh size is 25-m square. The surface elevations are based on DEMs constructed from
our GPS kinematic survey in 2009, and the bed elevations are based on boreholes drilled in
2007–2009.

20

3.1. SURFACE AND BED GEOMETRY

159.8

140
120

120
159.6

100
80

100

60

Northing (km)

80
60
159.4
40

40
20

Lake A
−20

20

0
−40

0

−20

159.2

GPS1

0

GPS2

−20

159
672

−40

Lake B
672.2

GPS3
672.4

672.6
Easting (km)

672.8

673

673.2

Figure 3.2: Diﬀerences in the bed elevation obtained in this study from bed elevation expectedfrom the ice radar data in 2000. The intervals of contour lines is 10 m. Circles indicate thelocation of GPS1–3 (red) and boreholes drilled in 2007 (black), respectively.

a range of 500–800 m from the terminus obtained from the ice radar data by comparison
with the borehole drilling in 2007. As described below, this study provides more accurate
bed elevation than previously reported data set. This information is crucial to predict thecollapse of the glacier terminus into the lake and the future development of the lake as
discussed later in this thesis.
Figure 3.3 shows the change in the surface elevation from 31 July 2008 to 29 July 2009.
The elevation lowered by 1–6 m in the study area over the year. The maximum change of−6 m a−1 was observed about 100 m north of GPS2. In the terminal area, the magnitude ofthe elevation change is minimum, which is less than −2 m a−1 . The mean thickening rates atsurface elevations of 2200–2250 m and 2250–2350 m are −2.15 and −3.44 m a−1 , respectively.
According to the ice thickness change obtained by comparing DEMs, the rates of thickness
change at the elevation of 2250–2350 m for the periods 1874–1929, 1929–1959, 1959–1980,
1980–1991 and 1991–2000 are −0.49, −0.92, −0.12, −0.92 and −1.87 m a−1 , respectively(Zahno, 2004). Sugiyama and others (2008a) reported that the rate at 2250–2350 m had

21

CHAPTER 3. FIELD DATA RESULTS

159.5

159.4

0
−1

−6

Lake A

159.3

159.2

−3
−4

159
672

−2

GPS3

−4

−5
159.1

GPS2

−4

Northing (km)−2

−6Lake B

−7
672.1

672.2

672.3

672.4
672.5
Easting (km)

672.6

672.7

672.8

672.9

Figure 3.3: Changes in the surface elevation from 31 July 2008 to 29 July 2009, as measured
by the GPS kinematic survey. The interval of contour lines is 1 m.
increased to a value of −2.75 m a−1 from 2000 to 2007. Accordingly, as a result of this study,
the rate of surface elevation change has accelerated over the past two decades.

3.2

Time series of glacier motion and borehole water level

Continuous GPS survey and borehole water level measurements were carried out in the summer seasons of 2007–2009. In this section, short-term ﬂuctuations in the vertical displacement,
horizontal ﬂow velocity and borehole water level obtained at GPS1–3 are presented.
2007 (from 14 July to 6 September)
A series of data taken from 14 July to 6 September, 2007 is shown in Figure 3.3. In the
beginning of the observation in 2007, the weather was ﬁne with minimum temperature ofover 15 ◦ C. On 30 and 31 July, weather turned to cold with occasional snowfall. After 9
August, the cold and warm weather came alternately for about a week.
The vertical displacement at GPS1 and GPS3 showed the downward movement over theentire measurement period (Fig. 3.4a). The horizontal ﬂow velocity in the both sites varied
diurnally over the entire period (Fig. 3.4b). The ﬂow velocity in GPS1 was higher than the22Vertical displacement (m)3.2. TIME SERIES OF GLACIER MOTION AND BOREHOLE WATER LEVEL

0.8

a

0.4
0
−0.4
−0.8

b

0.1
0.08
0.06
0.04
0.02

Flow velocity (m day−1)

0.12

0
2300

c

Flotation level

2280
2260
2240

Lake level

2220

−1

Precipitation (mm hr )

2200
30
25

20

d

15

20

10

15

5

10

0

5

−5

0
14

18

22

26

30

03

07

11

July

15

19

23

27

31

04

Temperature (oC)

Water level (m a.s.l)

2320

−10

AugustFigure 3.4: Time series of data taken in summer season of 2007. (a) Vertical displacementof the stake at GPS1 (red) and GPS3 (blue) from its original position on 14 July 2007.
Dashed line indicates original elevation level on 14 July. (b) Horizontal ﬂow velocity. (c)Water level in GPS1. Dashed line indicates mean lake level. Dotted line is ﬂotation level ofice thickness. (d) Air temperature (orange line) and hourly precipitation.

23

CHAPTER 3. FIELD DATA RESULTS

velocity in GPS3 from 14 July to 20 August. The velocity in GPS3 approached that in GPS1
when weather was cold with maximum temperature of 10 ◦ C on 22 August (Figs. 3.4b andd). The mean velocity at GPS1 for the entire measurement period was 26.46 m a−1 . The
mean velocity at GPS3 before 22 August was 21.75 m a−1 and increased to 25.77 m a−1
after 22 August. During the period from 14 July to 6 August, the water level at GPS1
showed diurnal variations (Fig. 3.4c). In contrast to the variable peak water levels, the daily
minima were nearly constant until 1 August. The minimum levels were 5–10 m higher than
the surface level of the lakes. After 2 August, the water level gradually rose up and themagnitude of diurnal variation decreased. It implies that the connection of the borehole tothe basal drainage system was abandoned. This kind of distinct change in water level was
also observed in Bench Glacier, Alaska (Fudge and others, 2008).
2008 (from 19 July to 6 September)
The warm weather continued from beginning of observation period to early August. The
weather turned from warm to cold on 22 July, 9 and 16 August (Fig. 3.5d). On 22 July, 9
and 16 August, heavy thunderstorms were observed. The observation was interrupted on 15
August, because some of the instruments were damaged by the thunderstorm.
Clear diurnal ﬂuctuations in the horizontal ﬂow velocity were observed in GPS1–3 (Fig. 3.5b).
The magnitude of the ﬂow velocity at GPS3 was comparable to those at GPS1 and GPS2.
The mean velocities over the entire measurement period in GPS1–3 are 26.94, 28.00 and
25.73 m a−1 , respectively. The amplitude of diurnal variations in velocity was smaller at
GPS3 than GPS1. The daily maximum velocity at GPS2 was larger than at GPS1 andGPS3. The vertical movement of the glacier surface at GPS1 and GPS2 were downward at
rates of −3 and −13 mm d−1 , respectively (Fig. 3.5a). In contrast to these stakes, the surface
moved upward at GPS3 by up to 150 mm from 10 to 14 August. Then, the movement was
downward until 26 August. Surface at GPS3 uplifted again at a rate of 30 mm d−1 from 26
August. The period of this uplift event corresponded to the reduction of the amplitude ofhorizontal ﬂow velocity in GPS3. Borehole water levels at GPS2 and GPS3 showed diurnal
ﬂuctuations over the entire observation period. The amplitude of those ﬂuctuations was lessthan 0.5 m. Water levels in both measurement sites were nearly equal to the mean lake level(Fig. 3.5c). It implies that the subglacial water pressure in the regions of GPS1 and GPS2
was directly controlled by the lake water.
2009 (from 1 July to 5 September)In the beginning of observation period of 2009, the study site was still covered with snow up
to 0.4 m thick. the snow disappeared by late July. On 17 and 18 July, temperature dropped
to 7 ◦ C and peak precipitation reached 9 mm h−1 . On 2 August, the cold weather cameagain with heavy rain or snowstorm and the precipitation was up to 30 mm h−1 (Fig. 3.6d).

24

Vertical displacement (m)3.2. TIME SERIES OF GLACIER MOTION AND BOREHOLE WATER LEVEL

0.8

a

0.4
0
−0.4
−0.8

b

0.1
0.08
0.06

Flow velocity (m day−1)

0.12

0.04

2230
2220
2210

c
Flotation level
Lake level−1

Precipitation (mm h )

2200
30
25

20

d

15

20

10

15

5

10

0

5

−5

0
19

23

27

31

04

08

12

July

16

20

24

28

01

05

Temperature (oC)

Water level (m a.s.l)

2240

−10

AugustFigure 3.5: Time series of data taken in summer season of 2008. (a) Vertical displacementof the stake at GPS1 (red), GPS2 (black) and GPS3 (blue) from its original position on 19
July 2008. Dashed line indicates original elevation level on 19 July. (b) Horizontal ﬂow
velocity. (c) Water level in GPS2 (black) and GPS3 (blue). Dashed line indicates mean lakelevel. Dotted line is ﬂotation level of ice thickness. (d) Air temperature (orange line) andhourly precipitation.

25

Vertical displacement (m)CHAPTER 3. FIELD DATA RESULTS

0.8

a

0.4
0
−0.4
−0.8

b

0.1
0.08
0.06

Flow velocity (m day−1)

0.12

0.04

2230
2220
2210

c
Lake level
Flotation level−1

Precipitation (mm h )

2200
30
25

20

d

15

20

10

15

5

10

0

5

−5

0
01

05

09

13

17

21

25

29

02

July

06

10

14

18

22

26

30

03

Temperature (oC)

Water level (m a.s.l)

2240

−10

AugustFigure 3.6: Time series of data taken in summer season of 2009. (a) Vertical displacementof the stake at GPS3 from its original position on 1 July 2009. Dashed line indicates original
elevation level on 1 July. (b) Horizontal ﬂow velocity. (c) Water level in GPS3 (blue) andBH904 (purple). Dashed line indicates mean lake level. Dotted line is ﬂotation level of ice
thickness. (d) Air temperature (orange line) and hourly precipitation.

26

3.3. GLACIER FLOW FIELDS IN 2008 AND 2009

The horizontal ﬂow velocity at GPS3 varied diurnally until early August (Fig. 3.6b). From
11 August, the amplitude of the diurnal ﬂuctuations decreased. The glacier surface levelchanged little from early July to early August (Fig. 3.6a). The rate of the vertical displacement increased and the amplitude of the diurnal ﬂuctuations reduced at about 11 August.
The glacier uplift continued until 5 September at a rate of 30 mm d−1 , and the verticalmovement turned to downward on 6 September. During the period of upward motion, thevertical displacement showed small diurnal ﬂuctuations. Borehole water level at GPS3 varied
diurnally, as observed in 2008. The water level in BH904, located about 300 m upglacierfrom GPS3 (dark gray square in Fig. 2.5b) showed little variation from 3 to 14 July. Then,
diurnal ﬂuctuations were observed from middle July. It implies that the connection of basal
drainage system was developed at this time of the season. The daily minimum level was
nearly constant, which was 15–20 m higher than the mean lake level.

3.3

Glacier flow fields in 2008 and 2009

The surface ﬂow velocity ﬁelds in the summers of 2008 and 2009 are shown in Figure 3.7aand Table 3.1. In 2008, the greatest velocity was 35.92 m a−1 at Stake 15 which was locatedvery close to the terminus. The velocity was generally larger near the terminus than in theupper reaches. For example, the velocities at Stakes 10 (26.38 m a−1 ) and 13 (25.13 m a−1 )were 6% greater than those of Stakes 2 (24.92 m a−1 ) and 3 (23.81 m a−1 ). From Stake 10
to Stake 15, the velocity increases by 36% over a distance of 150 m. In 2009, the velocity
at Stake 15 was 46% less than in 2008. The upper reaches also decelerated: the velocities
of Stakes 1–4 reduced by 18% in average. Despite this trend, the ice at the lake front still
ﬂowed rapidly in 2009. The velocities at Stakes 16 (21.52 m a−1 ), 17 (23.79 m a−1 ) and 18(21.23 m a−1 ) are large compared to those observed at the termini of other valley glaciersof similar size (e.g. Hooke and others, 1989; Iken and Truﬀer, 1997; Luckman and others,2007).
Very large upward motion was observed at the stakes located near the lake front. The verticalvelocities at Stakes 9, 15 and 16 were more than 20 m a−1 in 2009 (Fig. 3.7b and 3.1). The
data at Stake 15 show that the ice moved upwards at a similar rate in 2008. The verticalvelocity at GPS3 increased from 4.61 m a−1 in 2008 to 6.48 m a−1 in 2009. The ice motion
was downwards at all other stakes in the studied region.

27

CHAPTER 3. FIELD DATA RESULTS

Table 3.1: Horizontal (uh ) and vertical (uz ) velocities measured in summer seasonsof 2008 (18 July–7 September) and 2009 (27 June–6 September).
Stake No.

GPS2
GPS3
Stake 1
Stake 2
Stake 3
Stake 4
Stake 5
Stake 6
Stake 7
Stake 8
Stake 9Stake 10
Stake 11
Stake 12
Stake 13
Stake 14
Stake 15
Stake 16
Stake 17
Stake 18
Stake 19
Stake 20

2008
uh
m a−1
29.62
25.93
24.82
24.92
23.81
15.69
27.45
27.59
22.54
24.65
–
26.38
–
28.55
25.13
22.84
35.92
–
–
23.99
23.03
18.21

2009

uz
m a−1
2.72
4.61
0.78
1.23
−0.02
−1.45
−0.45
0.67
−0.28
7.67
–
−1.43
–
−0.89
0.04
0.63
25.10
–
–
7.19
0.94
−0.80

28

uh
m a −1
–
25.60
18.71
20.92
19.94
13.91
24.20
24.34
16.68
–
17.45
–
22.90
–
–
17.47
19.44
21.52
23.79
21.23
–
19.13

uz
m a−1
–
6.48
−0.79
−0.41
0.87
−1.18
−3.83
0.99
−2.22
–
28.13
–
−4.23
–
–
−2.66
20.82
21.27
1.21
1.59
–
−1.03

3.3. GLACIER FLOW FIELDS IN 2008 AND 2009

159.5

a

1
2

159.4

3

Northing (km)5

6Lake A

159.3

8
9 10

159.2

15

11

16

7

GPS2

12

GPS3

17

14

13

19

18

4

20

20 m a−1

159.1
Lake B

2008
2009

159
159.5

b

1
2

159.4
Northing (km)

3

159.3

5

Lake A
8
9

159.2

10

15

16

17

12
18

19

159.1
Lake B
159
672.1

672.2

672.3

7

GPS2

11

GPS3

672.4

4

6

14

13
20

20 m a−1

2008−20 m a−1

2009

672.5
672.6
Easting (km)

672.7

672.8

672.9

Figure 3.7: (a) Horizontal ﬂow vectors measured in 2008 (blue) and 2009 (red). (b) Verticalﬂow velocities measured in 2008 (blue) and 2009 (red).

29

CHAPTER 3. FIELD DATA RESULTS

3.4

Borehole water level

The mean water levels during the measurement periods in 2008 and 2009 are depicted along
the longitudinal proﬁle of the glacier bed in Figure 3.8b. In the upper reaches, at BH801, 806,
807, 808 and 920, subglacial water pressure varies signiﬁcantly. In contrast, at BH801 and819, water levels were at or near the ice surface with little or no variation during the entire
measurement period. Borehole water levels were nearly equal to the lake level within 5 mover the range of 300 m from the glacier terminus. According to the bed geometry obtainedin this study, the bed elevations are below the lake level at boreholes located in the terminal
area (Fig. 3.8a). At BH813 and 909, in the eastern side of the glacier, water had compleately
drained from the borehole and the tip of ﬂoat sensor had hit on solid rock at the bottom of
the borehole. The bottom of these boreholes are located slightly above the lake level.

3.5

Summary

GPS survey and borehole water level measurements were carried out with a high spatial resolution during the ablation seasons of 2007–2009 in Rhonegletscher. Important observationsin the ﬁeld measurements are summarized below.
1. Surface and bedrock DEMs are constructed by GPS survey and borehole drilling. Obtained bedrock elevation is up to 40 m lower at the terminus and 120 m higher at the
upglacier than those from the previously reported ice-radar data (Zahno, 2004). Mean
surface lowering rate from 2008 to 2009 is −2.15 m a−1 in 2200–2250 m and −3.44 m a−1
in 2250–2350 m, respectively.
2. Horizontal ﬂow velocity was greater than 20 m a−1 at Stakes 8, 9, 15, 16, 17 and 18 andGPS3 near the glacier terminus. These ﬂow velocities were similar to the velocity at
Stakes 1–7, located in the upper reaches of the study area. In the vicinity of the lake,at Stakes 9, 15 and 16, the ice surface moved upward at a rate greater than 20 m a−1
in 2008 and 2009.
3. Mean borehole water levels were nearly equal to the lake level within 5 m over the rangeof 300 m from the glacier terminus. In the upper reaches, at BH801, 806, 807, 808
and 920, subglacial water pressure varies signiﬁcantly during the ablation season. At
BH813 and 909, in the eastern side of the glacier, water had completely drained fromthe borehole.
The surface velocity and borehole water level were observed with a high spatial resolution.
The rate of ice thinning has increased over the past 20 years. To investigate the processes
and mechanisms of rapid glacier retreat caused by lake formation, these observed data are
examined and discussed in the next chapter.

30

3.5. SUMMARY

Northing (km)Lake A

159.3

7

159.2

9
14

16

24
5

15

50

20
7

8

16

17
11

13

19
6

12

17
8

3 12

15 6

23

3 4
22

22
11

1
1

159.4

22

21
2

a

22
00

159.5

14

13
18
10

159.1

9

Lake B
159
672.1

672.2

672.3

672.4

672.5
672.6
Easting (km)

672.7

672.8

672.9

2350

Water level (m a.s.l)

b
2300

ace

rf
er su
Glaci 6

Boreholes in 2008
1

Boreholes in 2009

4

1

2250
12

1516

3 11 10
7

6

2200

1411

17

8
9
17

15
16

22 3
14
12

24

13
10
18 23

5
1
5 1
2
8
21

7

19

2
9

20

Lake level

Bedrock
2150

0

100

200
300
400
500
Distance from the terminus (m)

600

700

Figure 3.8: (a) The Locations of boreholes used for water level measurement in 2008 (blue,
square) and 2009 (red, circle). The contours indicate bedrock elevation with intervals of
50 m. Along the dotted line, the bed elevation is equal to the lake level. (b) Mean waterlevels measured in the boreholes in 2008 (blue, square) and 2009 (red, circle). The markers
are indicated using the distance from the boreholes to the glacier terminus as the abscissa.
The vertical lines indicate the range of water level during the measurement periods. The
dashed line is the lake level. The shaded area indicate the bedrock along the dashed purple
line depicted in (a).

31Chapter 4
Field data interpretations
Observed horizontal ﬂow ﬁeld and surface upward movement are analyzed in detail andinterpreted in this chapter. Horizontal ﬂow velocity is compared with that observed before
the formation of Lake B. Horizontal strain rate is derived from the spatial distribution ofhorizontal ﬂow velocity to interpret dynamic thinning of ice thickness. Spatial distributionof the eﬀective pressure was calculated by using DEMs of surface and bed to test the ﬂoating
condition near the lake.

4.1

Ice flow acceleration in the terminus

4.1.1

Changes in ice flow speed before and after the lake formation

We investigate the inﬂuence of the lake formation on the ice ﬂow speed by comparing ourobservations at GPS1 and GPS3 from 2007 to 2009 with those reported in previous studies.
Horizontal ﬂow velocities before the formation of Lake B were measured by analysis of aerial
photographs by Nishimura (2008). Photographs taken in 9 September 1999, 23 August 2000,
15 September 2005 and 5 September 2006 were used for the analysis. The annual horizontal
ﬂow speed was measured at the grid points of 100 m mesh during the periods of 1999–2000
and 2005–2006. Estimated error of the measured ﬂow velocity is 4 m a−1 . To compare the twodata, the ﬂow velocity measured using aerial photographs was interpolated to the coordinatesof GPS1 and GPS3. Note that our measurements were made in summer, while the reported
data represent annual velocities. Annual velocity was estimated from the summer velocity
as described below. In this study, annual ﬂow velocities at Stakes 2 and 3 were measured
from 7 September 2008 to 26 June 2009. Measured annual velocities were 14.19 m a−1 at
Stake 2 and 13.06 m a−1 at Stake 3. The annual velocity at Stake 2 was 57% of the summer
velocity in 2008 and 68% of that in 2009. At Stake 3, the annual velocity was 55% of thesummer velocity in 2008 and 66% of that in 2009. Assuming the same relationship at GPS1
and GPS3, annual velocity was estimated as 16.64 and 13.64 m a−1 in 2007–2008 and 16.93
and 16.68 m a−1 in 2008–2009. Time series of annual ﬂow velocities are shown in Figure 4.1.

33

CHAPTER 4. FIELD DATA INTERPRETATIONS

0Lake B formation

Up−glacier (GPS1)

30

−1
−2

Thickning rate

20

−3
10

0

Terminus (GPS3)

2000

2002

−4

2004
Year

2006

2008

Thickning rate (m a−1)

Horizontal flow velocity (m a−1)

40

−5
2010

Figure 4.1: Horizontal ﬂow velocities at GPS1 and GPS3 from 2000 to 2009. Thin and blacklines indicate the velocities at GPS1 and GPS3, respectively. Thin line with open diamondindicates the thickening rate. Vertical dashed line indicates the time of Lake B formation. The
ﬂow velocity of 2000 and 2006 were obtained by the interpolation of ﬂow velocity calculated
by aerial photographs (Nishimura, 2008).

From 1999–2000 to 2005–2006, before and after Lake B forming, the ﬂow velocity at GPS3
increased by 40% and decreased by 17% at GPS1. The velocities at both measurement sites
had changed signiﬁcantly from 2005–2006 to 2007–2008. The velocity increased by 100%
at GPS3 and decreased by 33% at GPS1. After the speed up, the ice ﬂow velocity at theterminal part of Rhonegletscher is signiﬁcantly faster than that observed in similar temperate
alpine glaciers without proglacial lakes (e.g. Hooke and others, 1989; Iken and Truﬀer, 1997;
Luckman and others, 2007). From 2007–2008 to 2008–2009, The velocities at GPS1 andGPS3 increased by 2% and 18%, which became relatively steady. The velocity at GPS3
closed to that at GPS1 is also shown in Figure 3.5b.
Decreases in the surface ﬂow velocity at GPS1 is probably due to the thinning of the ice.
The surface velocity us in an uniformly inclined inﬁnitely wide glacier is expressed as:
u s = ub +2A
(ρi g sin α)n H n+1 ,
n+1

(4.1)

where ub is the sliding velocity, ρi is the density of ice, α is surface slope and g is thegravitational acceleration (e.g. Nye, 1952; Hooke, 2005). A is the rate factor. The powerindex is often taken as n = 3. Equation (4.1) indicates that the surface velocity is proportional
to the 3rd power of the surface slope and to the 4th power of the ice thickness. The meanchanging rate of the ice thickness at elevations of 2250–2350 m during the periods 2007–2008
and 2008–2009 are depicted in Figure 4.1. Sugiyama and others (2008a) reported that the34

4.1. ICE FLOW ACCELERATION IN THE TERMINUS

Effective pressure (MPa)

0.5
0.4

23

12

9

0.3
0.2

2008

0.1

2009

17
6

0
−0.1
−50

15 16

0

3

16

50

3

12

11
7

10
11

8

17
15

14

21

18

13

2

10

22

9

52

14

100
150
200
250
Distance from the terminus (m)

300

350

400

Figure 4.2: Mean eﬀective pressure calculated from each borehole depth and water level
drilled in 2008 (blue, square) and 2009 (red, circle). The vertical lines indicate the range ofeﬀective pressure during the measurement periods. Numbers of borehole are listed in Table 2.1.
rate had increased from −1.87 m a−1 in 1991–2000 to −2.75 m a−1 in 2007. This study
shows the rate for the same elevation range as −3.04 m a−1 in 2007–2008 and −3.44 m a−1
in 2008–2009. This result indicates that the glacier is thinning at a progressively increasingrate in the 21st century. Assuming that the basal sliding is 0 m a−1 and surface slope isconstant in time, surface velocity at GPS1 estimated from Equation (4.1) as 29.7, 19.0 and13.7 m a−1 in 2000, 2006 and 2009, respectively. Ice ﬂow decelerated in the upper reaches
probably because the ice deformation rate decreased as the ice thinned.

4.1.2

Mechanisms of flow acceleration

The subglacial water pressure in the range of 300 m from the terminus was directly controlled
by the lake water (Fig. 3.8). Water cavity formation and its sustainability are controlled bywater pressure. Once a water cavity is formed, water pressure is considered to push the icesole forward with hydraulic-jack eﬀect (Röthlisberger, 1981). It is suggested that a subglacial
drainage system in the terminal part of glacier has been developed during the entire ablationseason. Water level of Lake A was about 1.7 m below the ice surface in 2008. If we consider theice thickness at this location, 102% of the ice overburden pressure was cancelled by the lakewater pressure. It is likely that the formation of the lake increased subglacial water pressure
at the glacier terminus. The spatial distribution of eﬀective pressure Pe is calculated as:
Pe = ρi g(zs − zb ) − ρw g(zw − zb ) ,

35

(4.2)

CHAPTER 4. FIELD DATA INTERPRETATIONS

where ρi = 910 kg m−3 and ρw = 1000 kg m−3 are ice and water densities, respectively,
and g = 9.81 m s−2 is the gravitational acceleration. Glacier surface, bed elevation and lakelevel are represented as zs , zb and zw , respectively. Figure 4.2 shows the eﬀective pressure
plotted against the locations of borehole along the longitudinal proﬁle of the glacier. The
eﬀective pressure was obtained from water pressure measured in the periods from 24 July
to 6 September 2008 and from 26 June to 5 September 2009. The overburden pressure wascalculated from the local ice thickness determined from the hot water drilling (Table 2.1).
A scatter plot of the data from the two observation periods shows that eﬀective pressure
approaches zero at the borehole near the terminus. At BH807, 809, 912, 914, 915 and 916,
subglacial water pressure exceeded ice overburden pressure.
The acceleration from 2005–2006 to 2007–2008 at GPS3 occurred within a period of 2–3 years
after the ﬁrst recognition of Lake B in 2005. It is implied that high water pressure enhanced
basal motion. The relationship between subglacial water pressure and surface ﬂow velocity
has been studied theoretically and by ﬁeld measurement with high temporal resolution (e.g.
Weertman, 1957; Iken, 1981; Iken and Bindschadler, 1986; Sugiyama and Gudmundsson,2004). According to these works, the high subglacial water pressure reduces the friction at theice-bed boundary. This is because water submerges small obstacles on the bed. The surface
velocity increases exponentially when the subglacial water pressure attains ice overburdenpressure (e.g. Iken and Bindschadler, 1986; Kamb and Engelhardt, 1987; Sugiyama andGudmundsson, 2004). Ice ﬂow mechanisms at the terminus in the lake terminating glacier
have been discussed in previous studies. Motyka and others (2002) calculated the ﬂow velocity
at the terminus of Mendenhall Glacier in Alaska, using a simple ﬂow low of ice. They notedthat the deformational ﬂow can only account for about 5 m a−1 of the surface velocity, andthe rest (87 m a−1 ) is due to basal motion. In Rhonegletscher, assuming the ice thickness
at GPS3 in 2008 as 20 m, surface ﬂow speed estimated from Equation (4.1) is only several
millimeters per year. Thus, nearly 100% of the surface ﬂow observed in this study was caused
by basal ice motion.
An additional eﬀect on glacier ﬂow velocity is the separation of glacier terminus in front of
Lake B from the bedrock bump (Fig. 2.2b). Meier and Post (1987) studied rapid velocity
increases at the terminus of Columbia Glacier in Alaska. They concluded that the speedup
was caused partly by the release of back pressure (longitudinal normal stress) due to theseasonal calving retreat of the terminus. Naruse and Skvarca (2000) suggested that rapid
glacier retreat observed in Glaciar Upsala, Southern Patagonia should be aﬀected by the bed
topography in terms of normal stress.

4.2

Dynamic thinning

The velocities near Lake A and Lake B are comparable with those in the upper reaches(Fig. 3.7a). In this respect, the ﬂow regime of Rhonegletscher is similar to the observation

36

4.2. DYNAMIC THINNING

by Motyka and others (2002) at Mendenhall Glacier. They calculated strain rates fromtriangular net measurement of horizontal ﬂow velocity near the glacier terminus. Results
showed 0.25 and 0.16 a−1 of tensile strain rates, which were oriented in the direction of
glacier ﬂow. Figure 4.3a shows the plot of horizontal ﬂow velocity at GPS1–3 measured in
1999–2000, 2005–06, 2007–08 and 2008–09 against the locations of GPS measurement along
the longitudinal proﬁle. The velocity in the upper reaches (GPS1) was higher than that near
the terminus (GPS3) in 1999–2000 and 2005–06 before the formation of Lake B. After thelake formation, the velocity at GPS3 was nearly equal to that at GPS1.
Here, we deﬁne a coordinate system with the x-axis along the ﬂow direction pointing upglacier, the y-axis across of the glacier pointing East, and the z-axis vertical upward. Figure 4.3b shows horizontal strain rates ε̇x calculated as:ε̇x =ux2 − ux1,x2 − x1

(4.3)

40
30

1999−2000
2005−2006
2007−2008
2008−2009

20

GPS3

10
0

GPS1
GPS2

a
0.02
0
−0.02
−0.04
−0.06
−0.08

b
0

100

200

300
400
500
Distance from the terminus (m)

600

−0.1
700

Longitudinal strain rate (a−1)

Horizontal flow velocity (m a−1)

where ux1 and ux2 are ﬂow velocities measured at x1 and x2 , which are the coordinates of
GPS position. Result shows tensile strain rates in 1999–2000 before the formation of Lake
B: −0.079 a−1 between GPS2 and 3, and −0.029 a−1 between GPS1 and GPS2, respectively.
In 2005–06, the strain rate is −0.079 a−1 at GPS2–3 and −0.009 a−1 at GPS1–2. The strain

Figure 4.3: (a) Horizontal ﬂow velocity and (b) strain rate in 1999–2000 (red), 2005–2006(blue), 2006–2007 (green) and 2007–2008 (purple).

37

CHAPTER 4. FIELD DATA INTERPRETATIONS

rate is signiﬁcantly more tensile near the glacier terminus in 2007–08 after the formationof the lake. The strain rate between GPS2 and 3 was −0.004 a−1 . In valley glaciers, thetransverse strain rate ε̇y is usually suﬃciently smaller than the longitudinal strain rate ε̇x .
If we neglect the transverse strain rate, the vertical strain rate ε̇z is obtained as ε̇z = −ε̇x(Fujii and others, 1997). The vertical strain rates measured at GPS3 from 24 July 2008 to 17
July 2009 shows that ε̇z was negative over the entire measurement period (Yoshizawa, 2010).
This result indicates that the horizontal ﬂow regime near the terminus would cause thinningof ice thickness.
To discuss the observed increase in the ice ﬂow speed, the spatial distribution of surface
strain rate is calculated from horizontal velocities measured between 3 July and 5 September
2009 (Fig. 4.4). The GPS network was tessellated into individual triangles. Two dimensionalsurface strain on the glacier was analyzed with the method described by Brunner and others(1981). The spatial strain distribution shows a clear tensile strain regime along the ﬂow
direction in the entire of measurement area. The highest strain rate (0.32 a−1 ) was observedat the triangle constructed from GPS3–9–15. Similarly high strain rate was observed at thetriangles of 9–11–18 and GPS3–9–18 (0.31 a−1 ). The strain rates at GPS3–9–15 and GPS3–
9–18 oriented approximately west–east, across the glacier ﬂow. Ice is compressed in thearea between these triangles. According to these results, tensile ﬂow regime has aﬀected todecrease in ice thickness after the proglacial lake formation. Similar tensile strain regime near
the terminus has been observed previously before a signiﬁcant calving event in Mendenhall
Glacier and Columbia Glacier (Venteris and others, 1997; Boyce and others, 2007). The
important aspect of the temporal and spatial variations in horizontal strain regime is thatboth ice dynamics and ablation were aﬀecting the change in the ice thickness. During thelast decade, the increase in the thinning rate is inﬂuenced by these factors.

4.3

Surface uplift

4.3.1

Uplift and crevasse formation in the terminus

Continuous GPS measurements at GPS3 show upward movement of glacier surface in Augustof 2008 and 2009 (Figs 3.5a and 3.6a). The uplift might have been caused by subglacial waterpressure elevated above the ﬂotation level. To test this hypothesis, we compare the borehole
water level with the ﬂotation level of ice thickness hf calculated as:
hf = zb + H

ρi
,
ρw

(4.4)

where zb is the bed elevation, H is the ice thickness, and ρw and ρi are densities of waterand ice, respectively. Temporal changes in the ice thickness due to surface melt and verticalstrain were corrected. Water level in borehole showed diurnal ﬂuctuations within 0.5 m
during the entire periods in 2008 and 2009 (Fig. 4.5a and c). A clear relationship between

38

4.3. SURFACE UPLIFT

159.5

Extension

1Compression
159.4

0.1 a−12
3

5
Northing (km)

6

4

159.3
11

9
159.2

14

15
16

159.1
672.1

7

17

18

20

GPS3

672.2

672.3

672.4

672.5
Easting (km)

672.6

672.7

672.8

Figure 4.4: Spatial distribution of horizontal strain rate, calculated from measured velocities
for the time period 3 July–5 September 2009 (Fig. 3.7a). Red and blue bars indicate extending
and compressive ﬂow regime, respectively. Vectors indicate horizontal ﬂow velocities.

vertical displacement and subglacial water pressure was not found in this study, though thisrelation has been observed at the terminus of Mendenhall Glacier in Alaska (Boyce and others,2007) and during a lake outburst ﬂood event from ice-dammed lake at Kennicott Glacier in
Alaska (Walder and others 2005; 2006). As a result of ice thinning due to surface melt andcompressive vertical strain, the water level exceeded the ﬂotation level about two days before
the uplift in 27 August 2008 (Fig. 4.5b). The uplift in 2009 occurred more than a monthafter the ﬂotation condition was satisﬁed (Fig. 4.5d). Mean rate of upward movement isapproximately 3 cm d−1 in both years.
The uplift of ice surface was also observed at Stakes 9, 15, 16 (Fig. 3.7b). As shown in
Figures 4.2, 4.5b and d, subglacial water pressure near the terminus has exceeded the ice
overburden pressure since the ablation season of 2008. To examine whether the conditions forﬂoating are met in the entire part of Rhonegletshcer tongue, the eﬀective pressure distribution
is computed from Equation 4.2. Hydraulic head with in the glacier was assumed to be equal
to the lake level, which is constant in time (zw = 2211.4 m). The ice surface zs and bed
elevations zb are given by the DEMs in 2009 constructed in this study (Fig. 3.2a and b). In

39

Vertical displacement (m)CHAPTER 4. FIELD DATA INTERPRETATIONS

1
0.8
0.6

a

c

b

d

0.4
0.2
0
−0.2

Water level (m a.s.l.)

2213

2212

2211

2210

2209
19 24 29 03 08 13 18 23 28 02 01 06 11 16 21 26 31 05 10 15 20 25 30 04

July

AugustJuly

AugustFigure 4.5: (a) Vertical displacement of glacier surface, and (b) borehole water level andﬂotation level at GPS3 in 2008. (c) Vertical displacement, and (d) borehole water level andﬂotation level at same borehole in 2009. Error bars in ﬂotation level are 0.3 m. The dashedline in (b) and (d) indicates mean lake level (2211.4 m).

2008, the eﬀective pressure reached zero at the shore of Lake A and in an area including Stake
15 (Fig. 4.6a). Eﬀective pressure was relatively high near GPS3, indicates that the glacier isthinner in that area, and thus the ﬂotation level is higher than other locations. Region whichreached ﬂotation extended farther to the southeast in 2009 as a result of glacier thinning(Fig. 4.6b). In the upper reaches, the eﬀective pressure is smaller than that near the lake.
Assuming that the thickening rate is constant in time (−3.44 m a−1 ), the eﬀective pressure
will reach zero at the entire area of the glacier terminus after two or three years.

404.3. SURFACE UPLIFT

3

0

0.1

8

10
159.2
0

Northing (km)0.

Lake A

0.2

159.3

5

a

15

GPS3

18

159.1

Lake Bb0.

Lake A3

159.3

Northing (km)

0.2
0.1

9
159.2

0

GPS3

15

17

16

11

18

159.1

Lake B
672.1

672.2

672.3
Easting (km)672.4

Figure 4.6: The eﬀective pressure in MPa (a) 27–31 July 2008 and (b) 29 July 2009. The
contour intervals are 0.05 MPa. The ice overburden pressure was calculated from the surface
and bed DEMs constructed in this study. The dashed line in (b) indicates the crevassee
described in the text and depicted in Figure 4.7.

41

CHAPTER 4. FIELD DATA INTERPRETATIONSab




Figure 4.7: Photographs showing the terminus of Rhonegletscher on (a) 29 July 2009 and(b) 3 September 2009. The approximate locations of survey stakes are indicated. Bar depicted
between points A and B indicates longitudinal proﬁle shown in Figure 4.9.

4.3.2

Interpretations of the uplifts

As a result of reduction in eﬀective pressure near the lake, a large crevasse began to form
along the northern margin of Lake A between Stake 9 and GPS3 and towards Stake 16 (dottedline in Figure 4.6b) in late July 2009; see Figure 4.7a for a photograph of this crevasse. The
north-western side of the crevasse had gradually risen relative to the south-eastern side by the
beginning of September (Fig. 4.7b). This uplifted area corresponds to the region where theeﬀective pressure was vanishing in 2009. Stakes 9, 15 and 16 located on the ice that moved
upwards. GPS3 was on the other side, but only a few meters from the crevasse. Figure 4.8
shows the time series of vertical displacement of ice surface at these four measurement points.
To interpret the surface uplift and the crevasse formation, vertical displacement in the three
periods (1–16 July, 17 July–19 August and 20 August–5 September) is discussed. Schematic
diagrams show mechanisms related with the crevasse formation and uplift in each period(Fig. 4.9).
Upward movement of glacier surface was observed at Stake 9 and 15 when the ﬁeld measurements were launched on 1 July, suggesting that the ice ﬂoated and moved upward (Fig. 4.9a).
Predominant uplift (0.1 m−1 ) occurred at Stake 15, which is the stake nearest the terminus.
In this period, the glacier tongue was subjected to a buoyancy force, which was greater than
the ice overburden load. Nye (1976) examined the water ﬂow within and under the ice during
a glacier outburst ﬂood (jökulhlaups) from ice dam in Grı́msvötn, Iceland. According to his
prediction, when the lake water head reaches the ﬂotation level, a wedge of water would
penetrate beneath the ice dam and incrementally jack the ice oﬀ its bed. This scenario is theso-called cantilever eﬀect. He argued that the ice dam would be subjected to a force which will42

4.3. SURFACE UPLIFT

65

Period 1

Period 2

Period 3

43

Stake 92
1
0
5

Vertical displacement (m)43Stake 15

2
1
0
5
4
3

Stake 16

2
1
0
5
4
3

GPS3

2
1
0
01Jul

11Jul

21Jul

31Jul

10Aug

20Aug

30Aug

Figure 4.8: Vertical displacement of glacier surface at (a) Stake 9, (b) Stake 15, (c) Stake 16
and (d) GPS3. The horizontal bars indicate the diﬀerent mechanisms for crevasse formation
and uplift depicted in Figure 4.9.

43

CHAPTER 4. FIELD DATA INTERPRETATIONS




GPS3

16

9

15


M

a

GPS3

15

16

9

16

9 15

b

GPS3

c
Figure 4.9: Schematic diagrams showing the mechanisms of crevasse formation and surface
uplift. The diagrams correspond to the periods for (a) 1–16 July (Period 1 in Figure 4.8),(b) 17 July–19 August (Period 2) and 20 August–5 September (Period 3). The glacier crosssection is taken along the line AB in Figure 4.7b.

44

4.4. FUTURE EVOLUTION OF RHONEGLETSCHER

bend the glacier margin upwards because isostatic adjustment is not instantaneous. Walderand others (2005 and 2006) observed similar uplift event during jökulhlaups from Ice-dammed
Hidden Creek Lake, Kennicott Glacier. Warren and others (2001) studied such uplift by ﬁeld
measurements in Glaciar Nef, Chilean Patagonia and interpreted the observation using a
buoyant calving model. They suggested that buoyant forces impose a bending moment M(depicted in Figure 4.9a) and tensile stress on the marginal ice, resulting in formation of acrevasse and calving. Before the crevasse formed, tensile stress ﬁeld occurred at the bottomof glacier due to the bending moment.
According to visual and photograph observation, the crevasse began to form between 29 Julyand 5 August. This is when vertical displacement increased signiﬁcantly at Stakes 9 and
16 located along the crevasse (Fig. 4.8). Mean uplift rate at Stakes 9 and 16 are 0.05 and0.03 m d−1 before 6 August, and 0.14 and 0.08 m d−1 afterwards. In contrast, increasingrate of displacement at Stake 15 became gradually small. It suggests that the north-westernside of the crevasse had gradually risen relative to the south-eastern side. According to theobserved stake movement and crevasse patterns, the crevasse formation can be explained byfault formation cutting through the entire ice thickness (Fig. 4.9b). Gagnon and Gammon(1995) experimentally determined tensile strength of ice as about 1 MPa at the pressuremelting point. Vaughan (1993) calculated lower limit of the tensile strength to form a crevasse(about 0.1–0.2 MPa) from the occurrence of crevasse on temperate glaciers. If tensile stressexceeds 0.1–0.2 MPa, the crevasse would begin to form at the glacier bed. To predict a timingof crevasse formation, further discussion is needed with a buoyant calving model.
In the third period, the rates of upward motion at Stakes 9 and 16 are similar, 0.08 and0.06 m d−1 , respectively (Fig. 4.8). At Stake 15, the rate of vertical movement became
steady, which is 0.02 m d−1 . This value is nearly equal to that observed at GPS3. Totalamount of vertical displacement during entire of measurement period is 4.69 m (Stake 9),3.48 m (Stake 15), 3.32 m (Stake 16) and 0.93 m (GPS3). The glacier surface was 3.8 m
higher in the northwestern side of the crevasse than the southwestern side (Fig. 4.9c).

4.4

Future evolution of Rhonegletscher

The formation of crevasse and huge uplift were observed in the ﬁeld measurements during
the ablation season of 2009. It is expected that the upward movement of glacier would beobserved in a larger area if ice thinning continues in the future. Our ﬁeld measurements werecompleted in early September 2009. After the measurements, the study site has been observedby operating an automatic digital camera one a day by Section of Glaciology, VAW, ETH
Zurich (http://people.ee.ethz.ch/ glacier/acam.html). Figure 4.10 shows the photographs ofRhonegletscher tongue taken on 11 October 2009 and 11 October 2010. In October 2009, theposition of glacier terminus was nearly equal to that observed in late July by GPS survey(Fig. 4.10a). However, the terminus disintegrated and the marginal ice detached from the45

CHAPTER 4. FIELD DATA INTERPRETATIONSab

Figure 4.10: Photographs showing the terminus of Rhonegletscher on (a) 11 October 2009
and (b) 11 October 2010. Dashed line indicates the approximate area where the eﬀective
pressure was less than zero in 2009 as shown in Figure 4.6b. These photographs were taken
by Section of Glaciology, VAW, ETH Zurich (http://people.ee.ethz.ch/ glacier/acam.html).

glacier body in October 2010 (Fig. 4.10b). The disintegrated area corresponds roughly tothe uplifted region in 2009. Accordingly, the rapid terminus retreat occurred only 5 years
after the formation of the proglacial lake, as observed in Triftgletscher, Switzerland (Müller,
2004).
Figure 4.11 shows processes of rapid glacier retreat after the formation of proglacial lake
revealed by this study. Lake formation in the terminus triggers increase in subglacial waterpressure. On the other hand, ice overburden pressure decrease as the ice thins as a resultof surface ablation. These two processes reduces the eﬀective pressure, which causes theacceleration of ice ﬂow at the terminus. Speed up of glacier terminus changes in horizontal
ﬂow regime from compression to extension. Tensile strain regime causes the thinning of ice.
Benn and others (2007) suggested positive feedbacks between longitudinal stretching andice thinning: longitudinal stretching leads to ice thinning and decrease in eﬀective pressure,which will lead to further ﬂow acceleration and longitudinal stretching. It is suggested thatthese positive feedbacks was activated and the ice thinning accelerated in the terminal partof Rhonegletscher after the formation of Lake B. When subglacial water pressure exceeds
the ice overburden pressure, surface uplift and the formation of crevasse occurred, resulting
in the integration of the glacier terminus as observed in 2010. According to the change inspatial distribution of eﬀective pressure, the eastern side of glacier terminus in front of Lake
A may ﬂoat and disintegrate over the next few years if the glacier continues to thin.
The bed elevation map obtained in this study provides important information for predicting
future expansion of the proglacial lake. We predict that the lake will expand nearly 1 km

46

4.4. FUTURE EVOLUTION OF RHONEGLETSCHER

Figure 4.11: Flow diagram of inﬂuence of proglacial lake formation on glacier retreat.

47

CHAPTER 4. FIELD DATA INTERPRETATIONS

from the current terminus to the area bounded by the dotted line in Figure 3.8a as the glacierretreats. The maximum depth of the lake upon reaching this size will be approximately 50 m.
At a constant thinning rate of −3.4 m a−1 , the lake will continue to expand approximately
600 m up-glacier and reach the location of GPS1 in 2034. The future evolution of Rhonegletscher has been predicted by numerical modeling based on the ice-radar data (Sugiyama
and others, 2007). Because the bedrock depression reported in the ice-radar data does notexist, ice ﬂux into the terminal part is less than expected. Thus, the retreat rate of the glacierwould be greater than this previous prediction. Sugiyama and others (2008a) suggested thatthe lake will expand to the location of GPS1 in 2040, which was based on the thinning rateof −2.8 m a−1 . This prediction is 6 years later than that in this study. Accordingly, increasein thinning rate due to extending ﬂow regime and increase in summer ablation will cause
more rapid glacier retreat than expected by previous studies. Mass-balance changes in Swissglaciers are probably related to the increase in the thinning rate. Huss and others (2008)
computed the seasonal mass balance of four glaciers, including Rhonegletscher, for the period
1865–2006. According to their results, the rate of mass loss progressively increased after ashort period of mass gain from 1974 to 1981. The period 1998–2006 was characterized bystrongly negative mass balance due to high summer ablation in all four glaciers. To carryout more accurate prediction for glacier retreat, numerical investigations using a glacier evolution model incorporating DEMs of surface and bedrock, and processes of acceleration anddisintegration of glacier terminus revealed in this study are required.

Proglacial lakes in many alpine glaciers pose a sudden outburst of the lake water, the socalled Glacial Lake Outburst Flood (GLOF) in Himalaya (e.g. Bolch and others,2008; Fujita
and others, 2009), Switzerland (e.g. Huggel and others, 2003; 2004) and other countries(e.g. Clague and Evans, 2000). In Rhonegletscher, GLOF is not likely as it is dammedby the bedrock bump. However, one of the possibilities of GLOF is due to ice avalanches.
Ice avalanches are caused by frontal ice brocks failure, ice slab failure and ice-bedrock failure (Richardson and Reynolds, 2000). Waves generated by ice avalanches can overtop thedamming bump, and cause a signiﬁcant hazard in areas where human activities impinge upon
the upper glaciated valley catchments. Changes in eﬀective pressure at the western side of
upglacier area between Stakes 5 and 10 is more steady than that at the terminus (Fig. 4.6aand b). It is implied that the glacier terminus at this area would be remain over the next
few years. The surface slope at this area is relatively steep (9◦ ). Because of the steep slope,a crevasse has formed from the western margin toward the center part (Fig. 4.10). If themarginal part of the ice detaches from this crevasse and fall into the lake, large waves toward
the damming bump, resulting in occurrence of outburst ﬂoods.

48

4.5. SUMMARY

4.5

Summary

Comparisons of our data to the study analyzed the velocity in 1999–2000 and 2005–2006(Nishimura, 2008) revealed change in the ﬂow velocities after the lake formation. The ﬂow
velocity approximately tripled from 2006 to 2007 at the glacier terminus. The eﬀective
pressure reached zero at the glacier terminus in 2008 and 2009. Additionally, horizontal
velocities were greater than 20 m a−1 in the region where the ice thickness was only about
20 m. Thus, most of the ﬂow at the terminus was due to basal ice motion. Flow velocity
decreased after the lake formation in upper reaches. This velocity change is due to thethinning of ice.
The longitudinal strain rate revealed the ice ﬂow regime under the inﬂuence of proglacial lakeformation. The longitudinal strain rate at the glacier terminus changed from compressive totensile after the lake formation. Calculated spatial distribution of horizontal strain rate showsthat the horizontal ﬂow regime near the terminus was tensile in the longitudinal direction.
This ﬁnding suggests that increase in ice thinning observed in the last decade has been causedby both the extending ﬂow regime and negative mass balance.
A huge uplift at the terminus was observed when the borehole water level exceeded the ﬂotation level of ice thickness as a result of ice thinning. Analysis of the eﬀective pressure conﬁrms
that water pressure exceeded the ice overburden pressure along the shore of Lake A in 2008.
The region of excess water pressure extends even farther in the terminal area in 2009 as aresult of ice thinning. The uplift is related to the formation of a crevasse. The temporal variations in vertical stake movements around the crevasse revealed the mechanisms of crevasse
formation. Before the crevasse formed, surface uplift at the shore of Lake A occurred because
a water wedge penetrated beneath the ice dam. The glacier margin decoupled from the bedby this process. The crevasse has formed due to movement along steeply dipping faults thatdips towards the lake and cut through the entire ice thickness.
After the huge uplift and the formation of crevasse were occurred, disintegration of glacierterminus was observed in uplifted area. The entire glacier terminus will ﬂoat and disintegrate
over the next few years. The processes of glacier retreat caused by proglacial lake formation
were observed particularly in this study. At the elevation range of 2250–2350 m, the glacieris thinning at a progressively increasing rate. Assuming that the thinning rate of −3.4 m a−1
observed in 2008–2009 is sustained, the glacier will retreat approximately 600 m and thelake will expand to its maximum size by 2034. The possibility of GLOF in Rhonegletscher
is not likely as it is dammed by the bedrock bump. However, ice avalanches generate large
waves and pose outburst ﬂoods after the glacier terminus will retreat up to steep part locatedupglacier from the western side of lake A.

49

Chapter 5
Numerical model of Rhonegletscher
In this chapter, a three-dimensional (3D) glacier ﬂow model is developed to evaluate theeﬀect of proglacial lake formation on the ﬂow ﬁeld. The model computes ﬂow speed, stressand strain ﬁelds under prescribed basal sliding conditions. In the ﬁrst section, equations
to be solved in the model, mesh generation, boundary conditions and model calibration are
described. In the second part, conducted experiments and results are presented.

5.1

Field equations

5.1.1

Stokes equations

The numerical ﬂow model developed in this study is based on Stokes equations under steadystate condition. The total mass of a material body is the integral of the density over its
volume. For an incompressible medium, such as ice, the density ρ remains constant duringmotion. The equation of mass conservation can be written as∇ · v = vi,i = 0,

(5.1)

where vi,i are the derivatives of each component of the velocity in its direction (Helbing,2006). Momentum balance equation is,
σij,i + ρbi = 0,

(5.2)

where b = (b1 , b2 , b3 ) is the gravitational force vector andσ
σ12 σ13 11
σ =  σ21 σ22 σ23 
σ31 σ32 σ33(5.3)

is the stress tensor. From the balance of the angular momentum, which equals the rate ofchange of the angular momentum with the vector sum of all moments of external forces,
follows that the stress tensor σ is symmetric (Hutter, 1983)51

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

σij = σji .

5.1.2

(5.4)

Constitutive equations

Solutions of Equation (5.1) and (5.2) require a constitutive equation which prescribes therelationship between velocity changes (deformation) and resulting stresses. In the case of an
incompressible isotropic material, the strain rates ε̇ij are related to the deviatoric stresses(d)σij with some scalar function f(d)ε̇ij = f σij(5.5)

the strain rates describe the spatial changes in the velocity ﬁeld and are deﬁned as1(d)σij = (vi,j + vj,i ).
(5.6)
2
Established through numerous experiments (e.g. Glen, 1955) and widely tested in ﬂow modeling studies (e.g. Pattyn, 2003), the constitutive equation of ice seems to be well approximatedbyf = A(T 0 )τ n−1 ,(5.7)

where T 0 is a temperature relative to pressure melting, and τ is the eﬀective stress deﬁned as√

1 (d) (d)
σ σ .
(5.8)
2 ij ji
The constitutive relation of ice is given by Equations (5.5) and (5.8) and is deﬁned asτ=ε̇ij = A(T 0 )τ n−1 σij .
(d)

(5.9)

The rate factor A and the ﬂow-law exponent n are material parameters. The homologicaltemperature T 0 of temperate ice constantly equals zero, because the ice is always at thepressure melting point. Thus, Equation (5.9) can be modiﬁed as(d)ε̇ij = Aτ n−1 σij .

(5.10)and so called Glen’s ﬂow law (Glen, 1952, 1955; Nye, 1953). The value of n = 3 is commonly
accepted, and the rate factor is assumed to be constant for the temperate ice condition.
When the ﬂow model is calculated by implementation of Equation (5.10) into MSC.MARC,
the analysis type of rigid plastic ﬂow is used. Each component of the deviatoric stress tensor
is assumed to be proportional to the corresponding component of the strain rate tensor anda viscosity η of ice. This relationship is deﬁned as(d)σij = 2η ε̇ij .

52(5.11)

5.2. FINITE ELEMENT MESH

5.2

Finite element mesh

To calculate Equations (5.1), (5.2) and (5.10), we used a commercial ﬁnite element software
package MSC.MARC. MSC.MARC has been used for some ﬂow models of temperate valley
glacier in Switzerland. Gudmundsson (1999) constructed the three-dimensional ﬂow model ofthe conﬂuence area of Unteraargletscher based on the observational data for surface velocity
and ice deformation (Gudmundsson, 1997; Gudmundsson and others, 1997). Helbing (2006)
discussed ﬂow laws by using the observational data and numerical model of Unteraargletscher.
Riesen and others (2010) discussed the inﬂuence of a glacier-dammed marginal lake drainage
on glacier dynamics in Gornergletscher. Raymond and Gudmundsson (2005) applied themodel to ice sheet and discussed the inﬂuence of basal disturbances on the steady state surface
topography and on surface velocities. In this study, 3D ﬁnite element mesh of Rhonegletscher
tongue has been constructed.
The ﬁnite element mesh was constructed from following inputs:

159.8

Northing (km)

159.6

159.4

159.2

159
672.1

672.3

672.5

672.7

Easting (km)

672.9

673.1

Figure 5.1: Surface nodes used for ﬁnite element mesh generation.

53

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

1. Digital glacier surface elevation model
2. Bed elevation model
3. Coordinates of glacier margin
4. Coordinates of mesh node on the surface
DEMs of surface and bed were constructed by ﬁeld measurements described in Section 3.2.
Note that the elevation model and glacier margin in 2009 was used. In Figure 5.1, nodes of theconstructed mesh on the surface are depicted. The spacing between the nodes depends on theglacier width. From the terminus to the upper boundary cross section, 26 longitudinal proﬁlesapproximately normal to the centre ﬂow line have been positioned. Therefore, there are 286
nodes on the upper surface of the model. The vertical nodal positions zi were determined aszi = zb + ai (zs − zb )(5.12)

where ai ∈ [0, 0.04, 0.16, 0.36, 0.64, 1] and zs , zb are surface and bed elevation, respectively.
Equation (5.12) produced 5 layers (6 nodes) of hexahedral, eight-node brick elements from thesurface to the ice-bedrock interface. The regarding vertical node columns in the margin havea height of ﬁve meters. An additional nodal layer one meter below the ice boundary provided
the sixth element layer, which needed for introducing basal sliding (see Section 5.3.1). The
ﬁnal mesh consists of 1500 elements and 2002 nodes (Fig. 5.2).

54

5.2. FINITE ELEMENT MESH

Figure 5.2: Oblique view of the three-dimensional ﬁnite element mesh of Rhonegletscher
tongue. Only lines connectivity nodes on the node surface are drawn. The glacier terminus
is situated at the lower left and the up-glacier cross section is in the upper right.

55

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

Elevation (m)

2350

2300

z

2250

2200

y

x
−300

−200

−100

0
x (m)

100

200

300

Figure 5.3: A ﬁnite element mesh on the upper boundary of the model.

5.3

Boundary conditions

The model has four surfaces on which appropriate boundary conditions have to be given:• Glacier surface• Bed and margin• Transverse cross-section of up-glacier boundary
For the glacier surface, no accumulation or ablation is considered. The model calculations are
snapshots of a velocity distribution and the evolution of glacier surface will not be considered.
To the bottom layer of nodes corresponding to the bedrock surface, non-displacement condition is applied. Along the eastern and western margin except for the boundary to the lake,
a ﬁxed boundary condition is given as well.

5.3.1

Basal sliding

The basal motion of the glacier was simulated by introducing a thin deformable sub-basal
layer into the ﬁnite element model (Fig. 5.4). As the bottom of the elements is ﬁxed, thesub-basal layer deforms by basal shear stress. The strain rate for the element isε̇xz =

1 ∂u
2 ∂z(5.13)

From Equations (5.11) and (5.13), we can express the strain rate in terms of basal shear
stress τb ,56

5.3. BOUNDARY CONDITIONS

z
ub



b

d
x
Figure 5.4: Scheme of simple shearing of one element. The upper side of the element
corresponds to the ice-bed interface with basal sliding by ub . The element thickness d and the(d)shear stress τb (deviatoric stress component σxz ) are depicted.

1
1 ∂u
=
τb
2 ∂z
2η

(5.14)

Integration of Equation (5.14) gives the basal sliding velocity ub∆zdτb = τb ≡ Cτb(5.15)
ηη
where d is the element thickness, η is a viscosity of the sub-basal layer. Basal ﬂow velocity is
introduced by prescribing the basal ﬂow coeﬃcient C. In MSC.MARC, the value of C could
be given to each element, which allows spatial variability in the basal slipperiness.
ub =

5.3.2

2D cross-section flow models

In our model, we focus on the terminal part of Rhonegletscher. We have to describe realistic conditions on the open transverse section of up-glacier. To the open glacier crosssection, nodal velocity distributions were applied, which were derived separately from a twodimensional (2D) cross-section ﬂow model. Figure 5.3 depicts upper boundary cross section.
The input parameters for 2D ﬂow model are surface slope α, rate factor A and the coeﬃcient
C for the basal sliding law. We deﬁne the value of α by estimating a mean surface slope
between BH707 and BH704 near the cross-section, yielding a value of α = 9.94o (Fig. 5.5).
The value of A = 75 MPa−3 a−1 was used. This value was proposed for temperate glaciers
based on a three-dimensional numerical modeling and ﬁeld data in Unteraargletscher (Gudmundsson, 1999). The basal sliding coeﬃcient C at the upper boundary was given so thatthe 2D ﬂow model reproduces the summer ﬂow velocity measured at stake 0608 by VAW,ETH Zurich (Turi, 2009) (Fig. 5.4).

57

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

159.9
234

0

BH707
232

0608

0

159.7
00
23

Northing (km)

159.8

BH704

159.6
80

22

159.5
672.3

672.4

672.5

672.6

672.7

672.8

Easting (km)

672.9

673

673.1

673.2

Figure 5.5: Plane view of theodolite stake position [0608] and the upper boundary of themodel. The slope at the boundary was calculated from the surveys at two boreholes, BH704
and BH707.

First, the basal sliding coeﬃcient was set to zero (no sliding). Figure 5.6 shows the result.
The computed surface ﬂow velocities are too small compared to the measured summer ﬂow
velocity at the stake position. Second, the basal sliding coeﬃcient was set to reproduce themeasured summer ﬂow velocity. The result is depicted in Figure 5.7. The result shows thebasal sliding is about 74% of total ﬂow speed. For computation of the three-dimensionalmodel, calculated ﬂow velocity with basal sliding will be used.

58

5.3. BOUNDARY CONDITIONS

2350

a

10

5

2300
5

Altitude (m a.s.l)

2400

2250
2200

−300

−200

−100

0
x (m)

100

200

300

−200

−100

0
x (m)

100

200

300

Flow velocity (m a−1)

40
30

b

20
10
0

−300

Figure 5.6: Computation of ﬂow velocities in the upper boundary for A = 75 MPa−1 a−1
and C = 0 with ﬁxed slope of tanα = 0.1752. (a) Contour plots indicate the calculated ﬂow
velocities. Black dot indicates measured summer ﬂow velocity. (b) Computed surface ﬂow
velocity (solid) and basal velocity proﬁles (dash).

30

5

30

5101

25

2200

−300

15

20

2250

2250

25
20

2300

a
35

2350

20

Altitude (m a.s.l)

2400

25

−200

−100

0
x (m)

100

200

300

−200

−100

0
x (m)

100

200

300

Flow velocity (m a−1)

40
30

b

20
10
0

−300

Figure 5.7: Computation of ﬂow velocities in the upper boundary for basal sliding (C = 97).
(a) Contour plots indicate the calculated ﬂow velocities. Black dot indicates measured summer
ﬂow velocity. (b) Proﬁles of computed surface ﬂow velocity (solid) and basal velocities (dash).

59

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER









Figure 5.8: Sketch of the model boundary against to the lake. Water pressure is calculated
according to the mean elevation of side surface of element (∆z) and then loaded to the element.

5.3.3

Lake water pressure

Riesen and others (2010) considered the inﬂuence of lake water pressure on the ice dynamics.
They introduced the lake presence as pressure loads onto the elements being underwater. In
our study, lake water contacts side surface of elements. In Figure 5.8, a schematic diagram ofthe boundary of ice and lake water is given. A subroutine calculates the mean water pressure
on the side of the elements whose mean elevation is below the lake water. Elements in contact
with the lake water has to be deﬁned in advance. Figure 5.9a shows the elements on whichlake-water pressure was applied. The lake pressure was uniformly applied on the surface ofthe element. The pressure load was resolved in x and y directions to introduce it into MARC
(Fig. 5.10).

60

5.3. BOUNDARY CONDITIONS

159.4

Northing (km)

159.3

159.2

159.1

159
672.1

672.2

672.3
Easting (km)

672.4

672.5

Figure 5.9: Model boundaries on which lake water pressure was applied (red). Blue line
indicates the lake margins.
5

1.593

x 10

Px

Northing (km)θPy
1.5925

1.592
6.722

6.7225

Easting (km)

6.723
5

x 10

Figure 5.10: Vector components of lake pressure load. Px and Py indicate x and y components of the load. Blue line indicates the lake margins.

61

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

5.4

Sensitivity tests

To test the sensitivity of applied boundary conditions to the three-dimensional model, easy
sensitivity tests were done.

5.4.1

Test 1In the Test 1, diﬀerent experiments have been conducted to investigate the sensitivity of themodel on the upglacier boundary condition listed in Table 5.1.
1. Comparison of the surface ﬂow ﬁelds calculated by 3D ﬂow model with a non-sliding
condition for application of 80, 100 and 120% of the upper boundary ﬂow velocities.
2. Comparison of the ﬂow ﬁelds with a uniform sliding condition for 80, 100 and 120% of
calculated velocities by 2D ﬂow model.
The velocity ﬁelds for non-sliding condition was computed with MSC.MARC. This sensitivity
test was applied the velocities for upper boundary cross-section calculated from 2D ﬂow
model. The 3D model runs for 80, 100 and 120% of calibrated initial velocities ui for upperboundary condition (Experiments 1–3 in Table 5.1). The calculated ﬂow ﬁelds for three initialboundary conditions were plotted at upper boundary cross-section and at the interpolated
ﬁve transverse cross-sections (Fig. 5.11a). Figure 5.11b shows the interpolated velocities forthe locations of GPS measurement in 2009.
The sensitivity test for a uniform sliding condition was conducted. The initial condition of thevelocity at the upper boundary cross-section was applied as well as in Test 1 (Experiments 4–6
in Table 5.1). The results are plotted in Figure 5.12.

Table 5.1: Summary of conducted sensitivity tests in Test 1.
Experiment No.
Experiment 1
Experiment 2
Experiment 3
Experiment 4
Experiment 5
Experiment 6

C (m a−1 M P a−1 )
=0
=0
=0
6= 0
6= 0
6= 0

62

Upper boundary conditionui × 0.8
ui × 1.0
ui × 1.2
ui × 0.8
ui × 1.0
ui × 1.2

5.4. SENSITIVITY TESTS

159.8

a

Northing (km)

159.6

159.4

159.2
20 m a−1
159

672.2

672.4

672.6

Easting (km)

672.8

673

673.2

159.5

159.4

1

b

2
3

Northing (km)

5

6

159.3

4

11

7

9
159.2

GPS3
15

16

17

20

14

18

159.1
20 m a−1
159
672.1

672.2

672.3

672.4

672.5

Easting (km)

672.6

672.7

672.8

672.9

Figure 5.11: Computed surface ﬂow vectors without sliding in Test 1. (a) Surface velocities:
Red vectors mark 100% of initial applied velocities (Experiment 2), whereas blue and black
vectors correspond to Experiments 1 and 3, respectively. (b) Interpolated surface velocities atthe locations of GPS measurement in 2009.

63

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

159.8

a

Northing (km)

159.6

159.4

159.2
20 m a−1
159

672.2

672.4

672.6

Easting (km)

672.8

673

673.2

159.5

159.4

1

b

2
3

Northing (km)

5

6

159.3

4

11

7

9
159.2

GPS3
15

16

17

20

14

18

159.1
20 m a−1
159
672.1

672.2

672.3

672.4

672.5

Easting (km)

672.6

672.7

672.8

672.9

Figure 5.12: Computed surface ﬂow vectors with basal sliding in Test 2. (a) Surface velocities: Red vectors mark 100% of initial applied velocities (Experiment 5), whereas blueand black vectors correspond to Experiments 1 and 3, respectively. (b) Interpolated surface
velocities at the locations of GPS measurement in 2009.

64

5.4. SENSITIVITY TESTSTest results
In the non-sliding conditions, the diﬀerence in velocities for each experiments is able to see
clearly on the boundary faces. As for the upper boundary cross-section, the results shows theexact same ﬂow regime, only the magnitude of ﬂow vectors is aﬀected. This is actually true forall vectors, regardless of position on the nodal points or on the interpolated stake positions.
Despite increasing ﬂow speed, ﬂow direction of all vectors have little change (Figs 5.10b and5.11b). The ﬂow speeds do not diﬀer in the terminal area, while ﬂow speed is increased in
the upper area (Fig. 5.11b).

5.4.2

Test 2

The ﬁnite-element mesh was consisted by 1500 elements as described in section 5.2. The
smallest surface elements are situated near the terminus, having approximate dimensions of
20 × 20 m surface area and about 10 m thickness. The thickness of the elements decreases
gradually towards the bottom (Eq. 5.12) because the vertical velocity proﬁle is more accurate
at the bed, where most ice deformation occurs. The constructed mesh is rather coarse
compared to the dimensions of the glacier. To investigate the eﬀect of numerical errors due
to discretization, a second mesh consisting of 10-ice element layers (+ 1 sediment layer) was
generated. The vertical node spacing was determined by Equation (5.12), where ai ∈ [0, 0.01,
0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81, 1]. The element dimensions for the surface nodes
distribution were kept the same, only vertical resolution was increased, resulting in 2750
elements and 3432 nodes, respectively. Models with coarse and ﬁne mesh were computed forthe uniform sliding case, and the results were compared in Figure 5.13. The vectors for ﬁnemesh case have same length and point the same direction as those for coarse mesh in theentire area. The results suggest that the model with the ﬁne mesh has no signiﬁcant inﬂuenceon the ﬂow ﬁeld. Therefore, the ﬁrst (coarse) mesh has suﬃcient resolution to reproduce thegeneral ﬂow regime.

65CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

159.8

a

Northing (km)

159.6

159.4

159.2
20 m a−1
159

672.2

672.4

672.6

Easting (km)

672.8

673

673.2

159.5

159.4

1

b

2
3

Northing (km)

5

6

159.3

4

11

7

9
159.2

GPS3
15

16

17

20

14

18

159.1
20 m a−1
159
672.1

672.2

672.3

672.4

672.5

Easting (km)

672.6

672.7

672.8

672.9

Figure 5.13: Computed surface ﬂow vectors with basal sliding in Test 2. (a) Red vectors
indicate computed velocities with the coarse mesh (1500 elements). Blue vectors indicatecomputed velocities with the ﬁne mesh (2750 elements). (b) Interpolated surface velocities atthe locations of GPS measurement in 2009.

66

5.5. MODELING EXPERIMENTS

5.5

Modeling experiments

In this section, two modeling experiments were carried out to investigate the observed ﬂow
ﬁeld in Rhonegletscher tongue. The ﬁrst modeling experiments with the applied initial condition are listed in Table 5.2. The lake water pressure load described in Section 5.3.3 wasapplied with 2211 m a.s.l. of lake level.

5.5.1

Experiment A: Non or uniform sliding

Surface ﬂow velocities were computed with non-sliding condition were computed (Experiment
A1). Diﬀerent values for the sliding coeﬃcient C have been set spatially uniformly over theglacier bed in model runs to ﬁnd a value of C which best reproduces the observed summer
velocities. At ﬁrst, the model applied for 100 and 200 m a−1 MPa−1 of C was calculated tocompare the ﬂow ﬁeld under the diﬀerent basal condition (Experiment A2). The model wasthen adjusted to the observed summer ﬂow speeds of Stakes 2–4 by tuning C (Experiment
A3).
Figure 5.14 shows the results of the experiment without basal sliding (C = 0 m a−1 MPa−1 ),compared to summer ﬂow velocities from 27 June to 6 September in 2009. Despite nosliding condition is not a realistic condition, the compared ﬂow directions agree well with theobservations. General ﬂow direction is reproduced best in the western area of the glacier. The
computed ﬂow speeds are less than those observed. In Figure 5.15 the results for diﬀerent
coeﬃcients are compared to the observed summer velocities in 2009.
At the stakes located in the central part of the glacier, there is almost no diﬀerence in the
direction of surface velocity computed with C = 100 and 200 m a−1 MPa−1 . The computed
velocities underestimated the observation in the western margin (e.g. Stakes 1 and 5) whereas
those at the eastern margin (e.g. Stake 7). In the terminal area, at Stakes 15, 16 and GPS3,
computed ﬂow directions are more to the west than the observation.
For our model we prescribed ﬂow velocities as a boundary condition at the upper boundary
cross-section (Section 5.3.2). In the work of Gudmundsson (1994), stresses instead of velocities
where prescribed as boundary conditions. The adjustment of the calculated velocities to theTable 5.2: Summary of conducted modeling experiment A.
Experiment
Experiment A1
Experiment A2Experiment A3

Subject
Non-basal sliding
Spatially-uniform basal sliding
Spatially-uniform basal sliding67

C (m a−1 MPa−1 )0
100 and 200
166CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

159.5
1
2

159.4

3

Northing (km)

5

6

4

159.3
11

7

9
159.2

15

14

GPS3
16
17
18

20

159.1
−1

20 m a
159
672.1

672.2

672.3

672.4

672.5
Easting (km)

672.6

672.7

672.8

672.9

Figure 5.14: Computed ﬂow velocities for C = 0 (no-sliding, blue). Green vectors indicate
observed summer ﬂow velocities in 2009 (27 June to 6 September).

measured surface velocities was done by adjusting the sliding coeﬃcient C, which deﬁnes
the viscosity of bottom of the elements in the implemented basal sliding law (Section 5.3.1),
uniformly for the entire glacier. In this study, we present a small error analysis in order toquantify the diﬀerences between observed and calculated velocities.
The coeﬃcient of determination R2 is calculated as∑

R ≡ 1−
2mc 2
i (ui − ui )2(um
i − ū)(5.16)cwhere umi and ui are measured and calculated horizontal ﬂow vectors at Stake i, and ū isthe mean value of measured ﬂow vectors. The error values of R2 is given for the computed
velocity for C = 166 m a−1 MPa−1 (Fig. 5.15). According to the error estimate, the best ﬁtof modeled velocity to the observations was achieved with C = 166 m a−1 MPa−1 , in which
R2 = 0.965.

68

5.5. MODELING EXPERIMENTS

159.5
1
2

159.4

3

Northing (km)

5

6

4

159.3
11

7

9
159.2

15

14

GPS3
16
17
18

20

159.1
−1

20 m a
159
672.1

672.2

672.3

672.4

672.5
Easting (km)

672.6

672.7

672.8

672.9

Figure 5.15: Computed ﬂow velocities for diﬀerent spatially uniform basal sliding coeﬃcients
C. Blue and red vectors indicate computed velocities with C = 100 and 200 m a−1 MPa−1 ,respectively. Green vectors indicate observed summer ﬂow velocities in 2009.
159.5
1
2

159.4

3

Northing (km)

5

6

4

159.3
11

7

9
159.2

15

14

GPS3

16

17

18

20

159.1
20 m a−1
159
672.1

672.2

672.3

672.4

672.5

Easting (km)

672.6

672.7

672.8

672.9

Figure 5.16: Computed ﬂow velocities for uniform sliding (C = 166 m a−1 MPa−1 ). Measured (green) and computed surface velocity (red) are depicted.

69

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

5.5.2

Experiment B: Locally enhanced sliding

In experiment B, experiments were repeated with non-uniformly distributed C. ExperimentA2 was divided into multiple sub-experiments in which the impact of local changes in C on
the surface ﬂow ﬁeld was investigated at the shore of proglacial lakes.
The glacier bed in the lake shore was introduced larger sliding coeﬃcients C (Fig. 5.16). The
initial value of C for entire of the glacier was set to C = 166 m a−1 MPa−1 . To set the locallyenhanced sliding coeﬃcient, we introduced the distribution of eﬀective pressure depicted in
Figure 4.5. The sliding coeﬃcient C was increased in two stages. First stage is the area of
Pe < 0 (red colored area: C = 18000 m a−1 MPa−1 ) and 0 < Pe < 0.05 (green colored
area: C = 25000 m a−1 MPa−1 ), respectively. The resulting model velocities are depicted in
Figure 5.17.
The horizontal ﬂow ﬁeld in the lake area is strongly aﬀected by sliding coeﬃcients (Fig. 5.18a).

159.4

Northing (km)

159.3

159.2

159.1

159
672.1

672.2

672.3

Easting (km)

672.4

672.5

Figure 5.17: Deﬁned sliding area in the shore of lake. Red colored area indicates
Pe < 0 (C = 25000 m a−1 MPa−1 ). Green colored area indicates 0 < Pe < 0.05
(C = 18000 m a−1 MPa−1 ).

70

5.5. MODELING EXPERIMENTS

159.5

a

1
2

159.4

3

Northing (km)

5

6

159.3

4

11

7

9
159.2

15

14

GPS3

17

16

18

20

159.1
20 m a−1
159
672.1

672.2

672.3
30

672.4

672.5

Easting (km)

672.6

672.7

672.8

672.9

b

−1

Measured velocity (m a )

25
20
15
10
Uniform sliding
Enhanced local sliding

5
0

0

5

10

15

20

−1

25

30

Calculated velocity (m a )Figure 5.18: The computed ﬂow vectors with locally enhanced basal sliding. (a) Green
vectors indicate measured summer ﬂow vectors in 2009. Red is the best ﬁt model ﬂow velocities
with spatially uniform constant C = 166. Blue is the computed vectors with spatially uniform
basal sliding. (b) Scatter plot of measured towards computed velocities with locally enhanced
sliding.

71

CHAPTER 5. NUMERICAL MODEL OF RHONEGLETSCHER

In the shore of proglacial lake, the computed ﬂow vectors rotate toward the west with increasing C (e.g. Stakes 9, 11, 15, 18 and GPS3). The eﬀect of glacier acceleration is minor
at upper reaches (e.g. Stakes 1–7). The magnitude of computed ﬂow velocities correspondwell with measured velocities (Fig. 5.18b). The coeﬃcient of determination R2 is −1.69 forthe computed velocity with locally enhanced sliding and −8.04 for the velocity with uniform
sliding.

5.6

Summary

A three-dimensional numerical ﬁnite-element model for the tongue of Rhonegletscher has been
constructed. The model solves Stokes equations, using Glen’s ﬂow law as constitutive equation. Basal sliding speed was introduced as a linear function of the basal shear stress. Lakewater pressure was applied to the elements along the ice-lake boundaries. Boundary conditions on the open transverse section of up-glacier were deﬁned using a two-dimensional crosssection ﬂow model. Velocity distributions on cross-section were derived using surface slope α(9.94o ), rate factor A (75 MPa−3 a−1 ) and the basal sliding coeﬃcient C (97 m a−1 MPa−1 ).
Despite no-sliding condition is not a realistic condition, the compared ﬂow directions agree
well with the observations. General ﬂow direction is reproduced best in the western areaof the glacier. By tuning the linear coeﬃcient of the basal ﬂow law, the model reproduced
the observed ﬂow speed at Stakes 2, 3 and 4 with the coeﬃcient of determination of 0.965.
However, the computed ﬂow speeds are less than those observed in the lake shore. The
horizontal ﬂow ﬁeld in the lake area is strongly aﬀected by sliding coeﬃcients. In the shoreof proglacial lake, the computed ﬂow vectors rotate toward the west with increasing C.
The magnitude of computed ﬂow velocities correspond well with measured velocities when
C applied the area where Pe < 0 MPa (25000 m a−1 MPa−1 ) and 0 < Pe < 0.05 MPa(18000 m a−1 MPa−1 ). The coeﬃcient of determination R2 is −1.69 for the computed velocity
with locally enhanced sliding.

72

Chapter 6
Conclusion
6.1

Field observation

Field measurements were carried out in Rhonegletscher, Switzerland during the ablationseason of 2007–2009 to investigate the impact of proglacial lake formation on glacier ﬂow.
The measurements were conducted with high spatial resolution focusing on temporal andspatial change in horizontal ﬂow velocity, surface vertical displacement (uplift), subglacial
water pressure. To conduct subglacial and englacial measurements, the hot water drillingsystem was developed and used on the glacier.
Annual surface velocities observed at the glacier terminus increased as much as 200% from2005–06 to 2007–08, though those decreased by 33% at the upglacier (Fig. 4.1). The surface
ﬂow velocity of more than 20 m a−1 was observed near the terminus, and its magnitude wassimilar to the velocity in the upper reaches. After the proglacial lake formation, subglacial
water pressure exceeded ice overburden pressure in the range of approximately 200 m fromthe terminus. Thus, most of the ﬂow at the terminus was due to basal ice motion. Decrease
in ﬂow velocity observed at upper reaches is due to thinning of ice thickness.
Longitudinal strain at the terminus changed from compression to tensile after the lake formation. In 2009, horizontal strain regime was tensile toward the ice ﬂow direction. Observed
extending ﬂow corresponded to thinning rate by 1.2–2.3 cm d−1 , which were 21–41% of thetotal amount of glacier surface lowering. Accordingly, increase in ice thinning observed inlast decade has been caused by both the extending ﬂow regime and negative mass balance.
The huge uplift at the terminus was observed in the shore of both Lake A and Lake B in thelate ablation season of 2009. Analysis of the eﬀective pressure conﬁrms that water pressure
exceeded the ice overburden pressure in 2008 along the shore of Lake A. The region of excesswater pressure extends even farther in the terminal area in 2009 as a result of ice thinning.
Associate with the uplift event, a crevasse formed from the shore of lake A toward Lake B.
Before the crevasse formed, surface uplift in the shore of Lake A was occurred as a result ofa wedge of water would penetrate beneath the ice dam and incrementally jack the ice oﬀ its

73

CHAPTER 6. CONCLUSION

bed, which is the so-called cantilever eﬀect by Nye (1976). The crevasse has formed due tomovement along steeply dipping faults that dip towards the lake and cut through the entire
ice thickness. Similar crevasse formation due to this mechanism was observed in previous
study in which the crevasse formed in front of the ice-dammed lake during the occurence ofoutburst ﬂood.
Signiﬁcant calving was observed in the late ablation season of 2010. This integrated area
corresponded to the calculated eﬀective pressure reach to zero. At the elevation range of2250–2350 m, the glacier is thinning at a progressively increasing rate. Assuming that thethinning rate of −3.4 m a−1 observed in 2008–2009 is sustained, the glacier will retreat
approximately 600 m and the lake will expand to its maximum size by 2034. This result isearlier than that reported in previous studies. The possibility of GLOF in Rhonegletscher
is not likely as it is dammed by the bedrock bump. However, ice avalanches generate large
waves and pose outburst ﬂoods after the glacier terminus will retreat up to steep part locatedupglacier from the western side of lake A.

6.2

Numerical modelingA three-dimensional numerical ﬁnite-element model for the tongue of Rhonegletscher has
been constructed. The model solves Stokes equations, using Glen’s ﬂow law as constitutive
equation. Basal sliding speed was introduced as a linear function of the basal shear stressand lake water pressure was applied to the elements along the ice-lake boundaries. Despite
no-sliding condition is not a realistic condition, the compared ﬂow directions agree well withthe observations. General ﬂow direction is reproduced best in the western area of the glacier.
By tuning the linear coeﬃcient of the basal ﬂow law, the model reproduced the observed
ﬂow speed at Stakes 2, 3 and 4 with the coeﬃcient of determination of 0.965. However, thecomputed ﬂow speeds are less than those observed in the lake shore.
The locally enhanced basal sliding in the lake shore had a great impact on the ice ﬂow
regime. The computed ﬂow vectors rotate toward the west with increasing C. The coeﬃcientof determination R2 is −1.69 for the computed velocity with locally enhanced sliding.

6.3

Future prospects of the study

The glacier ﬂow and subglacial water pressure measurements with high spatial resolution
revealed the rapid ice acceleration and surface uplift in the lake area takes place after the
proglacial lake formation in 2005. This was the ﬁrst intensive ﬁeld measurements to investigate the acceleration in glacier retreat inﬂuenced by lake formation. As the next step of thestudy, it is beneﬁcial to continue similar measurements at the eastern side of the terminus in
Rhonegletscher because the glacier evolution is signiﬁcantly changing due to the accelerationof ice thinning from year to year. Another way in the next step of this study is to carry74

6.3. FUTURE PROSPECTS OF THE STUDY

out similar measurements on the other glaciers with similar situation. The comparison ofassessment of many glacier evolution with the case in Rhonegletscher can be achieved further
comprehension to the interaction of proglacial lake formation and caused dramatic glacierretreat.
According to the results of the presented numerical investigation, the calculated general ﬂow
distribution in front of both Lake A and Lake B was relatively to the observed ﬂow ﬁeld thanthat at the upper reaches. To achieve more accurate results, it is required to accurate boundary conditions at that area. In particular, it is need to survey a bed topography beneath both
Lake A and Lake B and to incorporate these information to the model. The implementationof basal sliding is also crucial to reproduce the general ice ﬂow ﬁeld of Rhonegletscher bynumerical modeling. The process of basal sliding plays a major role in the overall summer
ﬂow regime of Rhonegletscher, thus it would be useful to investigate diﬀerent approaches
of describing basal sliding, such as non-linear sliding law (e.g. Raymond and Gudmundsson, 2009) and inverse modeling (e.g. Kaufmann and lambeck, 2002), and their applicability
on Rhonegletscher to ﬁnd a solution which best reproduces the surface ﬂow ﬁeld of Rhonegletscher.

75

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Yoshizawa, T. 2010. Spatial distribution of surface ablation in the terminus of Rhonegletscher, Switzerland. Master thesis, Hokkaido University. (in Japanese)
Zahno, C. 2004. Der Rhonegletscher in Raum und Zeit: neue geometrische und klimatische
Einsichten. Diplomarbeit, Abteilung für Glaziologie, VAW, ETH Zürich. (in German)

84

Appendix A
Performance test of the hot water drillingsystemTo test the performance of the drilling system, its water temperature and ﬂow rate were
measured in the Institute of Low Temperature Science from March to April 2007. The
drilling performance on Rhonegletscher in 2007 is also indicated.

A.1

Test setting

The test was conducted using hoses with lengths of 1, 50, 100 and 150 m, straight jet nozzles
with diameters of 1.6, 2.0, 2.5 and 3.0 mm, and a conic spray nozzle with a diameter of
2.0 mm. The cleaning nozzle provided by the manufacturer was also used to change the ﬂow
rate. Because the water jet was very narrow, an accurate measurement of water temperaturein the vicinity of the nozzle was diﬃcult (see Fig. 2.4e). The jet was trapped in a 10 l plastic
bottle, and the water temperature in the bottle was measured every 15 seconds as it ﬁlledusing a temperature logger (HIOKI 3633). During the measurement, the temperature settingof the heater was gradually raised from 50 to 135–150 ◦ C. The water ﬂow rate was calculated
from the time required to ﬁll a box of 0.02 m3 . The consumption rates of petrol and diesel
during the experiments were measured as well. The drilling performance of the system wastested by drilling ice blocks of 0.5 × 0.25 × 1 m3 with the 50 m hose, the 2.0 mm straight jet
nozzle, and water supplied from the basin.

A.2

Performance test results

Using the 2.0 mm straight nozzle, we measured the water temperature as a function of timefor various hose lengths (Fig. A.1a). The maximum temperatures ranged from 64 to 76 ◦ C.
The temperature is generally higher for shorter hoses, although the maximum temperature
at 150 m length hose exceeds that at 100 m. As the water pressure from a tap is expected
to be unstable, the ﬂow rate may have ﬂuctuated in these experiments and inﬂuenced the85

APPENDIX. A

a

80

°

Temperature ( C)

90

70
60
1m
50 m
100 m
150 m

50
40
0

20

30

Time (min)

b

80

°

Temperature ( C)

90

10

70
60
1.6 mm
2.0 mm
2.5 mm
2.0 mm wide

50
40
0

Temperature (°C)

110
100
90

10

20

30

Time (min)cCleaning nozzle

80
70
60
50
400

1.6 mm
2.0 mm
2.5 mm
600

800

−1

1000

Flow rate (l h )Figure A.1: Water jet temperature vs. time with (a) various hose lengths and (b) various
jet nozzle diameters. (c) Flow rates and water jet temperatures obtained with the three jet
nozzles and the cleaning nozzle.

86

water temperature. When we ﬁxed the hose length at 50 m, the maximum temperature for
1.6–2.5 mm nozzles ranged from 60 to 65 ◦ C (Fig. A.1b). The temperature reached 80 ◦ C
for the conic spray nozzle, as its ﬂow rate was much lower. These results indicate that thetemperature of the water jet is higher than 60 ◦ C and it is slightly inﬂuenced by hose lengthand nozzle diameter. The jet temperature is saturated when the heater setting is above 70 ◦ C
because the heater is designed for a ﬂow rate lower than our use.
The relationship between ﬂow rate and temperature was obtained using a 50 m long hoseby and the cleaning nozzle (Fig. A.1c). The temperature is very close to the boiling point
when the system is operated at 450 l h−1 , and decreases as the ﬂow rate increases. For thejet nozzles with diameters of 1.6–2.5 mm, the temperature is about 60 ◦ C and the ﬂow rates
are 950–1000 l h−1 . This rate is the upper limit of the pump capacity. With the 3000 l waterbasin, drilling can be continued for 3 hours at this rate.
The 3.0 mm diameter straight nozzle was not suitable for the system because the pressure
dropped below operating range and the heater was automatically shut down by the safety
device. In laboratory tests the diesel consumption rate of the heater was 4.7 l h−1 , and thepetrol consumption rate of the pump was 1.9 l h−1 .

87

APPENDIX. A

a

b

50 mm

100 mmFigure A.2: Drilling nozzle and water jet in the ice block used for the test. The nozzle waslowered quickly in (a), while it was lowered slowly to enlarge the borehole diameter in (b).

A.3

Ice block drilling

Testing the system on an ice block conﬁrmed that the drilling process is very fast. It took
about 30 seconds to drill through a 1 m thick ice block, excavating a hole of 50 mm diameter(Fig. A.2a). A wider hole can be drilled by lowering the nozzle more slowly (Fig. A.2b). The
times required to drill through 1 m of ice were measured at various temperature settings ofthe heater (Table A.1). As expected from the abovementioned results (Fig. A.1a, b), thedrilling speed is nearly constant when the heater setting temperature is higher than 70 ◦ C.

Table A.1: Time required for drilling through 1 m thick ice blocks and drilling
speed. Water temperature was 7.4 ◦ C in the case of no heating.
Heater setting◦C
no heating
30
50
70
90
110
135
150

Time
sec
124
53
43
27
39
28
31
31

88

Speed
m h−1
29
68
84
133
92
129
116
116

Drilling is even possible with cold water (7.4 ◦ C).

A.4

Borehole drilling in Rhonegletscher

From 13 to 29 July 2007, eight boreholes (BH701–708) were drilled to the glacier bed at
positions 300–800 m from the terminus (Fig. A.3). The depths of BH701–708 range from
87–138 m (Table A.2). Figure A.4 plots borehole depth vs. drilling time. The mean drillingrates ranged from 27–70 m h−1 . Hubbard and Glasser (2005) used the same hot watermachine at an altitude of 2800 m a.s.l in Haut Glacier d’Arolla, Switzerland. The pumpdrew water from a 4000 l basin which was ﬁlled by melting snow. They obtained drillingrates of 120 m h−1 near the ice surface and 30 m h−1 at depths greater than 120 m. They
reported the water temperature as 80 ◦ C. In order to detect the bedrock from a change
in hose tension, the drilling rate was deliberately decreased during the last 10–20 minutes.
This eﬀect can be observed in the plots for BH701, BH702, BH703, BH706 and BH708. In
BH704, BH706 and BH707, the drilling rate decreased when water drained from the borehole.
Drilling in an empty borehole is more diﬃcult. This was because the loss of buoyancy force
makes the operation of the hose hanging in the borehole more diﬃcult. Other factors may
have inﬂuenced the drilling rate in some cases, such as the experience of the operator andinterruptions due to refuelling or ﬁlter cleaning.
Two other relatively important factors are the distance and elevation diﬀerence between the
hot water machine and the drilling site. Table A.2 shows that BH701 and BH702, locatedclosest to the machine (0 and 95 m), had relatively high drilling rates (50 and 70 m h−1 ).

Northing (km)

159.8
159.6
159.4

BH707
BH706

BH708

BH704
BH701
BH705
BH702
BH703

159.2
159
672

672.2 672.4 672.6 672.8
Easting (km)

673

673.2

Figure A.3: Map of the borehole locations from 2007 marked (•).

89

APPENDIX. A

Table A.2: Depth and mean drilling rate of the boreholes in 2007. Horizontal
distance and elevation diﬀerence between the drilling sites and the hot water machine
are also indicated.
Borehole
BH701
BH702
BH703
BH704
BH705
BH706
BH707
BH708

Borehole depth
m
138
120
119
124
99
87
135
103

Drilling rate
m h−1
50
70
49
32
66
40
27
40

Distance
m
0
95
163
103
121
113
216
254

Elevation
m
0
-10
-17
15
4
-2
35
-29

BH707 and BH708, situated farther from the machine (216 and 254 m), had rather small
drilling rates (27 and 40 m h−1 ). This relationship is expected because the temperature of
the water decreases with distance from the heater. BH704 and BH707, situated at elevations
15 and 35 m higher than the machine, also had smaller drilling rates (32 and 27 m h−1 ). Thiseﬀect is probably due to the fact that the ﬂow rate decreases when the pump sends water tohigher elevation. During drilling at BH707, the machine often turned itself oﬀ because thewater pressure dropped below the threshold.
The mean petrol consumption rate was 1.8 l h−1 in both 2007 and 2008, which corresponds
approximately to the result of our laboratory tests (1.9 l h−1 ). However, there is a signiﬁcantdiﬀerence between the mean diesel consumption rates on the glacier (6.9 l h−1 ) and in thelaboratory (4.7 l h−1 ). The former rate is also 1.7 times greater than that obtained at
Haut Glacier d’Arolla (Hubbard and Glasser, 2005), even though our petrol consumption
rate agrees with that experiment within 90%. It is not clear why drilling at Rhonegletscher
consumed more diesel than drilling in the laboratory or at Haut Glacier d’Arolla, althoughboth pumps drew cold water from supraglacial stream or melted snow and the drillings
conducted at a high altitude. If we take the mean drilling rate observed in BH701–708(47 m h−1 ) and the consumption rates measured at Rhonegletscher as benchmarks, oursystem is able to drill 100 m of ice in a little more than two hours with 14.7 l of diesel and3.9 l of petrol.

90

0

BH701

BH705

BH702

BH706

BH703

BH707

BH704

BH708

50
100

Borehole depth (m)

150
0
50
100
150
0
50
100
150
0
50
100
150
0

100 200 300 0

100 200 300

Time (min)Figure A.4: Drilling depth as a function of drilling time for the boreholes from 2007. The
borehole locations are indicated in Figure A.3.

91

Acknowledgements
The author would like to express his gratitude to Prof. Ralf Greve, Chair of the doctoral
degree supervisory committee, for the encouragement he provided to this study. Appreciation
goes to Dr. Shin Sugiyama, who supervised the author throughout the doctoral program,supported this research with frequent discussions, and guided the author in the right direction.
Prof. Kazuomi Hirakawa, Dr. Takayuki Shiraiwa and Prof. Hiroyuki Enomoto, memberof the doctoral degree supervisory committee, encouraged the study and made importantcomments on the thesis.
Daisuke Nishimura and Takeshi Yoshizawa, member of Glacier and Ice Sheet Research Groupin the Institute of Low Temperature Science, Hokkaido University, helped all activities in
Zurich and on the glacier. Thanks are also due to Arne Keller, Giuliana Turi and Flavio
Lehner. They supported the ﬁeld work and provided pleasant atmosphere during the ﬁeld
campaign on the glacier.
Prof. Martin Funk, Dr. Andreas Bauder and Thomas Wyder, the Section of Glaciology,
Laboratory of Hydraulics, Hydrology and Glaciology (VAW), at the Swiss Federal Instituteof Technology (ETH), helped with measurements on the glacier and research work in Zurich.
Prof. Heinz Blatter, Institute for Atmospheric and Climate Science, ETH Zurich and Patrick
Riesen, member of the Section of Glaciology, VAW, ETH Zurich, supported my life in Zurich
and this study with valuable suggestions. Materials for the ﬁeld campaign were loaned by
Section of Glaciology, VAW, ETH Zurich. Glacier Research Group in the Institute of Low
Temperature Science, Hokkaido University, was a supportive base for this study: researchplans were developed, many ideas acquired, and theories reﬁned through discussions withgroup members.
We would like to thank Kenta Chubachi of the Institute of Low Temperature Science at
Hokkaido University for designing and constructing the drilling stem. Kota Nakamura ofNakamura Service Inc., Kenichi Hirayama of Kärcher Japan Inc. and Satoshi Asai of Martech
Inc. provided useful information on the high-pressure hot water machine.
Finally, the author wishes to dedicate this thesis to his most enthusiastic supporters, his
parents, sister, brother, Maiko and Ryo for their constant support.
This research was funded by the Japanese Ministry of Education, Science, Sports and Culture93

ACKNOWLEDGEMENTS

through a Grant-in-Aid for Young Scientists (Start-up), 18840002, 2006–2007; and by aGrant-in-Aid for Scientiﬁc Research C (Capital), 20540418, 2008–2010. Additional funding
was provided by an internal program of the Institute of Low Temperature Science, Hokkaido
University, by the Inoue Scientiﬁc Field Study Foundation, and by the Global COE Program(Establishment of Centre for Integrated Field Environmental Science), MEXT, Japan.

94