2009 Accumulation Area Ratios and Little Ice Age Equilibrium Line Altitude Depression of Mount Baker Glaciers, Washington State, Usa

2009 ACCUMULATION AREA RATIOS AND LITTLE ICE AGE EQUILIBRIUM LINE ALTITUDE DEPRESSION OF MOUNT BAKER GLACIERS, WASHINGTON STATE, USA

Courtenay Brown

B.Sc. (Environmental Science), University of Ottawa, 2008

THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

in the Department of Earth Sciences Faculty of Science

All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for "Fair Dealing." Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately.

APPROVAL

Name: Courtenay Brown Degree: Master of Science Title of Thesis: 2009 Accumulation Area Ratios and Little Ice Age Equilibrium Line Altitude Depression of Mount Baker glaciers, Washington State, USA

Examining Committee: Chair: Dr. Dan Gibson Graduate Program Chair, Department of Earth Sciences

______

Dr. John J. Clague Senior Supervisor Professor, Department of Earth Sciences

______

Dr. Brian Menounos Supervisor Associate Professor, University of Northern British Columbia

______

Dr. Jon L. Riedel Supervisor Geologist, North Cascades National Park

______

Dr. Kevin M. Scott Supervisor Scientist Emeritus, USGS Cascades Volcano Observatory

______

Dr. Douglas H. Clark External Examiner Associate Professor, Western Washington University

Date Defended/Approved: ______

Partial Copyright Licence

ABSTRACT

Measurements made from a 2009 NAIP (National Agriculture Imagery

Program) orthoimage covering the Mount Baker area indicate that 2009 was a

negative mass balance year: On average, the accumulation areas of the glaciers

occupied 37 percent of total glacier area at the end of August. An accumulation area of at least 62 percent is required for Mount Baker glaciers to be in

equilibrium. Using spreadsheet models, I compared the modern and Little Ice

Age glacier thicknesses.

During the Little Ice Age, glaciers on Mount Baker were, on average, 1.6

times larger and approximately 20 m thicker than present. The equilibrium line

altitudes of these glaciers were, on average, 300 m lower during the maximum

Little Ice Age than today. Average ablation season temperatures were about

2.0°C lower at the peak of the Little Ice Age than today, assuming that

precipitation was 7 percent greater at that time.

Keywords: Glaciers; equilibrium line altitude; accumulation area ratio; balance ratio; Little Ice Age; Mount Baker

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ACKNOWLEDGEMENTS

This thesis would not have been possible without the help of many people

who know a great deal more than I do and have much more patience. I would like to thank my senior supervisor John Clague for the opportunity to conduct MSc research and for his guidance and encouragement. I also wish to thank the other members of my supervisory committee, Brian Menounos, Jon Riedel, and Kevin

Scott, for their advice and their assistance in reviewing and editing my thesis.

I extend my gratitude to several earth scientists for their valuable insight and counsel: Gwenn Flowers, Johannes Koch, Antoni Lewkowicz, Mauri Pelto,

Brice Rea, and Dave Tucker. I also wish to thank Brian Kelsey, Cooper Quinn, and Nick Roberts for their on-demand tech support, Marit Heideman, Stephen

Newman, and Dan Shugar for their assistance in the field, and all the graduate students in the department for their companionship.

I also would like to acknowledge the staff and faculty of the Department of

Earth Sciences for their valuable support (and sometimes rescue): special thanks to Bonnie, Cindy, Glenda, Matt, Rodney, and Tarja. Finally, I want to thank all of

my loved ones for their empathy and for trying to keep me sane (thank you for

trying).

This research was funded by an NSERC Discovery Grant held by John

Clague and a Geological Society of America Graduate Student Research Grant.

TABLE OF CONTENTS

Approval ...... ii Abstract ...... iii Acknowledgements ...... iv Table of Contents ...... v List of Figures ...... vii List of Tables ...... x Chapter 1 Introduction ...... 1 Geomorphology and Geology ...... 2 Late Pleistocene and Holocene Volcanism at Mount Baker ...... 5 YP tephra ...... 6 Climate and Glaciers on Mount Baker ...... 8 The Little Ice Age ...... 13 The Little Ice Age in the Pacific Northwest ...... 13 The Little Ice Age at Mount Baker ...... 14 Accuracy of Little Ice Age Chronologies ...... 17 Methods of Palaeo-Equilibrium Line Altitude Reconstruction ...... 18 The Terminus-Head Altitude Ratio and Accumulation Area Ratio...... 19 The Area-Altitude Method and Balance Ratio ...... 22 Selection of Methods for This Research ...... 26 Equilibrium Line Altitude-Based Climate Reconstruction ...... 26 Chapter 2 2009 Accumulation Area Ratios and Modern Balance Ratios of Mount Baker Glaciers ...... 30 Abstract...... 30 Introduction ...... 31 Rationale for Study ...... 31 Objectives ...... 32 Study Area ...... 32 Glacier Mass Balance and Equilibrium Line Altitude ...... 34 Accumulation Area Ratio and Area-Altitude Balance Ratio ...... 37 Methods...... 38 2009 Equilibrium Line Altitude ...... 39 Steady-State Parameters ...... 44 Results… ...... 46 2009 Equilibrium Line Altitude ...... 46 Steady-State Parameters ...... 54 Discussion ...... 59 v

2009 Equilibrium Line Altitude ...... 59 Steady-State Parameters ...... 68 Conclusions ...... 76 Chapter 3 Little Ice Age Equilibrium Line altitude reconstructions for Mount Baker glaciers ...... 79 Abstract...... 79 Introduction ...... 80 Rationale ...... 80 Objectives ...... 81 Mount Baker and Its Glaciers ...... 81 Equilibrium Line Altitude Depression ...... 84 Methods of Equilibrium Line Altitude Reconstruction ...... 86 Palaeo-Glacier Reconstructions ...... 88 Equilibrium Line Altitude-Based Climate Reconstructions ...... 89 Methods...... 91 Glacier Reconstructions ...... 92 Palaeoclimate ...... 97 Results… ...... 100 Glacier Reconstructions ...... 100 Palaeoclimate ...... 102 Discussion ...... 109 Glacier Reconstructions ...... 109 Palaeoclimate ...... 116 Conclusions ...... 120 Chapter 4 Conclusions ...... 122 References ...... 124 Appendix: Little Ice Age Climate Reconstructions ...... 131

LIST OF FIGURES

Figure 1-1 Mount Baker volcano; view north (John Scurlock, ©2008). The map below shows the locations of Mount Baker, South Cascade Glacier, and Mount Rainier...... 3 Figure 1-2 Summary of published information on Little Ice Age glacier limits on Mount Baker. See Tables 1-3 and 1-4 for sources of information. Glacier margins are from the 2009 NAIP 1-m orthoimagery, and elevation data from the U.S. Geological Survey National Elevation Dataset. Also shown are relevant features mentioned in the text: Remnants of Black Buttes are pink; rocks of Lava Divide are yellow; nunataks are light grey. Geology from Hildreth et al. (2003) and Kevin Scott (personal communication, 2010)...... 4 Figure 1-3 Conspicuous YP deposit inset into the right-lateral Little Ice Age moraine of Roosevelt Glacier. Photo courtesy of John Scurlock...... 7 Figure 1-4 Average annual temperature (°C) for the Mount Baker area 1971-2000. Data from the Oregon Climate Service, Oregon State University. 100-m contour lines are shown in pale grey...... 9 Figure 1-5 Average precipitation (mm) for the Mount Baker area 1971- 2000. Data from the Oregon Climate Service, Oregon State University. The 2009 extent of Mount Baker glaciers and 100-m contour lines, are shown in pale grey...... 10 Figure 1-6 The terminus to head altitude ratio (THAR) method of ELA determination. A THAR of 0.40 (40 percent of total elevation range) is shown. Modified from Porter (2001)...... 20 Figure 1-7 The accumulation area ratio method (AAR) of ELA determination. A 15 percent change in AAR for three glaciers (a, b, c) with different hypsometries is shown. The different amounts of ELA shift demonstrate that the method does not take hypsometry into account. Modified from Porter (2001)...... 21 Figure 1-8 The area altitude balance ratio method of ELA determination. Equations are from Furbish and Andrews (1984) and Rea (2009). Adapted from Furbish and Andrews (1984). See text for details of the equations...... 24

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Figure 2-1 Mount Baker and its glaciers. The map below shows the locations of Mount Baker, South Cascade Glacier, North Klawatti Glacier, and Mount Rainier...... 33 Figure 2-2 Conceptual model of the methods used in this chapter, including a brief explanation of each step. Model data that were obtained from other sources are circled; whereas data that were derived or generated in this study are outlined with rectangles...... 40 Figure 2-3 Part of Mazama Glacier on the 2009 NAIP orthoimage showing areas of ablation (glacier ice and firn) and accumulation (snow)...... 42 Figure 2-4 Glacier divides on Mount Baker before (red) and after (white) smoothing and corrections, determined using a 200-m DEM and the Basin Analysis tool in ArcGIS. Individual basins identified in the analysis are shown in grayscale...... 47 Figure 2-5 2009 end-of-summer accumulation and ablation areas on Mount Baker. The approximate location of the 2009 ELA is shown for each glacier...... 48 Figure 2-6 Sections of Mazama Glacier, with the boundary between snow and firn (or ice) indicated by a dashed line. Photos: John Scurlock, ©2009...... 50 Figure 2-7 2009 hypsometric curves of Mount Baker glaciers, organized counter-clockwise around the mountain from Easton Glacier. The 2009 ELAs and AARs are marked on each curve with an x and their values are labeled adjacent to it ...... 52 Figure 2-8 2009 (a) ELA and (b) AAR (b) of Mount Baker glaciers plotted against the average aspect of the glacier accumulation area (from north-facing at 0° and 360°). The aspect of Sholes Glacier was corrected from its calculated value and set to 360°. Glacier area (km2) in 2009 is shown adjacent to each data point...... 55 Figure 2-9 2009 (a) ELA and (b) AAR (b) of Mount Baker glaciers plotted against the average aspect of the glacier ablation area (from north-facing at 0° and 360°). The aspect of Mazama and Sholes Glacier were corrected from their calculated values and set to 360°. Glacier area (km2) in 2009 is shown adjacent to each data point...... 56 Figure 2-10 Linear regressions of net balance against AAR for Rainbow Glacier (1984-2009) and Sholes and Easton glaciers (1990- 2009), and net balance against ELA for North Klawatti Glacier (1993-2010). The steady-state ELA or AAR is shown as a red x at the y-axis intercept...... 58 viii

Figure 2-11 Steady-state net balance curve for North Klawatti Glacier for 1994-2004 and 2006-2008. Also shown are linear approximations of the net balance curves above and below the steady-state ELA, and the elevational distribution of glacier area. The BR of North Klawatti Glacier is 3.70...... 73 Figure 3-1 Mount Baker and its glaciers. The map below shows the locations of Mount Baker, South Cascade Glacier, North Klawatti Glacier, and Mount Rainier...... 82 Figure 3-2 Summary of published information on Little Ice Age glacier limits on Mount Baker. See Tables 1-3 and 1-4 for sources of information. Glacier margins are from the 2009 NAIP 1-m orthoimagery, and elevation data from the U.S. Geological Survey National Elevation Dataset...... 84 Figure 3-3 Conceptual model of the methods used in this chapter, including a brief explanation of each step. Model data that were obtained from other sources are circled, whereas data that are derived or generated in this study are outlined with rectangles...... 91 Figure 3-4 Bed elevations for four Mount Baker glaciers, calculated using the Benn and Hulton (2010) spreadsheet model. Also shown are the ice surface elevations corresponding to the calculated bed elevation profiles, and the actual ice surface elevations measured from the NED 1/3 arcsecond DEM...... 101 Figure 3-5 Mapped limits of four modern and reconstructed Little Ice Age glaciers on Mount Baker. Centreline profiles used to calculate ice thicknesses of four glaciers are shown in red, and reconstructed 100-m contours are displayed in grey. Also shown are the approximate limits of all Little Ice Age glaciers on the mountain...... 103 Figure 3-6 Reconstructed Little Ice Age ice surface elevations for four Mount Baker glaciers, calculated using the bed elevation profiles shown in Figure 3-3...... 104 Figure 3-7 Modern and Little Ice Age glacier hypsometries of four Mount Baker glaciers. The ELAs (0nb ELA) for an AAR of 0.66 are shown for both the modern and Little Ice Age hypsometries...... 106

LIST OF TABLES

Table 1-1 Late Pleistocene and Holocene eruptive periods at Mount Baker (summarized from Tucker et al., 2007; Kevin Scott, personal communication, 2010)...... 6 Table 1-2 Mount Baker glaciers, listed in order of decreasing size...... 11 Table 1-3 Radiocarbon ages on outermost Little Ice Age moraines of three Mount Baker glaciers...... 15 Table 1-4 Minimum limiting ages of outermost Little Ice Age moraines of five Mount Baker glaciers...... 16 Table 2-1 2009 areas, elevation range, AARs, and ELAs of Mount Baker glaciers, listed in order of decreasing glacier size...... 51 Table 2-2 Average aspect of the accumulation and ablation areas of Mount Baker glaciers, ranging from -1 (no aspect) to 360° (north)...... 53 Table 2-3 Modern steady-state AAR and ELA for Mount Baker glaciers listed in order of decreasing glacier area. Results for North Klawatti Glacier are also shown...... 57 Table 2-4 Steady-state AABRs for Mount Baker glaciers, listed in order of decreasing 2009 glacier area...... 60 Table 2-5 2009 AARs of three Mount Baker glaciers based on this study and the field-based measurements of the North Cascades Glacier Climate Project (NCGCP)...... 64 Table 2-6 AARs and corresponding mass balances for Mount Baker glaciers in 2009, listed in order of increasing glacier area. Mass balances measured by the NCGCP for three glaciers are also shown...... 66 Table 3-1 Temperature reductions for different increases in precipitation assuming ELA depressions of 900 m and 160 m, 30 km west of the North Cascades crest (Porter, 1977) and at Mount Rainier (Burbank, 1982)...... 90 Table 3-2 Input used in the Benn and Hulton (2010) spreadsheet to estimate present-day glacier thickness along centreline profiles of four Mount Baker glaciers...... 94

Table 3-3 Inputs used in the Benn and Hulton (2010) spreadsheet to calculate Little Ice Age glacier thickness along a centreline profile for four Mount Baker glaciers...... 96 Table 3-4 Ice thicknesses calculated for four 1970s glaciers using the Benn and Hulton (2010) spreadsheet...... 102 Table 3-5 Little Ice Age area ratios and ice thicknesses of four Mount Baker glaciers estimated using the Benn and Hulton (2010) spreadsheet...... 105 Table 3-6 Estimated Little Ice Age equilibrium line altitudes (ELA) and modern steady-state ELAs for four Mount Baker glaciers...... 106 Table 3-7 Calculated Little Ice Age ELA depressions for four Mount Baker glaciers, and associated temperature changes from modern using a lapse rate of 0.62°C/1000m...... 107 Table 3-8 Estimates of Little Ice Age temperature and precipitation for changes in ELA, based on methods of Kuhn (1981) and Hooke (2005)...... 108 Table 3-9 Temperature reductions calculated using lapse rate and equation-based methods for a 7 percent and 10 percent increase in winter precipitation for four Mount Baker glaciers. .... 109 Table 3-10 Average reconstructed Little Ice Age thicknesses of four Mount Baker glaciers using a range of values for the shape factor (f)...... 113 Table 3-11 Average reconstructed Little Ice Age thicknesses of four Mount Baker glaciers using a range of values for the shear stress (τ)...... 114 Table 3-12 Maximum Little Ice Age changes in ELA and temperature for four Mount Baker glaciers...... 119

CHAPTER 1 INTRODUCTION

This thesis comprises an introductory chapter, two journal-style chapters,

and a final summary chapter. The introductory chapter provides background on

the study area and the methods that I used in my research. First, I provide an

overview of Mount Baker and its postglacial eruptive history, with emphasis on

activity during the most recent, Sherman Crater eruptive period. I then review

present-day glaciation on Mount Baker and the Little Ice Age glacial record provided by lateral moraines of modern glaciers. Mount Baker’s glaciers are examined in the context of glacier activity in the North Cascades since the early to middle twentieth century. Finally, I examine the significance of the equilibrium line altitude (ELA) in Quaternary studies and review methods of ELA reconstruction and ELA-based climate reconstruction.

Chapter 2 presents results of mapping and characterization of glaciers on

Mount Baker near the end of the 2009 ablation season. It also reports the steady- state ELAs and associated area-altitude balance ratios based on the mapping.

Chapter 3 builds on the results from Chapter 2 to calculate ELA depression for glaciers on Mount Baker at the maximum of the Little Ice Age. To do this, I determined modern and Little Ice Age glacier thicknesses and hypsometries. I then used the ELA depressions to estimate the temperature decrease required to sustain the much lower ELAs. Chapter 4 is a summary of the major conclusions of my work. 1

Geomorphology and Geology

Mount Baker is an active stratovolcano and the highest peak in the North

Cascades of Washington State (3285 m asl; Gardner et al., 1995; Hildreth et al.,

2003) (Fig. 1-1). The basement of the volcano comprises Mesozoic and

Palaeozoic rocks that were assembled in the Cretaceous (Hildreth et al., 2003).

Episodic eruptive activity at Mount Baker extends back to at least 1.3 million years, but glaciers have removed much of the earlier record of volcanism

(Hildreth et al., 2003). The modern volcanic cone is inset into Black Buttes, a much older and now-extinct volcano. Eroded remnants of this extinct volcano are visible west of the summit of Mount Baker, from the northwest side of Deming

Glacier to the southern margin of upper Coleman Glacier (Fig. 1-2; Kevin Scott, personal communication, 2010). The modern cone formed in the past 40,000 years; it comprises more than 200 individual lava flows (Hildreth et al., 2003), with Carmelo Crater at the summit. This crater, about 400 m wide, is filled with ice and is breached on its north side by the upper accumulation area of

Roosevelt Glacier.

Recent eruptive activity at Mount Baker has been localized at Sherman

Crater, which is about 800 m south of the summit (Hildreth et al., 2003). This satellite crater is 600 m wide, likely formed around 6500 years ago, and has been the locus of volcanic activity since then (Tucker et al., 2007; Kevin Scott, personal communication, 2010). Sherman Crater likely achieved its present form in the mid-nineteenth century during the Sherman Crater eruptive period (Kevin

Scott, personal communication, 2010).

Figure 1-2 Summary of published information on Little Ice Age glacier limits on Mount Baker. See Tables 1-3 and 1-4 for sources of information. Glacier margins are from the 2009 NAIP 1-m orthoimagery, and elevation data from the U.S. Geological Survey National Elevation Dataset. Also shown are relevant features mentioned in the text: Remnants of Black Buttes are pink; rocks of Lava Divide are yellow; nunataks are light grey. Geology from Hildreth et al. (2003) and Kevin Scott (personal communication, 2010).

Mount Baker has been a source of significant landslides, lahars, and floods, as well as different types of eruptions and eruptive deposits. Landslides and lahars have removed some of the evidence of past glaciation on the 4

mountain. For example, much of the evidence of recent glacier activity at

Rainbow Glacier has been removed by frequent debris avalanches originating

from Lava Divide (Fig. 1-2; Hildreth et al., 2003; Tucker et al., 2007; Kevin Scott,

personal communication, 2010), a remnant of an old (ca. ~460 ka) volcano

between Park and Rainbow glaciers.

Landslides and floods have affected moraine preservation in the forefields

of many glaciers on Mount Baker. Over the past several centuries, there have

been several large debris avalanches and floods, and a collapse of the terminus

of Deming Glacier (Kevin Scott, personal communication, 2010). Some of these events covered parts of glaciers with debris, affecting their albedo and thus their mass balance.

Late Pleistocene and Holocene Volcanism at Mount Baker

Scott et al. (2003) and Tucker et al. (2007) identify four major eruptive periods at Mount Baker between the late Pleistocene and today (Table 1-1). The oldest, or Carmelo Crater, eruptive period dates to approximately 16,400-12,200

14C yr BP and marks the end of the growth of modern Mount Baker volcano;

subsequent volcanic events have dissected the volcano (Kevin Scott, personal

communication, 2010). The second, or Schreibers Meadow, eruptive period

dates to 8800-850014C yr BP. The Schreibers Meadow cinder cone,

approximately 4 km south of the modern terminus of Easton Glacier, formed at

this time (Tucker et al., 2007; Kevin Scott, personal communication, 2010). The

Mazama Park eruptive period occurred about 5930-5790 14C yrs BP (Kevin Scott,

personal communication, 2010). The Sherman Crater eruptive period is the most recent phase of volcanic activity and is marked by a historic eruption in AD 1843

(Kevin Scott, personal communication, 2010). The 1843 eruption was a phreatomagmatic event localized at Sherman Crater (Hildreth et al., 2003; Scott et al., 2003); no lavas were erupted.

Table 1-1 Late Pleistocene and Holocene eruptive periods at Mount Baker (summarized from Tucker et al., 2007; Kevin Scott, personal communication, 2010).

Eruptive Age Defining events period Carmelo 16,400- Several lava flows and lahar deposits originate from Crater 12,20014C Carmelo Crater. This eruptive period marks the end of the yrs BP construction of the modern Mt. Baker edifice Schreibers 8800- Formation of Schreibers Meadow cinder cone on the flank Meadow 850014C yrs of Mt. Baker. The eruption is followed by a large lahar- BP generating flank collapse Mazama 5930- Four large lahars and two eruptions of tephra, one Park 579014C yrs magmatic and one likely phreatomagmatic. Both eruptions BP originate from Sherman Crater Sherman AD 1843 - Phreatomagmatic eruption from Sherman Crater, Crater present producing the YP tephra. Collapse of east flank of Sherman Crater generates a large lahar. Elevated levels of thermal activity and volatile emissions continue to present

YP tephra

A conspicuous white tephra, termed YP (Young and Pale) by Scott et al.

(2003), was erupted from Sherman Crater in 1843. Tucker et al. (2007) report it over an area of 600 km2 around Mount Baker, but it is most noticeable near the source. Blocks of YP tephra, referred to as “Shermanite” and consisting of hydrothermally altered volcanic rock with crystals of elemental sulphur, are present in the forefields of several glaciers on Mount Baker, notably Easton, 6

Coleman, Roosevelt, and Boulder glaciers (Kevin Scott, personal

communication, 2010). More distally, YP is a thin, poorly sorted layer of clay- to

sand-size andesitic ash (Kevin Scott, personal communication, 2010).

The most conspicuous YP occurrence at Mount Baker is a thick deposit

underlying a terrace inset into the right-lateral moraine of Roosevelt Glacier,

referred to as the “Chromatic Moraine” (Fig. 1-3; Kevin Scott, personal communication, 2010). This moraine marks the maximum Little Ice Age extent of

Roosevelt Glacier, thus the YP deposit at that site was emplaced after Roosevelt

Glacier had thinned and retreated from that maximum position.

Figure 1-3 Conspicuous YP deposit inset into the right-lateral Little Ice Age moraine of Roosevelt Glacier. Photo courtesy of John Scurlock.

YP tephra also occurs in several moraines in the forefields of Easton and

Boulder glaciers. The outermost significant accumulations of YP tephra in

moraines delineate the extent of glaciers on Mount Baker shortly after 1843

(Scott et al., 2009). However, Mount Baker glaciers may not have been in

equilibrium during and immediately after the 1843 eruption, which means that

standard methods of ELA reconstruction cannot be applied for that date.

Climate and Glaciers on Mount Baker

Mount Baker is located in the tracks of storms that move inland from the

Pacific Ocean across the North Cascades. About 80 percent of the annual precipitation falls between October and April (Pelto, 2006). Glaciers are fed principally by direct snowfall, but wind drifting and avalanching are locally important (Pelto, 2006). Amounts of snowfall during the accumulation season and melt during the ablation season are large, on the order of metres. Annual balance for monitored Mount Baker glaciers since 1984 has ranged from about -

3.0 m w.e. (metres water equivalent) to nearly +2.0 m w.e. (Pelto, 2007).

Average annual temperature and precipitation for the Mount Baker area

are shown, respectively, in Figures 1-4 and 1-5. Average annual precipitation

increases with elevation and is highest on the south and southwest sectors of the

mountain. Average annual precipitation is, overall, greater on south-facing slopes

than on north-facing slopes. Lower elevations on the northeast side of Mount

Baker have the lowest average annual precipitation. Temperature decreases with

elevation, but does not differ around the mountain (Fig. 1-4).

Figure 1-4 Average annual temperature (°C) for the Mount Baker area 1971-2000. Data from the Oregon Climate Service, Oregon State University. 100-m contour lines are shown in pale grey.

There are 11 glaciers on Mount Baker (Table 1-2), although some of them share source areas. I have not included in this group Hadley Glacier (Fig. 1-2) or the western lobe of Mazama Glacier, which Heikkinen (1984) referred to as

Bastille Glacier. Hadley Glacier is detached from the main edifice, and there is no reason to divide Mazama Glacier into two separate glaciers. The glaciers range in area from about 0.8 km2 to nearly 10 km2 and terminate at elevations ranging from 1320 to 1850 m asl.

Figure 1-5 Average precipitation (mm) for the Mount Baker area 1971-2000. Data from the Oregon Climate Service, Oregon State University. The 2009 extent of Mount Baker glaciers and 100-m contour lines, are shown in pale grey.

Previous research in the North Cascades has shown that most glaciers advanced and retreated synchronously on timescales of 20 years or less during the twentieth century (Harper, 1993; Pelto and Riedel, 2001). Response lag times to climate change are two to nine years for Coleman Glacier and less than

20 years for other Mount Baker glaciers (Harper, 1993).

Long-term monitoring of glaciers on Mount Baker indicates they thinned and retreated during the first half of the twentieth century, advanced between the

1940s and 1970s, and the earliest recent thinning and retreating began in 1975

(Harper, 1993; Pelto, 2006). South Cascade Glacier, which is about 70 km 10

southeast of Mount Baker, has been monitored more-or-less continuously since the beginning of the U.S. Geological Survey Benchmark Glacier Program in 1957

(Fig. 1-1). It thinned and retreated from 1959 to 1970, advanced from 1971 to

1976, retreated a second time from 1977 to 1995, and fluctuated in a complex manner, but with little overall change, since 1995 (Josberger, 2007).

Table 1-2 Mount Baker glaciers, listed in order of decreasing size.

Glacier Area (km2) Elevation range (m) Coleman/Roosevelt 9.85 1375/1600 – >3200 Park 5.13 1320 – >3200 Mazama 4.97 1470 – 2940 Deming 4.77 1350 – >3200 Boulder 3.47 1540 – >3200 Easton 2.88 1680 – 2980 Talum 2.15 1830 – 3050 Rainbow 2.02 1370 – 2615 Squak 1.55 1715 – 2765 Sholes 0.94 1605 – 2035 Thunder 0.81 1850 – 2580 Note: All measurements were made from 1-m 2009 NAIP end-of-summer orthoimagery and the USGS National Elevation Dataset one-third arcsecond DEM.

Pelto and Hedlund (2001) found that 21 of the 38 of glaciers in the North

Cascades that they studied began retreating in the late 1970s, after a period of advance that began in the 1950s. Four of the 47 glaciers monitored by the North

Cascades Glacier Climate Project (NCGCP) disappeared by 2006 (Pelto, 2006), but none of the four were on Mount Baker. Pelto (2011) assessed accumulation zone thinning for ten North Cascade glaciers and concluded that, if the observed climate trends continue, only three can still recover and reach equilibrium. Easton and Rainbow glaciers, two of the ten that Pelto (2011) studied, are forecast to survive, albeit in reduced states. Recent and continuing retreat of glaciers on

Mount Baker, and elsewhere in the North Cascades, has been attributed to a warming and drying trend that began in the late 1970s (Pelto and Hedlund,

2001).

Harper (1993) documented historical changes in the extent of six Mount

Baker glaciers (Roosevelt, Rainbow, Boulder, Easton, Deming, and Coleman glaciers) from 1940 to 1990 based on comparison of sequential aerial photographs. He found that all six glaciers fluctuated approximately synchronously, but that the magnitude of the changes differed from glacier to glacier. He identified three phases of activity (his paper was published before the beginning of the fourth phase identified by Josberger, 2007): balance was negative and glaciers retreated from 1940 until the early 1950s; glaciers then advanced until the early 1980s; with the exception of Easton Glacier, they then retreated until the time Harper published his findings. Easton Glacier began to retreat around 1990. Mount Baker glaciers began to advance earlier than South

Cascade Glacier during the second of Harper’s phases, and they subsequently began to retreat slightly later. Coleman Glacier on Mount Baker began to advance earlier in the mid-twentieth century than 76 other glaciers in the

Cascade Range and Olympic Mountains (Grove, 1988), suggesting that it has an exceptionally short response time (Grove, 1988).

The Little Ice Age

The Little Ice Age is the most recent phase of the Neoglacial period; it is marked by significant glacier expansion during the past millennium (Grove,

1988). The term is entrenched in the scientific literature, but researchers disagree about its proper use. The main sources of disagreement are the times of its beginning and end, and whether the term should be applied to changes in glacier activity or climate (Clague et al., 2009). In most areas of the world, the

Little Ice Age culminated in the eighteenth or nineteenth century and ended at the beginning of the twentieth century (Grove, 1988).

The Little Ice Age in the Pacific Northwest

In the Pacific Northwest, Neoglaciation is characterized by successively larger advances of glaciers, beginning about 6000-7000 years ago (Menounos et al., 2008). Evidence exists for pre-Little Ice Age advances of glaciers in the North

Cascades, but most or all glaciers achieved their greatest Holocene extent in the eighteenth and nineteenth centuries (Sigafoos and Hendricks, 1972; Burbank,

1981; O’Neal, 2005; Davis et al., 2007; Ryane et al., 2007).

Burbank (1981) used lichenometric data to infer that glaciers on Mount

Rainier (Fig.1-1) were at or near their Little Ice Age maximum positions between the late eighteenth and early nineteenth centuries and began to retreat by the early twentieth century. Sigafoos and Hendricks (1972) came to similar 13

conclusions based on dendrochronological studies of the lateral moraines of

eight glaciers on Mount Rainier. Seven of the eight glaciers had reached their

Little Ice Age maxima and began to retreat by AD 1840. O’Neal (2005) used lichenometry to date recent retreat of five glaciers in the North Cascades. He concluded that the glaciers retreated slowly in the late nineteenth century, followed by accelerated retreat in the twentieth century.

The Little Ice Age at Mount Baker

Several researchers have studied Little Ice Age and twentieth-century moraines and trimlines in the forefields of glaciers on Mount Baker (Fig. 1-2;

Tables 1-3 and 1-4). Glaciers on Mount Baker retreated an average of 1440 m from their maximum Little Ice Age limits by AD 1950 (Pelto and Hartzell, 2004).

Research on post-Little Ice Age activity has been focused at Coleman-Roosevelt,

Boulder, Rainbow, Deming, and Easton glaciers (Long, 1955; Burke, 1972;

Fuller, 1980; Heikkinen, 1984; O’Neal, 2005; Thomas, 1997). Long (1955) used dendrochronology to date the outermost and oldest Little Ice Age moraine at

Boulder Glacier. He assigned an age of AD 1750 or older to this moraine and argued that the glacier retreated from this position sometime between the late eighteenth century and early nineteenth century, with accelerated retreat in the twentieth century. He also dated stabilization of recessional moraines at Boulder

Glacier to 1846, 1868, and 1912. He remarked that the outermost large moraines at Boulder and Easton glaciers could only have been constructed over a period of several hundred years, requiring near steady-state conditions.

Table 1-3 Radiocarbon ages on outermost Little Ice Age moraines of three Mount Baker glaciers.

Location 14C age Maximum Material Lab Reference (yr BP) calendric dated number age (AD) Easton 410 ± 1430 Log Beta- Davis et al., 2007 Glacier 40 221569 Coleman 690 ± 1190 Log N/A Easterbrook, 2007 Glacier 80 Deming 380 ± 1450 Tree UCIAMS- John Clague, Glacier 15 stump 68591 personal communication, 2011

Burke (1972) dated the outermost moraine of Boulder Glacier (his B1 moraine) using dendrochronology. He concluded that this moraine stabilized and was abandoned in AD 1588. Burke (1972) and O’Neal (2005) dated a recessional moraine that Long concluded had stabilized in AD 1888 to, respectively, 1920 and 1915.

Heikkinen (1984) reviewed previous work on Mount Baker and concluded that most of the Little Ice Age moraines on the mountain date to one of three periods: sixteenth, nineteenth, or twentieth centuries. He constructed a chronology for Coleman and Roosevelt glacier moraines based on dendrochronological research (Fig. 1-2).

O’Neal (2005) used lichenometry to date glacier retreat from moraines in the forefields of Rainbow, Easton, and Boulder glaciers, and two other Cascades glaciers. His lichen ages, summarized in Table 1-4, are based on a growth curve constructed using data from the Washington and Oregon Cascades, with an 15

accuracy of 10 years. He did not date pre-nineteenth century moraines, but found that glaciers in Washington and Oregon began to retreat slowly between the late

Table 1-4 Minimum limiting ages of outermost Little Ice Age moraines of five Mount Baker glaciers.

Glacier and dated Method2 AD date3 Reference feature1 Boulder terminal D 1750 Long (1955) moraine Boulder terminal D 1588 Burke (1972) moraine Coleman-Roosevelt D Early 16th century Heikkinen (1984) left-lateral moraine (>420 yrs) Coleman-Roosevelt D 1823 (>150 yrs) Heikkinen (1984) left-lateral moraine Deming left-lateral D Early 16th century Fuller (1980) moraine Deming terminal D Early 17th century Fuller (1980) moraine Easton right-lateral D 17th century (>350 yrs) Thomas (1997) moraine Easton left-lateral D Early-mid 19th century Thomas (1997) moraine (>140 yrs) Easton right-lateral L 1870s or 1850s Johannes Koch, personal moraine (different growth communication, 2011 curves) Easton right- lateral L 1869 O’Neal (2005) moraine Rainbow left- lateral L 1891 O’Neal (2005) moraine Rainbow terminal D 1900 Fuller (1980) moraine Rainbow left-lateral L Early 16th century Fuller (1980) moraine 1 Locations of dated moraines are shown in Figure 1.2; Lateral moraine locations are given looking down-glacier. 2 D = dendrochronology, L = Lichenometry. 3 Minimum age of moraine.

nineteenth and early twentieth century, followed by rapid retreat continuing until the mid-twentieth century.

Examination of the data in Tables 1-3 and 1-4 suggests that glaciers on

Mount Baker were near their maximum Little Ice Age positions between the twelfth and eighteenth centuries. They began to retreat in the nineteenth century, but were still near their Little Ice Age limits in the late nineteenth century. Retreat accelerated in the twentieth century.

Accuracy of Little Ice Age Chronologies

Estimates of times of glacier advance and retreat are subject to several sources of uncertainty, including the length of time between retreat and moraine stabilization, ecesis times of trees and lichens, and, in the case of lichens, possible errors in lichen growth curves (Koch, 2009). In addition, the oldest lichen or tree on a moraine may not have been sampled and dated. Finally, dendrochronology and lichenometry inform a researcher when a glacier retreated from a moraine, but provide only a minimum age for the moraine construction

(Burbank, 1981; Koch, 2009).

Radiocarbon ages on glacier activity are also imprecise, commonly with uncertainties in calibrated (calendric) ages in excess of 100 years. These uncertainties stem from unavoidable laboratory sources of imprecision and calculation of calendric ages from radiocarbon ages.

Methods of Palaeo-Equilibrium Line Altitude Reconstruction

An important objective of glacier reconstruction is to estimate the location

of the palaeo-equilibrium line altitude (ELA) and relate it to climate. Estimates of

former ELAs assume glaciers are in equilibrium, that is, in a steady state. The difference in ELA at two times is the ELA depression or rise (ΔELA), which is a

useful metric in palaeoclimate studies. Changes in ELA may be caused by a

change in temperature, precipitation, or both.

A challenge in reconstructing former ELAs is determining how to best represent the equilibrium line. A former steady-state ELA must exist within the

footprint of the former glacier and must respect the physics of glaciers

(Osmaston, 1975). Researchers have proposed several simple methods to approximate ELA; most of these are based on some proportion of total glacier area or elevation. Indices based on these methods were created with the goal of

facilitating comparison of results for glaciers (Meier, 1962). Proportion-and-

elevation-based indices provide accurate measures of the ELA of modern

glaciers (Meier, 1962) and thus are assumed to be most useful for reconstructing

former ELAs.

The ELA can be considered a proxy of glacier mass balance, and mass

balance depends on climate. Thus, ELA values are useful in palaeoclimate

studies, assuming former glacier margins can be accurately reconstructed.

Knowledge of the modern steady-state ELA and the limits of a former glacier,

however, are not, by themselves, sufficient for determining the palaeo-ELA. A

method of reconstructing an assumed steady-state palaeo-ELA must be chosen.

The steady-state ELA can be represented by a proportion of total glacier area, its

elevation range, or both (Osmaston, 1975). The most common methods are the

accumulation area ratio (AAR), terminus-head altitude ratio (or toe-to-headwall

altitude ratio, THAR), area-altitude (AA) ratio, and area-altitude balance ratio

(AABR) methods (Osmaston, 1975; Furbish and Andrews, 1984; Porter 2001).

I used the AAR and AABR methods in my research. The AAR method is

the most commonly used and accepted of the ELA reconstruction methods. It is

relatively easy to apply and has been shown to be reliable based on comparisons

with data derived from mass balance studies (Meierding, 1982; Torsnes et al.,

1993).

The Terminus-Head Altitude Ratio and Accumulation Area Ratio

The THAR method is the simplest of the proportion-based methods, as it

requires only maximum and minimum elevations (Fig. 1-6). It is expressed as a

value between 0 and 1, which is calculated as the proportion of the total elevation

range of the glacier that is below the ELA (Porter 2001). A THAR of 0.4, for

example, means that the elevation range in the ablation area represents 40

percent of the total elevation range of the glacier. Although the THAR is easy to

calculate, it is based only on the elevations of the glacier terminus and headwall

and does not take into account the hypsometry of the glacier. Hypsometry is the distribution of the area of a glacier over its elevation range; it is an important

factor in interpreting ELA values (Benn and Evans, 1998). Glacier hypsometry

can be visualized by plotting cumulative glacier area against elevation (Benn and

Evans, 1998).

Figure 1-6 The terminus to head altitude ratio (THAR) method of ELA determination. A THAR of 0.40 (40 percent of total elevation range) is shown. Modified from Porter (2001).

The AAR, which is also easy to compute, is much more commonly used than the THAR in modern and palaeo-glacier studies. Calculation of the AAR requires minimal topographic data and two areal values – total glacier area and the area of the accumulation area. The AAR represents the proportion of total glacier area occupied by the accumulation area (Fig. 1-7). A relatively debris-free glacier that is in equilibrium or steady-state (i.e., net balance bn = 0) will have an

AAR between 0.5 and 0.8, typically around 0.65 (Meier and Post, 1962;

Meierding, 1982).

The AAR method is an improvement over the THAR method, but it does 20

Figure 1-7 The accumulation area ratio method (AAR) of ELA determination. A 15 percent change in AAR for three glaciers (a, b, c) with different hypsometries is shown. The different amounts of ELA shift demonstrate that the method does not take hypsometry into account. Modified from Porter (2001).

not account for glacier hypsometry, which can cause error where glaciers do not have simple areal distributions. Figure 1-7 shows how a simple shift from an accumulation area of 50 to 65 percent of the total glacial area for three glaciers with different hypsometries can affect the location of the ELA.

The Area-Altitude Method and Balance Ratio

Determination of the area-altitude (AA) ratio requires an hypsometric curve and the ELA. Alternatively, the ELA can be determined if the glacier hypsometry and an area-altitude ratio are known. The AA method is a simpler version of the balance ratio method, described below, in that mass balance gradients are not considered. A trial ELA is selected, and the areas within each contour belt above the ELA (positive values) and below the ELA (negative values) are summed. Through an iterative process, the final steady-state ELA is determined when the sum of the area elevations above and below the ELA is zero (Osmaston, 2005).

The balance curve, or the plot of mass balance as a function of elevation, must be simplified to determine the location of the ELA. Fortunately, an accurate approximation can be made by fitting linear functions to the portions of the balance curve above and below the ELA (Osmaston, 1975). The mass balance gradients above and below the ELA differ because the climatic factors that govern the gradients in the accumulation and ablation areas of the glacier are different (Benn and Evans, 1998).Determination of linear mass balance gradients

in the accumulation and ablation areas is the basis for the area-altitude balance

ratio method (Osmaston, 1975).

The balance ratio or area-altitude balance ratio method incorporates area,

elevation, and mass balance gradients in calculating the ELA. Calculation of the balance ratio is shown in Figure 1-8.Three assumptions underlie the balance ratio method (Furbish and Andrews, 1984): (1) the mass balance curves above

and below the ELA can be approximated as linear functions; (2) the balance

curve is representative of a glacier that is in a steady state; and (3) changes in

glacier mass balance can be represented as changes from stationary position to

stationary position and are translated to glacier shape only as an advance or

retreat of the terminus.

If the mass balance gradients in the ablation and accumulation areas are,

respectively, bnb and bnc, the balance ratio (BR) for a glacier (Furbish and

Andrews, 1984) is:

A BR of 1 indicates that the mass balance gradients in the accumulation

area and ablation area are the same. A value greater than 1 means that the

mass balance gradient in the ablation area is steeper than in the accumulation

area. In a steady-state situation, a large BR value is associated with a relatively

small ablation area, as bnb is sufficiently steep enough that a smaller total area of

ablating ice is needed to balance accumulation above the ELA (Benn and Evans,

1998).

Figure 1-8 The area altitude balance ratio method of ELA determination. Equations are from Furbish and Andrews (1984) and Rea (2009). Adapted from Furbish and Andrews (1984). See text for details of the equations.

For palaeo-glaciers and glaciers for which mass balance data are sparse, the BR is a simple geometric calculation. This calculation, however, is only applicable to glaciers that are in equilibrium. An explanation of the logic of the BR method, from Furbish and Andrews (1984) and Benn and Evans (1998), follows.

In a steady-state situation, total net ablation must balance total net

accumulation, thus the area-weighted mass balance of the ablation area (dab)

multiplied by its area (Aab) must equal the area-weighted mass balance of the accumulation area (dac) multiplied by its area (Aac):

Assuming the balance gradients above and below the ELA are linear,

and are the mass balance values at the area-weighted mean altitude of the

ablation area and accumulation areas, and . These values are used to

calculate the balance gradients in the ablation and accumulation area (bnb, bnc):

By substitution, Equations 2, 3, and 4 become:

Equation 5 has been incorporated into a spreadsheet program (Benn and

Gemmell, 1997; Osmaston, 2005) that simplifies ELA calculations using the BR

method. The ELA is calculated in the spreadsheet through an iterative process

as the elevation that yields the pre-selected balance ratio (Benn and Gemmell,

1997). 25

Selection of Methods for This Research

Application of each of the methods mentioned above is situation-specific.

The THAR method should only be used where data are so limited that more precise cannot be used. The AA method is of some value, but the AAR or BR methods are generally used in lieu of it.

Increasingly, ELA reconstructions are made using the AAR and BR methods. Meierding (1982) and Torsnes et al. (1993) compared the common methods and found that the AAR method produced the most consistent results

(also see Porter, 2001). Recently, researchers have extended the observations of Meier and Post (1962) and Furbish and Andrews (1984) to include region- and area-specific AAR and BR values (Rea, 2009; Kern and Laszlo, 2010).

In view of these considerations, I use only the AAR and BR to calculate

ELAs. I calculate the modern steady-state AAR and BR of Mount Baker glaciers

(Chapter 2) and apply these modern estimates, as well as independent values commonly adopted for temperate alpine glaciers, to determine the amount of

ELA depression during the Little Ice Age (Chapter 3). Based on this analysis, I comment on the relative values of the AAR and BR methods.

Equilibrium Line Altitude-Based Climate Reconstruction

Climate and the location of glacier ELA are closely related, as the ELA is determined by a combination of air temperature, precipitation, and radiation

(Kuhn, 1981). Any prolonged change in climate produces a change in the ELA. If one assumes that a former glacier was approximately in steady-state at the time 26

of its maximum extent, then the climatic conditions required to sustain its advanced position can be approximated. It is not possible to directly record and analyse the response of former glaciers to changes in climate, so these reconstructions must be based on modern analogues and glaciological principles

(Kuhn, 1981).

Because the ELA is, by definition, the location on the glacier where net accumulation and ablation are zero (Meier, 1962), it is logical to consider glacier dynamics and climate in relation to this elevation (Kuhn, 1981). In this thesis, I reconstruct and compare past climatic conditions using two different ELA-based methods. I also evaluate the relative contributions of temperature reduction and precipitation increase on the ELA shift during the Little Ice Age.

I first use a summer lapse rate to determine the change in temperature responsible for different ELA depressions. This approach assumes no change in precipitation. Second, I consider both temperature and precipitation. There are two approaches to calculating temperature change as a function of precipitation change, using empirical relations between precipitation and temperature at the

ELA of modern glaciers: either a statistical approach (Leonard, 1989; Ohmura et al, 1992) or an energy balance approach (Kuhn, 1981; Hooke, 2005). I estimate the peak Little Ice Age ELA-based palaeoclimate using both the lapse rate and energy balance approaches, but do not use the statistical approach.

The approach that I use to account for both precipitation and temperature is described by Kuhn (1981) and elaborated by Hooke (2005). Based on energy-

balance considerations, the precipitation at the steady-state ELA, bw(ho), can be calculated as:

ℎ ℎ ℎ

where T is the length of the melt season in days, L is the latent heat of fusion

2 (334 kJ/kg), R(h0) is net radiation at the ELA in W/m , γ is a constant with units of

2 MJ/m day°C, Ta(h0) is the free air temperature in °C above the ELA, and Ts is surface temperature (Kuhn, 1981; Hooke, 2005). For simplicity, Ts is set to zero

to represent melting conditions and does not vary with elevation (Hooke, 2005). I

also ignore any summer snowfall, such that bw(ho) is only precipitation during the

accumulation season.

For a shift in ELA, Δh, the corresponding change in accumulation at the

new ELA (h = h0 + Δh ) is calculated as the difference between accumulation at the new ELA, b’w(h), and accumulation at h0:

′ ′ ′ ℎ ℎ ℎ

R is set to zero in Equations 6 and 7, as net radiation does not vary significantly with elevation (Hooke, 2005). I also assume that net radiation was not significantly different, for the purposes of this exercise, at the maximum Little Ice

Age than today. The change in winter balance, then, is calculated by differencing

Equations 6 and 7. This calculation is followed by a substitution for each parameter at the new ELA by relating them to the ELA shift, Δh:

′ ∆ ℎ ℎ ℎ

where Y is either temperature or precipitation, is its elevation gradient, and δY is the change in Y that contributed to the observed Δh (Hooke, 2005). Finally, a change in ELA can be related to a change in precipitation or temperature (Kuhn,

1981; Hooke, 2005):

∆ ∆ ℎ ℎ

An assumed change in precipitation or temperature at the ELA can be used in Equation 9 to solve for the corresponding change in precipitation or temperature required to produce the shift.

I compare results obtained using the energy balance approach of Kuhn

(1981) with those calculated using the straightforward lapse-rate method to determine the magnitude of the effect precipitation might have on climate at the

peak of the Little Ice Age.

CHAPTER 2 2009 ACCUMULATION AREA RATIOS AND MODERN BALANCE RATIOS OF MOUNT BAKER GLACIERS

Abstract

I estimated the 2009 mass balance of glaciers on Mount Baker,

Washington, using late summer, 1-m NAIP (National Agriculture Imagery

Program) orthoimagery. I mapped areas of accumulation and ablation on Mount

Baker glaciers at the end of August 2009 and computed the end-of-summer accumulation area ratio for each glacier. I also mapped glacier divides and calculated modern glacier areas, elevation ranges, and average aspects. Using long-term mass balance measurements made by others, I estimated the 2009 mass balance and steady-state equilibrium line altitude (ELA) of each glacier.

Finally, I utilized the steady-state ELA results and modern glacier hypsometric curves to calculate the area-altitude balance ratio of each glacier.

Introduction

Glaciers are sensitive to changes in climate, and their fluctuations over

time can provide information on past temperature and precipitation. One way of tracking the activity of glaciers, and thus relating them to climate, is to determine the location of the equilibrium line altitude (ELA). The ELA is the location on a glacier’s surface at which annual accumulation is balanced exactly by annual

ablation and net mass balance is zero (Benn and Evans, 1998).

I mapped accumulation and ablation areas on Mount Baker glaciers at the

end of the 2009 melt season to estimate their 2009 accumulation area ratios

(AAR) and calculate their steady-state ELAs and corresponding area-altitude

balance ratios (AABR). I calculated the AABRs using the methods of Furbish and

Andrews (1984), which have been refined by Benn and Gemmell (1997),

Osmaston (2005), and Rea (2009).

Rationale for Study

It is worthwhile to monitor glaciers and accurately record their changes

over time, because they are one of the most reliable indicators of past climate

change (Nesje and Dahl, 2000) and their fluctuations through time both directly

and indirectly affect human activity. Furthermore, the analysis of reconstructed

long-term records can inform future planning and research in a region subject to

future climate change.

It is possible to obtain estimates of annual glacier mass balance from

high-resolution, end-of-melt-season orthoimagery. Over time, these observations

can be used to strengthen empirical relationships between climate and glacier

mass balance and the ELA. Direct measurements made on North Cascades

glaciers as part of long-term mass balance monitoring programs provide an

independent check on the results obtained from the orthoimagery.

Glacier ELAs, accumulation area ratios (AARs), and area-altitude balance

ratios (AABRs) are useful and interrelated measures for effectively summarizing

changes in glaciers over time. Little work, however, has been done to establish

steady-state parameters for North Cascades glaciers, and no work has been

done on the large glaciers of Cascades volcanoes. These parameters can

additionally be used in palaeo-glacier studies to determine ELA shifts associated with significant past climatic events. There are several methods of palaeoclimate reconstruction, but one of the most common relates glacier ELAs to climatic conditions for specific times in the past (Carr et al., 2010).

Objectives

The four objectives of the research reported in this chapter are to: (1)

characterize and map the divides of glaciers on Mount Baker in 2009; (2)

approximate the end-of-summer 2009 ELA of all Mount Baker glaciers; (3)

estimate the steady-state ELA of each glacier; and (4) calculate the AABRs of

the modern steady-state glaciers.

Study Area

Mount Baker (3285 m asl; Fig. 2-1) is an active, glacier-clad stratovolcano

located in northwest Washington State (Hildreth et al., 2003). The regional

Figure 2-1 Mount Baker and its glaciers. The map below shows the locations of Mount Baker, South Cascade Glacier, North Klawatti Glacier, and Mount Rainier.

climate is temperate and maritime, and is largely controlled by moist air masses

moving east from the Pacific Ocean, less than 100 km away. Glaciers have

shaped the volcano throughout its history, which spans the past 1.3 million years

or more (Hildreth et al., 2003), and today Mount Baker supports 11 glaciers (Fig.

2-1).

Long-term mass balance data suggest that very few glaciers in the North

Cascades have been in equilibrium with climate over the past two decades

(Pelto, 2006, 2011). Pelto (2011) observed the emergence of rock outcrops and

thinning of the accumulation zones at 10 North Cascades glaciers over a 25-year period, and forecasted that seven of them will not equilibrate if modern climatic

conditions persist (Pelto, 2011).

Glacier Mass Balance and Equilibrium Line Altitude

The mass of a glacier fluctuates constantly. Accumulation and ablation at

any elevation are controlled by many factors and adjust continuously (Meier,

1962). The ablation season in the North Cascades generally extends from May to

September; the accumulation season extends from October through April (Pelto,

2006). Direct snowfall and blowing and avalanched snow are the main sources of

accumulation on North Cascades glaciers. The glaciers on Mount Baker are all

land-terminating, which makes direct melting the principal mechanism of ablation.

The difference between total winter accumulation and total summer

ablation for a balance year, averaged over the glacier surface, is net mass

balance (Nesje and Dahl, 2000). The average value of accumulation or ablation,

a thickness estimate, is expressed in equivalent metres of water (m w.e.) per unit glacier area (Nesje and Dahl, 2000). If the net balance of a glacier is negative, more mass has ablated than accumulated over the entire area of the glacier over the balance year.

The location of the ELA is closely related to climate and topography; ablation decreases and accumulation increases with elevation. With the exception of a glacier that has no snow remaining at the end of a balance year, there is an elevation on a glacier surface at which the two processes are, hypothetically, in balance (Benn and Evans, 1998).

If the annual ELA has shifted to a lower elevation over a monitoring period, the net mass balance of the glacier has increased. In response to the overall positive change in net balance, the glacier thickens and advances

(Bennett and Glasser, 2009). If the ELA has risen, the net balance is negative and the glacier thins and retreats (Bennett and Glasser, 2009). The ELA may be identified visually on temperate glaciers as the transient snow line at the end of the ablation season that separates glacier ice and firn below from snow above

(Benn and Evans, 1998).

For glaciers that are in equilibrium with their local climate, the steady-state

ELA is the elevation at which overall net balance is zero (Nesje and Dahl, 2000).

As long as the glacier remains in a steady state, it will maintain its size (Bennett and Glasser, 2009). The steady-state ELA is not measured, but it can be approximated through linear regression of long-term net balance and ELA data

(Nesje and Dahl, 2000). 35

The steady-state ELA is a useful parameter in modern mass balance

studies; it can be compared to annual ELAs to track changes in glacier health. In

addition, changes in the steady-state ELA over long periods of time may be

tracked as the geometry of a glacier changes. The steady-state ELA may also be used in palaeo-glacier studies to infer past climatic conditions, by considering modern glaciers as analogues for those of the past.

The steady-state ELA of a palaeo-glacier can be determined in several ways (Nesje and Dahl, 2000). The most widely used methods involve application of a ratio to glacier area, altitude, or both. Observations of modern glaciers are used to calculate reference values for these ratios. If we assume that these ratios, and the responses of glaciers to climate change, were the same in the past as today, palaeo-ELAs can be determined by applying the modern ratio to a reconstructed glacier. If a range of either average temperature or precipitation at the palaeo-ELA can be estimated, the other can be calculated from established empirical relations. These relations describe mean accumulation season precipitation as a function of mean ablation season temperature at the ELA

(Sutherland, 1984). They exist for Norwegian glaciers (Sutherland, 1984) and have also been derived from a global glacier data set (Ohmura et al., 1992).

Empirical relations between the climatic variables and a shift in the ELA are then used to solve for palaeoclimate (Kuhn, 1981; Ohmura et al., 1992; Hooke, 2005).

Accumulation Area Ratio and Area-Altitude Balance Ratio

The two methods that are most widely used to estimate modern and palaeo-equilibrium line altitudes of non-tropical glaciers are the accumulation area ratio (AAR) and the area-altitude balance ratio (AABR) (Meierding, 1982;

Porter, 2001). They are best suited to study areas where detailed topographic information is available and glacier limits can be determined (Osmaston, 2005).

The accumulation areas of most glaciers in western North America that are in equilibrium are 50 to 80 percent of the total glacier area (Meier and Post,

1962). Recent research by Rea (2009) and Kern and Laszlo (2010) has confirmed these values. Rea (2009) reported a representative range of AARs for

North American Pacific coast glaciers of 0.50 to 0.64; Kern and Laszlo (2010) found the mean steady-state AAR of 40 debris-free, non-tropical glaciers to be

0.552 ± 0.09.

The AABR or BR was first developed by Furbish and Andrews (1984) as a refinement of the more commonly used AAR. The AABR accounts for glacier hypsometry, which is the distribution of a glacier’s area over its elevation range

(Benn and Evans, 1998). Hypsometry is presented as a plot of elevation against cumulative glacier area, increasing from zero at the glacier terminus. The AABR is calculated as:

Using mass balance data, a BR is calculated for the first equality in

Equation 1 as the ratio of the net balance gradient in the ablation area (bnb) to 37

that in the accumulation area (bnc). However, this ratio is rarely calculated, because it requires detailed long-term mass balance and elevation data. The BR calculation can be simplified, for a glacier in steady-state, with knowledge of only

hypsometry and the ELA. It is calculated as the product of the area-weighted

mean elevation in the accumulation area ) and the total area of the

accumulation area (Aac), divided by the product of the area-weighted mean

elevation in the ablation area ) and the total area of the ablation area (Aab)

(Equation 1).

A balance ratio of 3, for example, signifies that the mass balance gradient in the ablation area is three times steeper than that in the accumulation area.

Balance ratios of some modern mid-latitude glaciers have been calculated as between 2.0 and 2.2 (Furbish and Andrews, 1984). Rea (2009) calculates a value of 1.75 ± 0.71 for a global dataset and 2.09 ± 0.93 for Pacific Coast North

American glaciers.

Methods

The results presented in this chapter are based on analysis of the Mount

Baker region in the 2009 NAIP (National Agriculture Imagery Program), 1-m,

1:40,000-scale orthoimage acquired on 20-24 August 2009. The NAIP is

overseen by the Farm Service Agency of the United States Department of

Agriculture and was created mainly to maintain land unit boundaries and to

provide free 1-2-m-resolution digital orthophotos to any interested party (NAIP

Information Sheet, 2009). The second cycle of imagery acquisition began in 2009 after a transition year in 2008 (NAIP Information Sheet, 2009).

Orthophotos are aerial photographs that have been corrected for tilt, topographic displacement, and, in some cases, camera lens distortion (Paine and Kiser, 2003). Accurate measurements of distance, area, and direction can be made directly on an orthophoto, which is not the case with conventional aerial photographs (Paine and Kiser, 2003). In addition to the orthophoto, I used the

National Elevation Dataset (NED), 1/3 arcsecond (approximately 10 m), Digital

Elevation Model (DEM) (vertical resolution ±7 m) of the Mount Baker area.

2009 Equilibrium Line Altitude

The first objective of this research -- to determine the 2009 ELAs of Mount

Baker glaciers -- was accomplished through a four-step procedure outlined in the following sections and shown in Figure 2-2. I first identified and mapped glacier divides on Mount Baker and then determined the area of each glacier and plotted its hypsometric curve. Next, I mapped the areas of net mass gain and net mass loss around the mountain from the late-summer 2009 NAIP orthoimagery. Finally,

I combined these data to estimate the 2009 AAR and ELA for each major glacier on the mountain.

Glacier Divides

I mapped glacier divides primarily using the U.S. Geological Survey

National Elevation Dataset DEM of the study area. To reduce the uncertainties in the location of divides on the mountain, I objectively determined the divides with

r, including a brief explanation of each step. Model data that each step. of a brief explanation r, including were obtained from other sources are circled; whereas data that were derived or generated in this study are in this study or generated derived were that data circled; whereas sources are other from were obtained outlined with rectangles. Figure 2-2 Figure 2-2 in this chapte methods used of the model Conceptual

the DEM at a range of resolutions: 50, 75, 100, and 200 m. Glacier divides were identified on each re-sampled DEM using the Basin Analysis tool within ArcGIS, which delineates drainage basins. This tool identifies distinct basins by analyzing the results obtained using the Flow Direction tool in ArcGIS. The Flow Direction tool determines the steepest descent of each cell. The Flow Direction and Basin

Analyses tools delineate the basin of each glacier. A glacier comprises all of the steepest paths that converge into a common drainage basin leading to its terminus. Glaciers were not permitted to cross divides generated by this process unless the analytical results were demonstrably incorrect. However, some glacier divides were created within single basins to allow comparison with named glaciers in the literature. In other words, I separated glaciers that are, physically, a single entity.

The 200-m resampled DEM provided the most realistic set of divides, and these divides were used for the remainder of the analysis. The DEM at this resolution did not produce any incorrect or physically impossible boundaries. The analysis using the 200-m DEM placed Talum and Boulder glaciers within the same drainage basin, thus I created a divide between them. All other glaciers were identified as separate drainage basins, or are separated by a topographic high that physically divides them.

After the divides were chosen, I refined them to ensure they crossed contour lines at 90° angles. Finally, I manually smoothed divides in areas where pixilation produced artificial blocky divisions.

Mass Balance

After finalizing the 2009 divides, I mapped areas of ablation and accumulation for all glaciers on the 2009 NAIP orthophoto. Areas containing

visible snow were discriminated from areas of firn or ice, and I classified the

resultant polygons as either accumulation or ablation. The two surface types

were identified based on obvious differences in appearance of the materials (Fig.

2-3). Exposed glacier ice and layers of firn are dirty, have a blue-grey colour, and

a rough texture. Snow is clean, lighter in colour than ice or firn, and has a

comparatively smooth texture.

Figure 2-3 Part of Mazama Glacier on the 2009 NAIP orthoimage showing areas of ablation (glacier ice and firn) and accumulation (snow).

I produced a map showing the extents of all mapped accumulation and ablation area polygons on the mountain. I then calculated the total area of both polygon types for each glacier and determined the total, accumulation, and ablation areas for 2009.

Accumulation Area Ratio, Equilibrium Line Altitude, and Aspect

I computed the 2009 AAR of each glacier as the sum of accumulation polygon areas divided by total glacier area. This value is the proportion of total glacier area that is snow-covered in the 2009 NAIP orthoimage. To determine the corresponding 2009 ELA, I required a hypsometric curve for each glacier.

I plotted cumulative area as a function of elevation (50-m contour interval), increasing from glacier terminus, and assigned an ELA using the 2009 AAR. It should be noted that these ELAs are theoretical values and were not determined from direct field measurements or observations. I did, however, compare my results with independent, field-based estimates of AAR and net balance for

Easton, Rainbow, and Sholes glaciers made by the North Cascades Glacier

Climate Project (NCGCP).

A secondary objective of this component of the project is to determine if there is any relation between the ELA, AAR, and glacier aspect. To address this objective, I computed the average aspects of each glacier’s accumulation and ablation areas. The averages values for dominantly north-facing glaciers yielded south-facing aspects, as both an aspect of 0-22.5° and 337.5-360°, are approximately due north. A north-facing glacier may include a similar number of

aspects from both sets of values, which would result in a final average aspect of

around 180° (south). For glaciers that are known to be north-facing, I set the

average aspect to 360° to correct this problem. I then plotted ELA and AAR

values as functions of the areal aspects and assessed the results.

Steady-State Parameters

After comparing the 2009 mass balance results with those of the NCGCP,

I estimated the steady-state AARs of Mount Baker glaciers from long-term mass

balance data provided by the NCGCP and the U.S. National Park Service. The steady-state ELA that corresponds to a net balance of zero can be determined

through a linear regression of long-term ELA and net balance. An accurate

estimate of steady-state ELA requires field-based mass balance data for many

consecutive years. The data I used span at least 16 years. I assumed that these

data encompass a representative range of net balance and ELA or AAR pairs

and thus that the intercept is an accurate approximation of the hypothetical

modern steady-state AAR or ELA.

Steady-State Accumulation Area Ratio and Equilibrium Line Altitude

I performed a linear regression of the net balance data for each of the

three NCGCP-monitored glaciers (Easton, Sholes, and Rainbow). For

comparison, I also analysed North Klawatti Glacier, which is another North

Cascades glacier monitored by the U.S. National Park Service and is similar in

size to glaciers on Mount Baker. The NCGCP data are in the form of net balance

and AAR; the National Park Service data are net balance and ELA. The analyses

produced three separate estimates of the steady-state AAR and one steady-state

ELA. A steady-state AAR assumes that the accumulation area of a glacier in equilibrium occupies a fixed percentage of the total glacier area (Rea, 2009).

After determining the zero net balance AAR of each glacier, I plotted the value on the hypsometric curve to determine the corresponding zero net balance

ELA. With one exception, I used data from all available measurement years. In the case of North Klawatti Glacier, I discarded data for years when the ELA was above the maximum elevation of the glacier.

Balance Ratio

After estimating the steady-state AAR of each glacier, I estimated the area-altitude balance ratios (AABRS or BR). Three major assumptions must be made when using the balance ratio approach, or to derive the relevant equations, for a glacier in steady-state (Furbish and Andrews, 1984). First, the mass balance curves above and below the ELA can be represented as linear functions.

Second, the relation between net mass balance and elevation does not change through time. And third, changes in mass balance result in changes from stationary position to stationary position; in other words, the glacier shape responds with a discrete amount of advance or retreat. These assumptions are discussed by Furbish and Andrews (1984) and Rea (2009).

There are no long-term, detailed mass balance and elevation data sets for

Mount Baker glaciers, therefore I used the second part of Equation 1 to calculate the BRs, which requires only topographic data and a steady-state ELA:

To solve for the BR, I used a spreadsheet first proposed by Benn and

Gemmell (1997) and later refined by Osmaston (2005). An estimate of the BR is made using glacier hypsometry, an ELA, and the “Goalseek” function in Excel™

(Rea, 2009). This function uses the equations and hypsometric inputs in the spreadsheet to iteratively determine the BR that will produce the desired ELA.

Rea (2009) concluded that the contour interval can significantly affect the calculated value of an AABR and that this issue is best dealt with on a case-by- case basis. I calculated the BR of each glacier using 50-m and 100-m contour intervals to evaluate the sensitivity of the BR to contour interval.

Results

2009 Equilibrium Line Altitude

Glacier Divides

Figure 2-4 shows glacier divides on Mount Baker based on the 200-m

DEM, before (red) and after (white) manual editing. The differences between the two sets of divides are minor and reflect smoothing to ensure the divides are perpendicular to contours, and to eliminate any blocky appearance resulting from pixelation. Additional changes were made at the glacier termini to correct areas that had not been properly classified using the Basin Analysis approach. The most significant modifications were the divides of Easton, Park, and Rainbow glaciers. Other glacier divides were easily delineated with detailed elevation data

and high-resolution imagery. Basin Analysis did not accurately delineate Sholes

Glacier, but the perimeter of this glacier is easily mapped; a topographic high separates it from Mazama Glacier, its only neighbour.

Figure 2-4 Glacier divides on Mount Baker before (red) and after (white) smoothing and corrections, determined using a 200-m DEM and the Basin Analysis tool in ArcGIS. Individual basins identified in the analysis are shown in grayscale.

Mass Balance

Figure 2-5 shows ablation and accumulation areas on Mount Baker near

the end of the 2009 balance year. The distribution of snow, glacier ice, and firn in the vicinity of the ELA of each glacier is patchy and discontinuous. In many areas, there is a clear separation between snow and firn or ice, which facilitated

Figure 2-5 2009 end-of-summer accumulation and ablation areas on Mount Baker. The approximate location of the 2009 ELA is shown for each glacier.

mapping (Fig. 2-6). Several glaciers, however, have much surface debris or are

shaded in the 2009 orthophoto, which introduced uncertainty into the analysis. It

would be difficult to locate precisely the 2009 ELA from Figure 2-5. Instead, the

total of all accumulation area polygons for each glacier, and total glacier area,

were used to calculate the 2009 AARs and corresponding ELAs.

Accumulation Area Ratio, Equilibrium Line Altitude, and Aspect

Table 2-1 and Figure 2-7 present the 2009 AARs and ELAs of Mount

Baker glaciers. The results are displayed on hypsometric curves in Figure 2-7 to show how they were obtained. The 2009 ELA is the elevation that corresponds to the 2009 AAR on the hypsometric curve.

Calculated values of the 2009 AAR range from less than 0.30 (30 percent

accumulation area) for the smallest glaciers to 0.49 for glaciers larger than 2.0

km2 (Table 2-1). The two lowest AAR values are from Sholes (0.18) and Thunder

(0.28), which are the smallest glaciers on Mount Baker. The largest AAR values are associated with mid-sized glaciers - Deming (0.47), Boulder (0.48), and

Rainbow (0.49). The mid-range of 2009 AARs, 0.30-0.44, apply to a wide range of glaciers, from relatively small ones (Squak, 1.55 km2) to the largest glacier on

Mount Baker (Coleman-Roosevelt, 9.85 km2).

My AAR values are similar to field-based values calculated from NCGCP

data for that year. All the AARs are less than typical values of 0.5 to 0.8 for

steady-state western North American glaciers reported by Meier and Post (1962).

Based on my results, there is no obvious relation between glacier size and AAR, other than that between the smallest AARs and the smallest glaciers.

Table 2-1 2009 areas, elevation range, AARs, and ELAs (in metres) of Mount Baker glaciers, listed in order of decreasing glacier size.

Glacier Area (km2) Elevation range (m) 2009 AAR 2009 ELA Coleman-Roosevelt 9.85 1375/1600 – >3200 0.40 2277 Park 5.13 1320 – >3200 0.44 2210 Mazama 4.97 1470 – 2940 0.36 2140 Deming 4.77 1350 – >3200 0.47 2305 Boulder 3.47 1540 – >3200 0.48 2311 Easton 2.88 1680 – 2980 0.35 2292 Talum 2.15 1830 – 3050 0.33 2480 Rainbow 2.02 1370 – 2615 0.49 1863 Squak 1.55 1715 – 2765 0.34 2280 Sholes 0.94 1605 – 2035 0.18 1903 Thunder 0.81 1850 – 2580 0.28 2277

Table 2-2 summarizes the average aspects of the accumulation and ablation areas of Mount Baker glaciers. The aspects of the glaciers differ considerably. Most glaciers have a range of aspects that include most, if not all, compass directions.

The original average aspects calculated for Sholes and Mazama glaciers are not accurate due to the large numerical range for a north-facing glacier, from

0°-22.5° to 337.5°-360°. A glacier with an equal number of cells with north-facing aspects in both ranges produces an average value of approximately 180°, which is south. The average aspects at Sholes are 133° and 165° (south to southeast),

th an x and their values are labeled adjacent to it adjacent are labeled their values th an x and organized counter-clockwise around the mountain from Easton Easton from mountain the around organized counter-clockwise Glacier. The 2009 ELAs and AARs are marked on each curve wi each curve on marked AARs are and 2009 ELAs Glacier. The Figure 2-7 Baker glaciers, of Mount curves 2009 hypsometric

and the average aspect of Mazama Glacier’s ablation area is 165° (south); these

are clearly incorrect when the glaciers are viewed on a map (Fig. 2-1). The

correct aspects of Mazama and Sholes glaciers are north, thus they were set to

360°. The analysis appears to have produced accurate results for all other

glaciers. Most accumulation areas, on average, face east or southeast.

Table 2-2 Average aspect of the accumulation and ablation areas of Mount Baker glaciers, ranging from -1 (no aspect) to 360° (north).

Aspect (degrees) Accumulation area Ablation area Glacier ave. (min, max) ave. (min, max) Rainbow 70 (-1, 359) 80 (0, 358) Park 81 (0, 359) 114 (37, 222) Mazama 94 (-1, 359) 165 (-1, 359) Boulder 111 (-1, 359) 110 (59, 175) Talum 146 (82, 338) 126 (84, 191) Squak 155 (86, 208) 136 (27,198) Sholes 133 (-1, 359) 165 (0, 359) Easton 201 (144, 260) 188 (99, 267) Deming 223 (73, 298) 202 (42, 325) Coleman-Roosevelt 282 (-1, 360) 267 (0, 359) Thunder 297 (1, 359) 269 (174, 322)

The average aspects of the accumulation and ablation areas of individual

glaciers are similar; many differ by no more than 20°. Glaciers with average accumulation and ablation aspects that differ by less than 20°, such as Easton

and Boulder glaciers, flow directly down Mount Baker, without significant

deflection, and thus possess relatively uniform aspects. The aspects of

accumulation and ablation areas at Park and Thunder glaciers differ by

approximately 30°. These two glaciers bend slightly at lower elevations.

Figures 2-8 and 2-9 show the 2009 AAR and ELA values as functions of

the average aspects of the ablation and accumulation area for Mount Baker glaciers. 2009 areas of the glaciers are shown next to each data point. Inspection of these figures shows that there is no relationship between area and AAR or

ELA or between aspect and AAR or ELA. There may be a weak correlation between accumulation or ablation area aspect and 2009 AAR. Figure 2-8b and

Figure 2-9b show a slight overall decrease in the 2009 AAR from Rainbow

Glacier, facing east, to Mazama and Sholes glaciers, facing north. No glaciers have northeast aspects.

Steady-State Parameters

Steady-State Accumulation Area Ratio and Equilibrium Line Altitude

The results of the zero net balance AAR and ELA analyses are

summarized in Table 2-3. Analysis of the NCGCP data indicates that the zero net

balance ELA of Mount Baker glaciers corresponds to an AAR of 0.62-0.66 (Fig.

2-10). Linear regression indicates excellent fits for all data sets. Steady-state

AARs for Easton and Rainbow glaciers are approximately 0.66, and Sholes

Glacier has a long-term AAR of 0.62. Additionally, I calculated the long-term AAR

of North Klawatti Glacier (Fig. 2-1) to be 0.65.

Figure 2-8 2009 (a) ELA and (b) AAR (b) of Mount Baker glaciers plotted against the average aspect of the glacier accumulation area (from north-facing at 0° and 360°). The aspect of Sholes Glacier was corrected from its calculated value and set to 360°. Glacier area (km2) in 2009 is shown adjacent to each data point.

Figure 2-9 2009 (a) ELA and (b) AAR (b) of Mount Baker glaciers plotted against the average aspect of the glacier ablation area (from north-facing at 0° and 360°). The aspect of Mazama and Sholes Glacier were corrected from their calculated values and set to 360°. Glacier area (km2) in 2009 is shown adjacent to each data point. 56

Assuming an AAR of 0.66 for all glaciers, except Sholes, the average

steady-state ELA on Mount Baker is approximately 2018 m. If I consider only the major glaciers located on the modern cone, thus excluding Sholes and Thunder

glaciers, the average steady-state ELA is 2040 m. If I include only glaciers that

extend up to either Carmelo or Sherman craters, and thus exclude Mazama,

Squak, and Rainbow glaciers, the ELA is still higher, 2096 m. The results indicate

that steady-state ELA rises with increasing glacier headwall altitude.

Table 2-3 Modern steady-state AAR and ELA for Mount Baker glaciers listed in order of decreasing glacier area. Results for North Klawatti Glacier are also shown.

Glacier Steady-state AAR Steady-state ELA (m)

Coleman-Roosevelt 0.66 2063 Park 0.66 2000 Mazama 0.66 1965 Deming 0.66 2180 Boulder 0.66 2105 Easton 0.66 2080 Talum 0.66 2147 Rainbow 0.66 1768 Squak 0.66 2050 Sholes 0.62 1792 Thunder 0.66 2048 Average ELA 2018

North Klawatti 0.66 2130

- (1993-2010). The steady-state ELA or AAR is shown as a AAR is shown ELA or The steady-state (1993-2010). Rainbow Glacier (1984-2009) and Sholes and Easton glaciers (1990 glaciers and Easton and Sholes (1984-2009) Glacier Rainbow 2009), and net balance against ELA for North Klawatti Glacier Klawatti for North ELA against balance and net 2009), y-axis intercept. red x at the Figure 2-10 Linear regressions of net balance against AAR for AAR for against balance of net Linear regressions Figure 2-10 58

Balance Ratio

Balance ratios calculated using 50-m and 100-m contour intervals, and the difference between the two estimates, are presented in Table 2-4. The average

BR calculated with 50-m contours is larger (3.75) than that calculated with 100-m contours (3.58). The largest differences (>0.10), in order of decreasing magnitude, were obtained for Thunder, Talum, Squak, Mazama, Sholes, and

Rainbow glaciers; the smallest differences (<0.10), in order of increasing magnitude, were obtained for Deming, Park, Boulder, Easton, and Coleman-

Roosevelt glaciers. The glaciers with the largest calculated differences between the 50-m and 100-m contour BRs are the smallest five glaciers. This result is not unexpected, because any differences between the 50-m and 100-m data sets should be larger for a small area than a large one.

Discussion

2009 Equilibrium Line Altitude

Glacier Divides

I have produced a map of glacier divides that is both physically plausible and reproducible (Fig. 2-3). Previous published maps of glacier divides on Mount

Baker have been subjective and lack a rationale for delineating divides other than relating them to crevasse patterns and field observations. Nevertheless, there is some error associated with the purely analytical method that I used to locate divides. Although I tried to be as objective as possible, I was forced to introduce a divide between Boulder and Talum glaciers, where the method did not identify

one, in order to maintain consistency with previous work. The analysis did not identify the divide that I added because it is based on subjective observations of previous researchers.

Table 2-4 Steady-state AABRs for Mount Baker glaciers, listed in order of decreasing 2009 glacier area.

AABR1 Steady-state ΔAABR (100 m- Glacier 100 m 50 m ELA 50 m) Coleman/Roosevelt 2063 3.66 3.74 -0.08 Park 2000 2.79 2.81 -0.02 Mazama 1965 3.51 3.71 -0.20 Deming 2180 2.27 2.28 -0.01 Boulder 2105 4.67 4.71 -0.04 Easton 2080 3.53 3.60 -0.07 Talum 2147 5.52 5.81 -0.29 Rainbow 1768 3.11 3.21 -0.10 Squak 2050 3.85 4.06 -0.21 Sholes 1792 2.14 2.33 -0.19 Thunder 2048 4.29 5.00 -0.71 1AABR calculated using both 50-m and 100-m contours.

On the other hand, I did not separate Coleman and Roosevelt glaciers, even though they have traditionally been identified as two separate glaciers. The basin analysis did not identify a divide between the two glaciers, and there is no rock ridge or topographic high on which to base the separation. There is a precedent in the literature for separating these glaciers, but it was not necessary

for my analysis, because they share a forefield and lack long-term mass balance data.

The basin analysis produced unnaturally blocky boundaries between glaciers. The smoothing that I did to eliminate this problem had no significant impact on the locations of the divides.

Mass Balance

The 1-m orthoimage is probably not a major source of error in my mass balance analysis. Most error comes from the discrimination of accumulation and ablation areas on the orthoimage. Bare ice and clean snow are easily distinguished, but problems arise where both ice and snow are dirty, or where they grade into each other. Additionally, many of the ablation areas on Mount

Baker include significant debris cover, which complicates identification of glacier margins. Another possible source of error is the assumption that the orthoimage depicts the end of the 2009 melt season. The aerial photographs, on which the orthoimage is based, were taken from August 20 through 24, 2009, near the end of the melt season. Although it is possible that melt continued for another several weeks following acquisition of the NAIP imagery, the additional ablated areas would not alter the conclusions presented in this chapter.

Patterns of ablation and accumulation on Mount Baker glaciers are spatially discontinuous (Fig. 2-5), consequently it was not possible to approximate the 2009 ELA visually. There is much complexity in the distribution of ablation and accumulation near the ELA of a glacier, and many small patches

of ablation are evident even in the upper accumulation areas of most of the glaciers (Fig. 2-6). Consequently, there is no specific elevation at any glacier below which there is only ablation and above there is only accumulation. Easton,

Squak, Deming, and Mazama glaciers have the most complex patterns of ablation and accumulation; the most regular transitions occur on Coleman-

Roosevelt, Boulder, and Park glaciers. Even in the case of those glaciers, however, it is not possible to estimate an ELA visually.

Elevation is not the only control on accumulation and ablation; shading, aspect, and relief can be equally important. Some combination of these factors produces the patchiness evident in Figure 2-5.

An interesting research question is whether localized patches of ablation and accumulation are in the same places each year or are more-or-less randomly distributed through time. Some evidence suggests that the patches may persist year to year (Mauri Pelto and Jon Riedel, personal communications,

2010). The patterns might be expected to persist as long as the topography and form of the glacier surface do not significantly change. This question could be addressed with repeat high-resolution vertical imagery taken at the end of several successive melt seasons.

My methods supplement, but do not replace, field-based measurement programs. Regular acquisition of NAIP coverage of Cascade volcanoes is unlikely, as glacier monitoring is not the purpose of the NAIP. My methods, however, are worth developing for several reasons. First, they are cost-effective

– they do not require field work, rather only access to ArcGIS, NAIP 62

orthoimagery, and elevation data. Also, if acquired at the end of the ablation

season, the high-resolution imagery provides accurate results. With this imagery,

it is possible to analyse all glaciers in a region, rather than only a few, as is

typically the case with traditional field glacier mass balance programs. Glacier mass balance has been assessed from imagery for several years (Meier and

Post, 1962; Furbish and Andrews, 1984), but only recently has it become possible to accurately measure and analyse the patterns of accumulation and ablation.

Accumulation Area Ratio, Equilibrium Line Altitude, and Aspect

AAR values on Mount Baker in 2009 are low and the corresponding ELAs

are high (Table 2-1), indicating a negative balance year. On average, the

accumulation areas of Mount Baker occupied only 37 percent of total glacierized

area. If I assume that a glacier in equilibrium has an AAR of at least 0.60, all

Mount Baker glaciers experienced a net mass loss in 2009. According to NCGCP

records, the AARs at Easton, Rainbow, and Sholes glaciers in 2009 were the

lowest in the period of measurement (19-25 years).

North Cascades glaciers are not in equilibrium with the current climate.

Data collected over the past 25 years show increasingly negative net balance

and cumulative balance (Pelto, 2006). I observe a continuation of this trend in my

2009 mass balance analysis.

My 2009 AAR values are similar to the NCGCP field-based values,

confirming that the method I used yields reliable ELA estimates (Table 2-5). The

only major discrepancy between my results and those of NCGCP is Rainbow

Glacier (Table 2-5). The difference between the two results may be due to the maximum elevation chosen for Rainbow Glacier. The NCGCP places the upper margin of the glacier at a much lower elevation than I did with my methods. My

AAR for Rainbow Glacier (0.49) is likely more accurate, as it is similar to the other AARs I calculated for Mount Baker. It is the largest of all the glaciers on

Mount Baker, but it is not anomalous; Deming (0.47), Boulder (0.48), and Park

(0.44) glaciers have only slightly lower AARs.

Table 2-5 2009 AARs of three Mount Baker glaciers based on this study and the field-based measurements of the North Cascades Glacier Climate Project (NCGCP).

Sholes Easton Rainbow

NCGCP 0.15 0.38 0.36 This study 0.18 0.35 0.49

The methods that I used here, although only attempted for one year, may be useful for better defining future annual net balances of Mount Baker glaciers.

It is possible to use annual ELA or AAR measurements to estimate net balance, because these parameters have been shown to be closely related (Benn and

Evans, 1998; Nesje and Dahl, 2000). If long-term data from North Cascades glaciers are used to establish a relation between net balance and AAR, and if this relation does not change over time, future net balance estimates can be made using only the AAR. Hock et al. (2007) proposed a version of this approach based on work by Dyurgerov (1996) at Storglaciären, a 3.2 km2 Swedish glacier

that has been monitored continuously since 1945-1946. They concluded that this approach has the potential for significant improvement in mass balance studies, once calibrated. They further concluded that it was possible to further simplify the method by substituting long-term net balance and ELA data for detailed mass balance and ELA measurements made over the course of a single year.

Efforts are being made by the NCGCP to establish a robust quantitative relationship between AAR and net balance. Using 20-26 years of AAR and net balance measurements on Easton, Rainbow, and Sholes glaciers, Mauri Pelto of the NCGCP (personal communication 2011) has established the following relation between annual balance and AAR:

0.65209/0.000159 (3)

where ba is the annual balance in millimetres of water equivalent, and AAR is the accumulation area ratio at the time of balance. The 2009 balance values for

Mount Baker glaciers calculated using this equation are shown in Table 2-6. The results are consistent with the 2009 NCGCP mass balance results and mass balance measurements made elsewhere by the NPS. The average calculated annual balance for all Mount Baker glaciers in 2009 is -1746 mm w.e. using

Equation 3; this value is close to the 2009 NPS balance of nearby North Klawatti

Glacier of -1830 mm w.e. (Fig. 2-1). This approach can be easily implemented to facilitate large-scale studies of North Cascades glacier mass balance, with continued glaciological monitoring to improve the accuracy of Equation 3. I

recommend that this method be further developed to supplement annual mass balance studies to glaciers within the region that are not monitored.

Table 2-6 AARs and corresponding mass balances for Mount Baker glaciers in 2009, listed in order of increasing glacier area. Mass balances measured by the NCGCP for three glaciers are also shown.

† * Glacier 2009 AAR 2009 ba (mm) 2009 ba (mm) Thunder 0.28 -2340 Sholes 0.18 -2969 -2680 Squak 0.34 -1963 Rainbow 0.49 -1019 -1980 Talum 0.33 -2026 Easton 0.35 -1900 -2060 Boulder 0.48 -1082 Deming 0.47 -1145 Mazama 0.36 -1837 Park 0.44 -1334 Coleman-Roosevelt 0.40 -1585 Average 0.37 -1746 † ba calculated from Equation 3 (Mauri Pelto, personal communication, 2011). * ba measured by the NCGCP.

There is general agreement between my calculated mass balances and those measured at three glaciers by the NCGCP, with one exception. The difference in mass balance at Sholes and Easton glaciers are small: less than

300 mm w.e. In the case of Rainbow Glacier, however, there is a significant difference between the calculated and measured balances: 961 mm w.e. My

AAR of 0.49 for Rainbow Glacier is likely the reason for this difference; the 66

NCGCP estimate of the 2009 AAR is 0.36 (see Table 2-5). To obtain the NCGCP

balance value using Equation 3, however, requires an even smaller AAR of 0.34.

Regardless of the numerical values, both my and the NCGCP work show that

Rainbow Glacier experienced a negative balance year in 2009, with an AAR less

than 0.60.

The 2009 ELAs do not differ greatly around the mountain: the ELAs of

eight of the 11 glaciers are within 180 m of one another. I also found no

significant relation between average aspect and 2009 ELA, probably because of

the variability of the aspects of individual glaciers (Table 2-2).

The 2009 mass balance map (Figure 2-5), however, may show some

west-east differences in ablation. Glaciers on the west side of Mount Baker have

smoother ablation areas than glaciers on the east; the patchiest ablation areas

are on glaciers on the southeast side of the mountain (Fig. 2-4). There is a weak

relation between glacier aspect and 2009 AAR. The average 2009 AAR for all

glaciers with accumulation and ablation areas that face north, northwest, and

west are, respectively, 0.29 and 0.31. These values are about 30 percent less

than the average values for all glaciers with accumulation and ablation areas that face east, southeast, south, and southwest. More data are required to determine if there is a significant difference between mass balance on west-to-north- and east-to-southwest-facing glaciers.

Glacier hypsometry is most likely an important factor in the position of the

ELA around Mount Baker. The hypsometric curve of each glacier is unique. By

using the 2009 AAR, which relates an ELA to the hypsometric curve, I am able to

better compare glaciers and detect differences in net balance trends.

Steady-State Parameters

Steady-State Accumulation Area Ratio and Equilibrium Line Altitude

The steady-state AAR of Mount Baker glaciers, estimated from NCGCP

data, is between 0.62 and 0.66. The zero net balance AAR for North Klawatti

Glacier, based on U.S. National Park Service data, is 0.66. Meier and Post

(1962) found that balance gradients in western North America are steepest on

glaciers closest to the Pacific Ocean; the steep balance gradients of North

Cascades glaciers result in a steady-state AAR that is greater than 0.50. If net balance is a linear function of elevation at these glaciers, and their areas are distributed evenly about their median elevations, an AAR of only 0.50 would hypothetically be required for steady-state conditions (Meier and Post, 1962).

Due to the steepness of the net balance gradients of North Cascades glaciers, a relatively high proportion of accumulation area is required to maintain equilibrium conditions, resulting in steady-state AARs between 0.62 and 0.66.

My steady-state AARs are slightly larger than the value of 0.58 for South

Cascade Glacier (Meier and Post, 1962) (location shown in Fig. 2-1). They are in

general agreement with previous estimates of steady-state AARs for North

American west coast glaciers of 0.50-0.80 (Meier and Post, 1962; Kern and

Laszlo, 2010). My AARs fall slightly above the range of reference values for west

coast North American glaciers of 0.50-0.64 (average 0.57) reported by Rea

(2009).

My steady-state ELA estimates, based on the steady-state AAR glacier

hypsometry, range from 1768 m asl at Rainbow Glacier to 2180 m asl at Deming

Glacier. To capture the full range of mass balances that a glacier experiences,

the zero net balance ELA should be estimated from data spanning many years.

The data I used span the period of mass balance measurements on Cascade

volcanoes -- between 19 and 25 years.

Kovanen and Slaymaker (2005) estimated the steady-state at ELA

Deming glacier to be 2155 m asl, based on an AAR of 0.60. An AAR of 0.60, if applied to my hypsometric curve for Deming Glacier, gives a much higher steady-state ELA of 2215 m asl. The 60 m difference between the two estimates is likely caused by differences in the assigned glacier terminus elevation;

Kovanen and Slaymaker (2005) place the terminus of Deming Glacier at 1210 m asl, whereas I place it at 1300 m asl. Deming Glacier does not extend below

1300 m asl in the 2009 NAIP imagery. My calculated steady-state ELA of 2180 m asl assumes an AAR of 0.66, which is based on the long-term mass balance data provided by the NCGCP and NPS.

Thomas (1997) estimated the steady-state ELA of Easton Glacier assuming an AAR of 0.65. His estimates are 2015 m asl for the main lobe of

Easton Glacier and 2095 m asl for the section that terminates on the shelf to the

east. The average of his values (2055 m asl) is comparable to my estimate of

2080 m asl, even though our studies are separated by more than a decade and 69

there is a 50-m difference between my elevation of the Easton terminus (1650 m asl) and that cited by Thomas (1600 m asl). Pelto and Hartzell (2004) estimated the mean ELA at Easton Glacier to be 2050 m asl based on data acquired between 1984 and 2002. Their estimate is derived from the same NCGCP mass balance data that I used, but I included an additional seven years of data. The two most negative net balance years for Easton Glacier occurred after the Pelto and Hartzell (2004) measurement period, in 2005 and 2009. These negative years raised the elevation of the steady-state ELA from that reported by Pelto and Hartzell (2004) to the value I report.

Changes in terminus location and glacier area complicate steady-state

ELA estimates and are difficult to account for in long-term mass balance studies.

Most of the differences between my ELA estimates and those of previous researchers are likely rooted in these changes. Glaciers are constantly changing, but, as noted by Rea (2009), changes in glacier area over time are not commonly considered in long-term mass balance studies. Failure to consider these changes may lead to significant errors in calculations based on the hypsometric curve, especially for small glaciers. The terminus locations and areas of North

Cascades glaciers, and thus their hypsometries, have undoubtedly changed over the NCGCP and NPS monitoring periods. I do not explicitly deal with this problem, but I do recognize the potential error. It is partially accounted for by using a steady-state AAR in place of an ELA. I assume that, even though the glaciers are not in a steady state, an AAR of 0.60-0.66 for steady-state conditions is still appropriate when applied to their 2009 perimeters. This approach is more

appropriate than using an actual ELA value, because it relates the steady-state

ELA to mapped glacier area and extent, and the former changes with the latter.

Kern and Laszlo (2010) recommend that steady-state AARs between 0.37

and 0.61 be applied to glaciers in northwest North America with areas between

0.1 and 4.0 km2. These values are lower than the AARs I determined for Mount

Baker glaciers of that size. Sholes Glacier (0.94 km2), for example, has an

observed long-term steady-state AAR of 0.62. Kern and Laszlo (2010) estimate

the steady-state AAR as a logarithmic function of glacier size:

0.062 0.479 4

Equation 4 returns a steady-state AAR of 0.48 for Sholes Glacier. This value is

lower than the AAR of 0.62 I calculated based on NCGCP mass balance data

from 1990 to 2002. Similarly, Equation 4 gives an AAR of 0.50 for North Klawatti

Glacier, which has an area of 1.34 km2. In contrast, the long-term mass balance

data (1993-2009) indicate a steady-state AAR of approximately 0.65. In these

cases, assuming an approximate reference value of 0.60 to 0.66 for all glaciers

yields a more realistic result than Equation 4.

The sensitivity of the calculated ELA to changes in the AAR differs among

Mount Baker glaciers. An increase in the AAR of 0.10, for example from 0.60 to

0.70, produces a range of results, depending on glacier hypsometry. ELAs calculated with an AAR of 0.60 are, on average, 64 m higher than those

calculated with the larger AAR; but the difference ranges from 26 m at Sholes

Glacier to 110 m at Park Glacier.

Balance Ratio

Balance ratio calculations require detailed knowledge of glacier

hypsometry and an accurate steady-state ELA. Mount Baker glaciers have a

large range of steady-state ELAs and hypsometries, resulting in a range of BR values (Table 2-4). The average AABR for all glaciers at Mount Baker is 3.57

(100-m contour interval) and 3.75 (50-m contour interval). Because the hypsometry of small glaciers is more sensitive to climate change than larger

ones, I excluded the five smallest glaciers (<2.5 km2) from the analysis and

recalculated an average balance ratio of 3.41 (100 m) and 3.48 (50 m).

The BR of Talum Glacier (5.52-5.81) is anomalously large for Mount Baker

glaciers; the closest values are 4.67-4.72 for Boulder Glacier. Talum Glacier has

a complex fragmented geometry and an unusual hypsometry: a wide terminus

and a narrow steep accumulation area with much bare rock. The narrow

accumulation area must have a higher mass balance gradient to compensate for

the wide ablation area below. Boulder and Coleman-Roosevelt glaciers also have

larger-than-average AABR values, with large rocky areas near their headwalls

that fragment their accumulation areas.

My average BR for Mount Baker glaciers is similar to that calculated for

North Klawatti Glacier (Fig. 2-1) based on NPS monitoring data. I obtained long-

term net balance and ELA data for North Klawatti Glacier from NPS for the period

1993-2009. Three years of these data were discarded because of measurement

errors, and the average net balance was calculated for the remaining 13 years of

data. The average net balance over these years is -0.38 m w.e. (Fig. 2-11). By

approximating the net balance curves in the ablation and accumulation areas as linear functions (steady-state ELA = 2129 m asl), I calculated a BR of 3.7. I calculated a BR of 1.9 for North Klawatti Glacier using the Osmaston (2005) spreadsheet and the same ELA. The reason for the discrepancy in the results obtained with the two methods is uncertain; I may not have been correct in approximating the net balance curves of North Klawatti Glacier as linear functions. There may also be significant errors in the North Klawatti long-term balance or hypsometric data that I used.

My value of 3.7 for the BR of North Klawatti Glacier compares to values of

4.33 (100-m contours) and 5.74 (50-m contours) calculated by Rea (2009) for nearby South Cascade Glacier using contour data provided by the World Glacier

Monitoring Service (WGMS) and the modified Osmaston (2005) spreadsheet.

Rea (2009) also calculated BRs of 1.61 (100-m) and 2.01 (50-m) for South 73

Cascade Glacier with contours derived from the 2007 annual report on South

Cascade by Bidlake et al. (2007). These results are closer to the value of 2.3 calculated by Furbish and Andrews (1984) using the mass balance approach.

The reason the large difference between the values calculated using the WGMS data and the Bidlake et al. (2007) contours is unknown; one set of contours may be incorrect.

There are significant differences in the BRs of North Klawatti and South

Cascade glaciers calculated using different methods and sets of contours, which is not reassuring for a researcher applying this approach in palaeo-glacier work.

Because of the large uncertainties in the BR calculations and an inability to independently verify their accuracy, I consider a reference steady-state AAR to

be more accurate than a reference BR. If the BR method is to be used in palaeo- glacier studies, it would probably be best to use a regional average, as it encompasses the range of BRs in an area.

My average BRs are larger than those previously reported for maritime mid-latitude glaciers. Rea (2009) calculates an average BR for maritime mid- latitude glaciers of 1.90, which is nearly identical to Furbish and Andrew’s (1984) average of 1.88. These estimates are based on calculations made for a large number of coastal Alaskan (Furbish and Andrews, 1984) and Canadian (Rea,

2009) glaciers. Their values, however, may not be directly comparable with my estimates because of the different climatic environments. Sholes Glacier has a low BR of 2.2, but it is so small that I have excluded it in the average BR result.

Deming Glacier, with a BR of 2.3, is the only glacier in my study that is similar to 74

the values reported in the literature. The next-lowest BR I calculated is for Park

Glacier, which is outside the range of values presented by Furbish and Andrews

(1984) and Rea (2009). Deming and Park glaciers have long thin tongues below wide steeper ablation areas; they also possess the largest elevation ranges of all

glaciers on Mount Baker.

Rea (2009) refined his average BR for maritime mid-latitude glaciers by

subdividing the results into several regional values. His average BR for glaciers

in northwest North America is 2.09 +/- 0.93, which is closer to my values. Only

three of my estimates, however, fall within this range. Rea’s regional estimate,

although more representative of Cascade glaciers than Furbish and Andrews’

(1984) estimate, includes only one glacier in Washington State (South Cascade

Glacier). The next-closest glacier in his data is Sentinel Glacier in Garibaldi

Provincial Park in coastal British Columbia, about 170 km northwest of Mount

Baker.

The Alaskan glaciers studied by Furbish and Andrews (1984) have high

ELAs relative to similar-size glaciers on Mount Baker. Balance ratios are thought

to increase from high latitudes towards the tropics (Benn and Gemmell, 1997;

Benn and Lehmkuhl, 2000), which may partly explain the difference between

Furbish and Andrew’s (1984) values and mine. Mount Baker glaciers probably

experience higher summer ablation than coastal glaciers at higher latitudes, thus

their balance ratios should be greater on average. In addition, temperate maritime glaciers have higher rates of mass turnover than similar glaciers at the

same latitude but at more inland locations. Rea (2009), for example, reported a 75

regional average BR for glaciers in the Rocky Mountains of 1.11 +/- 0.1, which is much lower than his average of 2.09 for coastal glaciers. Differing moisture sources and ablation rates likely explain this difference.

A potential source of error in the BR calculations is the inputs used in the

Osmaston (2005) spreadsheet. The original Osmaston (2005) and Benn and

Gemmell (1997) spreadsheet programs use 100-m contour intervals to calculate balance ratios, but any contour interval can be used. The difference between my

BRs calculated with 50-m and 100-m contours is generally small, but I recommend, as does Rea (2009), that the highest resolution contours available be used.

Conclusions

The method I outline in this chapter offers the advantages of providing estimates of mass balance for all glaciers on Mount Baker and of being based on spatially continuous data. It is not feasible to conduct field mass balance studies at a large number of glaciers. In addition, measurements can only be made at a relatively small number of locations on an individual glacier, raising questions about the accuracy of the resulting mass balance estimates.

My mass balance analysis indicates that 2009 was a negative balance year. The results are confirmed, in part, by glaciological work completed by the

North Cascades Glacier Climate Project.

Given the spatially complex pattern of ablation and accumulation on

Mount Baker, the accumulation area ratio is a more meaningful metric than the

equilibrium line altitude for describing the mass balance of glaciers on the

mountain. I find that no single elevation on a glacier separates net accumulation

from net ablation. To optimize an AAR-based mass balance monitoring program,

the glacier area should be re-photographed and mapped at the end of each

ablation season.

The ELA on Mount Baker shows little relation to the aspect of either the

accumulation or ablation areas of glaciers. There may be a weak relation

between aspect and AAR, but this conclusion must be tempered because my

data are limited.

Analysis of long-term mass balance data at Mount Baker and nearby

North Klawatti Glacier indicates a steady-state AAR of 0.60-0.70. The steady-

state AAR for glaciers on Mount Baker is between 0.62 and 0.66. Balance ratios

calculated for Mount Baker glaciers using the steady-state AAR with 100-m

contours are between 2.14 and 5.52; calculated BRs with 50-m contours are

larger. Average BRs for Mount Baker glaciers larger than 3 km2 are 3.41 (100-m)

and 3.48 (50-m). These averages are similar to the BR of 3.7 obtained using long-term mass balance measurements at North Klawatti Glacier. I calculated

BRs of less than 2.5 for only two Mount Baker glaciers, Deming and Sholes.

My balance ratios are larger than those reported in the literature. A

possible reason for the difference is that the BR calculation is sensitive to the

topographic information and steady-state ELA used as inputs. A change of

contour interval or mass balance data can significantly change the calculated BR.

Even using the same data sources and steady-state AAR, I found that the BRs of 77

the 11 glaciers on Mount Baker are very different. Consequently, I conclude that the steady-state AAR method is more accurate and should be used in palaeo- glacier studies, particularly when the modern BR of the studied glacier is unknown.

CHAPTER 3 LITTLE ICE AGE EQUILIBRIUM LINE ALTITUDE RECONSTRUCTIONS FOR MOUNT BAKER GLACIERS

Abstract

Glaciers on Mount Baker were much more extensive during the Little Ice

Age than today. The maximum Little Ice Age extent of these glaciers is marked

by large lateral moraines and trimlines on steep rock slopes. Based on these

features, I mapped the approximate maximum Little Ice Age extent of all glaciers

on Mount Baker. I then calculated the maximum Little Ice Age ELA (equilibrium

line altitude) depression for four of the glaciers: Coleman-Roosevelt, Deming,

Easton, and Boulder. I used the spreadsheet model of Benn and Hulton (2010) to estimate, for each of the four glaciers, present-day ice thickness, reconstructed ice thickness, and reconstructed glacier hypsometry. I compared three approaches to estimate the Little Ice Age ELA depression: an AAR (accumulation area ratio) of 0.66, an assumed AABR (area altitude balance ratio) of 2.2, and

AABR calculated individually for each glacier. I then reconstructed climate for peak Little Ice Age conditions at Mount Baker using the ELA depression estimates and two scenarios, one that assumes no change in precipitation and another that estimates changes in both precipitation and temperature.

My estimates of present-day ice thicknesses are similar to estimates

derived using direct glaciological methods, and my Little Ice Age glacier

reconstructions are similar to those made by previous researchers. The

calculated AABRs and an assumed AAR of 0.66 yield similar results. I estimate

an average ELA lowering of approximately 300 m for Mount Baker glaciers at the

maximum of the Little Ice Age, which likely resulted in part from an average depression of summer air temperature of 2.0°-2.1°C.

Introduction

Rationale

Glaciers respond to changes in climate by thickening and advancing, or by

thinning and retreating. Thus, contemporary and past glacier fluctuations provide

proxies of climate change. Conversely, scientists are interested in studying the

response of glaciers to recent and predicted future climate warming (Benn and

Evans, 1998). Also of interest are the relative roles played by temperature and

precipitation in glacier response to climate change.

Alpine glaciers in most mountain ranges around the world achieved their

maximum Holocene extent during the Little Ice Age, which began early in the last

millennium and culminated in the eighteenth and nineteenth centuries (Grove,

1988). The maximum extent of many Little Ice Age glaciers is recorded by

conspicuous and commonly large lateral and terminal moraines and by trimlines.

By mapping these landforms, it is possible to reconstruct the former, more

extensive glaciers and estimate their equilibrium line altitudes (ELAs), which in

turn can be used to reconstruct past climate. Glaciers on Mount Baker were near,

or had reached their maximum Little Ice Age extents in the eighteenth and

nineteenth centuries and began to retreat early in the twentieth century (Burke,

1972; Heikkinen, 1984; O’Neal, 2005; Easterbrook, 2007).

Objectives

The main objective of this study is to reconstruct ELAs of glaciers on

Mount Baker at their maximum Little Ice Age extents. I use the reconstructed

ELAs to determine ELA depression from today and to derive estimates of past climate. My approach involves the use of empirically derived glacier hypsometries, accumulation area ratios (AARs), and balance ratios (BRs). The resulting estimates of Little Ice Age ELA depression on Mount Baker are improvements over those previously reported in the North Cascades.

A secondary objective of my research is to estimate modern and maximum Little Ice Age thicknesses of Mount Baker glaciers. Ice thicknesses, which were required for calculating ELA depressions, may be useful to glaciologists attempting to model future and past volume and mass losses of

similar-sized mid-latitude coastal glaciers.

Mount Baker and Its Glaciers

Mount Baker is an active stratovolcano in the North Cascades of

Washington State (Fig. 3-1). It is located in a temperate maritime environment,

has a summit elevation of 3285 m asl, and is mantled by nine major glaciers; two

small glaciers are located on slopes off the main massif (Fig. 3-1). Snow

accumulates on Mount Baker and elsewhere at moderate and high elevations in

the Cascades from October through April; the ablation season is from May

Figure 3-1 Mount Baker and its glaciers. The map below shows the locations of Mount Baker, South Cascade Glacier, North Klawatti Glacier, and Mount Rainier.

through September (Burbank, 1982; Pelto, 2006). Long-term glaciological

measurements and other observations indicate that North Cascades glaciers, including those on Mount Baker, have been in disequilibrium for at least two decades and have significantly thinned and retreated since the early 1980s

(Pelto, 2006).

The Little Ice Age at Mount Baker

The Little Ice Age moraines of six glaciers on Mount Baker have been mapped and dated: Coleman and Roosevelt glaciers (Heikkinen, 1984); Deming

Glacier (Long, 1953; Fuller, 1980); Easton Glacier (Long, 1953; Thomas, 1997;

O’Neal, 2005); Boulder Glacier (Long, 1955; Burke, 1972; O’Neal, 2005); and

Rainbow Glacier (Fuller, 1980; O’Neal, 2005). Based on these studies, the following conclusions can be drawn about Little Ice Age glacier activity at Mount

Baker (Fig. 3-2): glaciers approached and achieved their maximum Little Ice Age extents between the twelfth and nineteenth centuries; they began to retreat during the late nineteenth century; they retreated at an accelerated rate early in the twentieth century; they advanced between the 1940s and 1980s; and they thinned and retreated over the past three decades (Harper, 1993; Thomas, 1997;

O’Neal, 2005; Pelto, 2006). Other climate proxies support this record. Graumlich and Brubaker (1986) concluded from dendroclimatic evidence that climate in the

North Cascades warmed, and winter precipitation decreased, in the second half of the nineteenth century.

Figure 3-2 Summary of published information on Little Ice Age glacier limits on Mount Baker. See Tables 1-3 and 1-4 for sources of information. Glacier margins are from the 2009 NAIP 1-m orthoimagery, and elevation data from the U.S. Geological Survey National Elevation Dataset.

Equilibrium Line Altitude Depression

Equilibrium line altitude reconstructions can be used to infer past climate where no meteorological data are available. The ELA is the approximate elevation on a glacier where there is no net gain or loss of mass over a balance year; in other words, it is the elevation at which the net balance is zero (Meier, 84

1962). The ELA and glacier mass balance are controlled mainly by air temperature and precipitation (Benn and Evans, 1998). Successive ELA measurements are a simple way of expressing adjustments in glacier mass balance, and by inference climate, over time. A rise in ELA signals mass loss and glacier recession, whereas a depression in ELA indicates mass gain and glacier growth (Bennett and Glasser, 2009).

To accurately reconstruct former ELAs, a researcher must assume that the glacier is in equilibrium or steady state, meaning that its mass is constant over a lengthy period (Meier, 1962). Glaciers may not exist in a steady state for long, but the assumption must be made to estimate the ELA of a former glacier.

At the peak of the Little Ice Age, when large moraines were constructed beyond present glacier margins, it is reasonable to assume that the palaeo-glaciers changed little over periods of perhaps many decades and thus were approximately in equilibrium. To calculate the ELA depression of a palaeo- glacier, the modern steady-state ELA must be determined or assumed. Modern steady-state ELAs are calculated from long-term mass balance data, or by simply assuming an accumulation area that occupies a specific proportion of total glacier area in steady state.

The difference between a reconstructed and modern steady-state ELAs is the ELA depression or rise. The difference in climate over the period can then be estimated by using empirical relationships between climate and ELA.

Methods of Equilibrium Line Altitude Reconstruction

Several methods are available to reconstruct the ELA of present-day and former glaciers. The two most commonly used methods, where detailed elevation data and the outlines of former glaciers are available, are the accumulation area ratio (AAR) and balance ratio (AABR or BR) methods (Meierding, 1982; Rea,

2009). In both cases, steady-state conditions must be assumed to successfully calculate an ELA.

The simpler of the two widely used methods is the AAR; it requires only a pre-chosen value, between 0 and 1, and glacier topography. The ELA is defined as the contour that divides a glacier into accumulation and ablation areas. The

AAR is the ratio of the accumulation area to the total glacier area. For example, if the AAR is 0.65, 65 percent of total glacier area is above the ELA. Most glaciers in western North America in steady state are assumed to have AARs between

0.50 and 0.80, based mainly on the work of Meier and Post (1962). The ELA for a specific AAR can be readily determined from a plot of a glacier’s hypsometry, which is the distribution of a glacier area over its elevation range (Benn and

Evans, 1998).

The BR method is a refinement of the AAR technique. It relates ELA to glacier area, elevation range, and mass balance gradients (Osmaston, 1975;

Furbish and Andrews, 1984; Benn and Gemmell, 1997; Rea, 2009). Because the

BR method uses more information that is specific to an individual glacier, it is thought to yield more precise estimates of ELA than the AAR method. Defined strictly in terms of mass balance, the BR is the ratio of the net balance gradient in

the ablation area (bnb) to the net balance gradient in the accumulation area (bnc)

(Furbish and Andrews, 1984; Rea, 2009):

Net balance gradients are difficult to determine accurately and must be based on steady-state conditions. That is, to be useful for ELA reconstruction, bnb

and bnc must be the net balance gradients of a glacier in equilibrium. A simpler

method for calculating the BR is described by Furbish and Andrews (1984); it is

based on the relation between balance gradients and geometric requirements for

a glacier that is in steady-state. It can be expressed as:

where is the area-weighted mean elevation of the accumulation area (ac) or

ablation area (ab), and A is the total area of the accumulation and ablation areas.

is a positive value above or below the ELA in metres, such that a contour band

far from the ELA accounts for significantly greater accumulation or ablation than

one close to it (Rea, 2009). The derivation of this relation and how it is used to

calculate BRs are detailed in Furbish and Andrews (1984) and Rea (2009). The

value of the balance ratio in Equation 2 is closely related to the ELA: a rise in

ELA will reduce Aac, and increase Aab, in effect decreasing the BR. The ELA is

calculated by preselecting a BR and applying it to the reconstructed glacier

hypsometry in order to calculate the elevation that satisfies Equation 2. This calculation is complex and tedious by hand, but has been simplified with the use 87

of a spreadsheet developed by Benn and Gemmell (1997) and modified by

Osmaston (2005). I calculated palaeo-ELAs using the Osmaston (2005) version, because it can be customized to meet individual needs.

Palaeo-Glacier Reconstructions

If moraines and trimlines are well preserved, the outline of a former glacier can be mapped relatively easily. Palaeo-glacier hypsometry, however, is far more challenging to reliably reconstruct. The surface contours of former glaciers typically must be approximated from current ice surfaces. Although this approach is subjective, the results must produce ice thicknesses that are in compliance with glacier flow laws (Paterson, 1994)

I reconstructed glaciers on Mount Baker using a modified version of the

Benn and Hulton (2010) Excel spreadsheet. Required input includes shear stress, step length, and a shape factor. With the necessary user-defined inputs, the spreadsheet iteratively calculates corresponding ice thicknesses along a centreline profile for each step based on a perfectly plastic glacier model. The spreadsheet calculates ice surface elevation at step i+1, hi+1,:

√ 4 2

In this equation,

∆ ℎ

where B is the bed elevation, H is ice thickness at the previous step, Δx is step-

length, τγ the yield stress, f is the shape factor, ρ is the density of glacier ice, and

g is the acceleration due to gravity. The subscript i refers the value of a parameter for the previous step, and i+1 is for the step being calculated (Benn and Hulton, 2010).

This model assumes the glacier ice behaves as a perfectly plastic material, meaning that the ice will deform only if stress reaches a critical value, known as the yield stress (Paterson, 1994). If the assumption of perfect plasticity is valid, the glacier surface profile will adjust continuously until the yield stress is reached (Benn and Hulton, 2010).

Equilibrium Line Altitude-Based Climate Reconstructions

Two common approaches are used in ELA-based climate reconstructions.

One approach assumes that changes in precipitation are negligible and that glacier regimen is primarily controlled by summer temperature. In some cases, changes in precipitation have had little or no effect on the ELA, but in many

others precipitation may have an equal or larger effect on glacier regimen than

temperature. In the latter cases, it commonly is difficult to disentangle the effects

of temperature and precipitation on observed or inferred changes in ELA. The

second approach incorporates some range of assumed changes in winter

precipitation and ablation season temperatures into a mass balance-based

calculation.

Results from previous work presented in Table 3-1 indicate, in the case of

North Cascade glaciers, that only large changes in precipitation have a

significant impact for an ELA depression of 160 m, which is within the calculated

range of ELA changes for these glaciers during the Little Ice Age (Burbank, 1981;

Thomas, 1997). In contrast, changes in precipitation may have played a larger

role in the case of Pleistocene ELA depressions (e.g., 900 m in Table 3-1; Porter,

1977). In the case of a 900-m ELA depression, an increase in precipitation of 20 percent reduces the change in mean ablation season temperature from -5.6 to -

4.6 °C (Table 3-1).

Table 3-1 Temperature reductions for different increases in precipitation assuming ELA depressions of 900 m and 160 m, 30 km west of the North Cascades crest (Porter, 1977) and at Mount Rainier (Burbank, 1982).

Annual ΔT (°C) Ablation season ΔT (°C) ΔELA = 900 m ΔELA = 900 m ΔELA = 160 m Increase in precipitation (%) Porter (1977) Porter (1977) Burbank (1982) 0 -4.2 -5.6 -0.92 7 -4.0* -5.2 -0.88 20 -3.5 -4.6 -0.77

* Value calculated based on Porter (1977)’s data.

Methods

The methods section of this chapter comprises two subsections. In the first subsection, I describe how I determined hypsometries of maximum Little Ice

Age glaciers and ELA depressions on Mount Baker. In the second subsection, I explain how I reconstructed climate. Figure 3-3 is a flowchart that summarizes my methodological approach.

Figure 3-3 Conceptual model of the methods used in this chapter, including a brief explanation of each step. Model data that were obtained from other sources are circled, whereas data that are derived or generated in this study are outlined with rectangles.

Glacier Reconstructions

I reconstructed the maximum Little Ice Age glaciers at Mount Baker using

a multistep procedure. The Little Ice Age ELA reconstruction requires knowledge

of the hypsometry of the palaeo-glaciers. Also required is detailed hypsometric

information on the present-day glaciers.

The first step in the procedure is to determine modern glacier perimeters,

hypsometry, ice thicknesses, and bed elevations. I obtained this information for

four glaciers: Coleman-Roosevelt, Deming, Easton, and Boulder glaciers. They were chosen because they are among the largest on Mount Baker and have the

best-preserved Little Ice Age moraines and trimlines. Their present-day margins

are also easily delineated, and the elevations of their Little Ice Age headwalls

and termini, which are required for the analysis, can be accurately determined.

The component required for the analysis that is most difficult to ascertain is a set

of bed elevations along each Little Ice Age glacier’s centreline.

Modern Ice Thicknesses and Bed Elevations

The area of the DEM that was used for this exercise was produced from

scans of topographic maps produced in 1974 and 1975. I created centreline

profiles of the surface of each of the four glaciers as a function of step-length in

ArcMap. Each profile follows the centreline of the glacier from its terminus to its

headwall and thus is much longer than a straight line representing the shortest

distance between those two points.

Glacier bed elevations are required to determine palaeo-glacier hypsometries, but these elevations must be inferred because most of the upper part of Mount Baker is currently glacierized. Benn and Hulton (2010) provide a spreadsheet for calculating glacier thicknesses along a centreline profile based on a perfectly plastic glacier model. The elevation of the glacier bed can be determined by differencing the elevation of the glacier surface and ice thickness.

I used the Benn and Hulton (2010) spreadsheet to derive bed elevations on ice-covered terrain. Bed elevations were iterated along each profile until the calculated ice surface elevations matched the known 1974-1975 surface elevations at each step, to within 10 m where possible. Present-day ice-surface elevations from the DEM provided a check on the accuracy of the modeled ice thicknesses. Ice thickness data on Mount Baker are sparse, but calculated values were checked against values determined by Harper (1992) in a radio- echo survey on Easton Glacier.

The shape factor and shear stress are also required inputs in the spreadsheet (Table 3-2). The shape factor (f) is a value between 0 and 1 that is used to characterize the shape of the terrain through which a glacier flows; it introduces side drag into the spreadsheet by reducing shear stress when the two are multiplied (Benn and Hulton, 2010). The shape factor decreases, and the glacier thickens, where the bordering valley walls steepen and are more confining. For a glacier that experiences no side drag from valley walls, is 1. One or two shape factors were determined for each present-day glacier. Larger values were chosen in the upper portions of the glaciers, where ice is not 93

confined by steep walls close to the summit. The value of shear stress used in all

calculations is 100,000 Pa, which is the average of values reported by Paterson

(1994) for alpine glaciers (50,000-150,000 Pa). This value is consistent with the

average estimated shear stress of approximately 103,000 Pa made by Driedger and Kennard (1986) for glaciers on Cascade volcanoes with lengths exceeding 2 km. A step length of 50 m was used in all reconstructions.

Table 3-2 Input used in the Benn and Hulton (2010) spreadsheet to estimate present-day glacier thickness along centreline profiles of four Mount Baker glaciers.

Glacier Profile Shape factor* Shear Step Ice length (m) stress (Pa) length (m) density (kg/m3) Coleman- 4700 0.55 100,000 50 900 Roosevelt Deming 5900 ≤3750m=0.55 100,000 50 900 ≥3800m=0.65 Easton 3950 0.55 100,000 50 900 Boulder 3900 0.60 100,000 50 900

*Calculated from the 1/3rd arcsecond NED DEM.

I adjusted bed elevations within the spreadsheet until they yielded ice

surface elevations that matched those obtained from the DEM ice surface

profiles. I obtained approximate bed elevations and average ice thicknesses

along a centreline profile for each of the four glaciers chosen for detailed study.

These results provided data required to reconstruct the Little Ice Age glaciers.

Little Ice Age Glacier Hypsometries

To obtain Little Ice Age glacier hypsometries, I mapped conspicuous moraines and trimlines in the forefields of Easton, Deming, Boulder, and

Coleman-Roosevelt glaciers both in the field and using 2009 NAIP orthoimagery.

I also used previous work on Mount Baker moraine chronologies as a check on my mapping (Burke, 1972; Heikkinen, 1984; Thomas, 1997; O’Neal, 2005).

I used modern glacier divides (Chapter 2) to determine Little Ice Age glacier hypsometries. I retained present-day large nunataks in the Little Ice Age analysis; they show no obvious trimlines, but are likely too large and high to have been ice-covered entirely at the Little Ice Age maximum.

The bed elevation profiles of the four study glaciers were used to determine the Little Ice Age glacier hypsometries. Each profile was extended beyond the present-day glacier limit to the Little Ice Age terminus of the glacier using topographic data from 1974-1975. The result is a single centreline profile of bed elevation for each glacier from its Little Ice Age terminus to the headwall.

The reconstructed Little Ice Age centreline profiles were then input into the

Benn and Hulton (2010) spreadsheet (Table 3-3). The spreadsheet calculated former ice surface elevations at points along the centreline profiles. The differences between these values and the corresponding bed elevations were taken to be maximum Little Ice Age ice thicknesses along the centreline of the glacier.

The ice surface elevations of the Little Ice Age glaciers were combined with elevations along the moraines and nunataks in a point file in ArcMap. The 95

file contains points with UTM eastings and northings taken from the centreline

profile and ice surface elevations. Points along lateral and end moraines were

assigned their DEM elevations, on the assumption that ice thickness was zero at

the moraines. I then constructed a DEM for each point file, using a tool that

creates a smooth 3D surface that passes through each point. I contoured the

interpolated surface at a 50-m interval. The resulting maps provided hypsometric

information for the four glaciers that could then be used to calculate ELA

changes from the present.

Table 3-3 Inputs used in the Benn and Hulton (2010) spreadsheet to calculate Little Ice Age glacier thickness along a centreline profile for four Mount Baker glaciers.

Glacier Profile Shape factor Shear Step Ice length (m) stress (Pa) length (m) density (kg/m3) Coleman- 6800 0.55 100,000 50 900 Roosevelt

Deming 7950 ≤5700 m=0.55 100,000 50 900 ≥ 5750 m=0.65

Easton 6300 0.55 100,000 50 900

Boulder 6350 ≤1500 m=0.50 100,000 50 900 1550- 2550m=0.55 ≥2600m=0.60

Equilibrium Line Altitude Depression

I used the AAR and AABR methods to calculate ELA differences between today and the peak of the Little Ice Age. The AAR, the simpler of the two

methods, involves the choice of the ratio of the accumulation area to the total glacier area, assuming steady-state conditions. My choice of an AAR was based on analysis of long-term mass balance data collected by the North Cascades

Glacier Climate Project (NCGCP) at Easton and Rainbow glaciers on Mount

Baker, and by the National Park Service at North Klawatti Glacier (Chapter 2).

The data were regressed to determine the AAR or ELA that coincides with a zero net balance, which hypothetically is the steady-state AAR or ELA. I then applied the calculated steady-state AAR to modern glaciers on Mount Baker to determine their steady-state ELAs. The steady-state AAR was also used to calculate the

Little Ice Age ELA in order to compare with results derived using alternative methods. The methods and results for present-day glaciers are presented in

Chapter 2.

I used the AABR method to produce another set of Little Ice Age ELAs for the four glaciers. I applied the AABR method twice, first using a BR of 2.2 for all glaciers (Furbish and Andrews, 1984), and second using BRs calculated in

Chapter 2. Both sets of BR-based ELA calculations were performed using the

Osmaston (2005) spreadsheet, which, in addition to a BR, requires detailed hypsometric information for a glacier.

Palaeoclimate

I estimated the Little Ice Age climate at the ELA of four Mount Baker glaciers using two techniques. I first used a summer lapse rate and assumed that precipitation did not change between the maximum of the Little Ice Age and

today. I applied the regional ablation-season lapse rate for the Cascade Range

reported by Porter (1977). This lapse rate, derived from data for the period May-

September at 17 meteorological stations, is 0.62°C/100 m (R2 = 0.86). The

temperature depression is the product of this lapse rate and the change in ELA in

metres.

Second, I calculated past temperature and precipitation using the following equation from Kuhn (1981) and Hooke (2005):

∆ ∆ ∆ ℎ ℎ ℎ

where is the winter precipitation gradient (assumed to be 1.0 kg·m-2m-1; consistent with hydrological modelling in the region (Dickerson, 2010)), Δh is the change in elevation of the ELA, δbw is the change in winter precipitation

associated with Δh, T is the length of the melt season (assumed to be 150 days),

L is the latent heat of fusion (334 kJ/kg), γ is a constant of proportionality (the

average value for glacier ice is 1.7 MJ/m2dK or 1700kJ/m2dK; Kuhn, 1981), is the summer lapse rate (assumed to be 0.0062 K/m), and δTa is the mean summer air temperature associated with Δh. I assume no changes in R over the

period of interest. In this case, is zero, because radiation does not change

significantly with elevation (Hooke, 2005). With this assumption, Equation 4

simplifies to:

∆ ∆ ℎ ℎ

I solved Equation 5 for precipitation and temperature with a set of pre- determined input values that span a reasonable range. Based on long-term temperature records from western Washington, Burbank (1982) documented a 7 percent decrease in precipitation since 1850. I used this information to constrain the possible increase in precipitation from modern at the peak of the Little Ice

Age to 10 percent, but also performed analyses for a 7 percent increase, and for no change in precipitation.

Computation of an absolute change in winter precipitation from Equation 5 requires an estimate of modern precipitation at the ELA. I determined this value using a precipitation gradient of 1.0 kg·m-2m-1. I calculated a modern winter

balance gradient from mass balance data collected at nearby North Klawatti

Glacier. I cannot estimate the precipitation gradient during the Little Ice Age, and

thus assumed that it was the same as the modern precipitation gradient. I

estimated winter precipitation at the present ELA from the modern precipitation gradient and meteorological data from nearby climatological stations summarized by Porter (1977). I used a range of precipitation gradients, 0.0-1.5 kg·m-2m-1, in the calculations, but below I include only results for 1.0 kg·m-2m-1, consistent with

the aforementioned assumption. Results for different winter balance gradients

are included in the Appendix.

Results

Glacier Reconstructions

Modern Ice Thicknesses and Bed Elevations

Centreline ice thickness profiles of the four studied glaciers are shown in

Figure 3-4. The figure also shows the bed elevations required to produce these ice surfaces. The results of the bed elevation analysis, including minimum and maximum ice thicknesses, their approximate elevations, and average ice thickness, are summarized in Table 3-4.

Little Ice Age Glacier Hypsometries

Figure 3-5 is a map of Mount Baker glaciers at the peak of the Little Ice

Age. This figure also shows the profile lines used to calculate ice thickness and

Little Ice Age glacier contours at Coleman-Roosevelt, Deming, Easton, and

Boulder glaciers. The Little Ice Age terminus of each glacier is several hundred metres lower than its corresponding modern (2009) terminus.

Reconstructed Little Ice Age glacier thicknesses and surface and bed elevations are shown in Figure 3-6. The thickest glacier during the Little Ice Age was Deming Glacier; the thinnest was Boulder Glacier. On average, the Little Ice

Age glaciers were about 22 m thicker than their modern counterparts. Both the modern and Little Ice Age glaciers are thickest in their ablation areas, because the slope of the bed is lowest there. Areas and area ratios of the Little Ice Age glaciers are presented in Table 3-5, together with calculated Little Ice Age glacier thicknesses.

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Figure 3-4 Bed elevations for four Mount Baker glaciers, calculated using the Benn and Hulton (2010) spreadsheet model. Also shown are the ice surface elevations corresponding to the calculated bed elevation profiles, and the actual ice surface elevations measured from the NED 1/3 arcsecond DEM.

Modern and Little Ice Age glacier hypsometries are plotted in Figure 3-7.

This figure also shows the ELA associated with an AAR of 0.66 for both the present-day and Little Ice Age glaciers.

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Table 3-4 Ice thicknesses calculated for four 1970s glaciers using the Benn and Hulton (2010) spreadsheet. Glacier Area Min/max Elevation of Average (km2) thickness (m) min/max thickness thickness (m) (m) Coleman- 10.4 11 / 107 3150 / 1380 52 Roosevelt Deming 4.9 17 / 141 2930 / 1500 65 Easton 3.1 35 / 88 2800 / 1870 61 Boulder 3.7 15 / 74 2790 / 1940 44 Average 2920 / 1670 56

Equilibrium Line Altitude Depression

Modern ELAs of Mount Baker glaciers, calculated assuming a steady- state AAR of 0.66, are presented in Table 3-6. The table also shows the Little Ice

Age ELA and the difference in ELA from the present determined using the three methods described above. In general, the calculated BRs gave the largest ELA depressions, and the assumed BR of 2.2 consistently gave the lowest ELA depressions. Deming and Boulder glaciers experienced the largest ELA changes, and Coleman-Roosevelt Glacier the smallest. The calculated BR method gave the lowest standard deviation in ELA depression, approximately 58 m. In contrast, the standard deviations using an AAR of 0.66 and the assumed BR of

2.2 are, respectively, 69 m and 67 m.

Palaeoclimate

The inferred Little Ice Age palaeoclimate based on the lapse-rate and equation-based methods are shown, respectively, in Table 3-7 and Table 3-8. 102

Both tables include results based on the three ELA depressions calculated for each glacier.

Figure 3-5 Mapped limits of four modern and reconstructed Little Ice Age glaciers on Mount Baker. Centreline profiles used to calculate ice thicknesses of four glaciers are shown in red, and reconstructed 100-m contours are displayed in grey. Also shown are the approximate limits of all Little Ice Age glaciers on the mountain.

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Figure 3-6 Reconstructed Little Ice Age ice surface elevations for four Mount Baker glaciers, calculated using the bed elevation profiles shown in Figure 3-3.

Ablation-season temperature changes range from -1.0°C, calculated for

Coleman-Roosevelt Glacier using an assumed BR of 2.2, to -2.4°C, determined for Boulder Glacier using a calculated BR (Table 3-7). The average temperature change for all glaciers calculated with an AAR of 0.66 is almost the same (-

1.9°C) as that determined using the calculated BR (-2.0°C). The average temperature change calculated with a BR of 2.2 is -1.5°C.

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Table 3-5 Little Ice Age area ratios and ice thicknesses of four Mount Baker glaciers estimated using the Benn and Hulton (2010) spreadsheet.

Glacier LIA area Area ratio* Average LIA thickness Δ Average (km2) (LIA/2009) (m) thickness (m)** Coleman- 13.53 1.30 79 27 Roosevelt Deming 7.09 1.45 88 23 Easton 6.26 2.02 82 21 Boulder 5.76 1.56 65 21 Average 1.58 79 23 *Ratio of Little Ice Age glacier area to 2009 glacier area. **Difference in average thickness between present-day and Little Ice Age glacier.

Table 3-8 summarizes results for the combined precipitation and

temperature analysis for all glaciers with each ELA estimate in Table 3-6. The

results, from left to right, are for no temperature change, no change in winter

precipitation, a 7 percent increase in winter precipitation, and a 10 percent increase in winter precipitation. Assuming no change in temperature, accumulation-season precipitation must increase 963 kg/m2 at Coleman-

Roosevelt Glacier to explain the ELA depression of 168 m, and 2253 kg/m2 at

Boulder Glacier to explain the ELA depression of 393 m. If, on the other hand, one assumes no change in winter precipitation, the temperature change during the Little Ice Age ranges from -1.3°C at Coleman-Roosevelt Glacier to -3.0°C at

Boulder Glacier. The largest temperature change is for Boulder Glacier

(maximum overall ELA depression = 393 m), and smallest is for Coleman-

Roosevelt Glacier (minimum overall ELA depression = 168 m). The average temperature change based on an AAR of 0.66 ranges from -1.9 to -2.3°C. 105

Figure 3-7 Modern and Little Ice Age glacier hypsometries of four Mount Baker glaciers. The ELAs (0nb ELA) for an AAR of 0.66 are shown for both the modern and Little Ice Age hypsometries.

Table 3-6 Estimated Little Ice Age equilibrium line altitudes (ELA) and modern steady- state ELAs for four Mount Baker glaciers. Little Ice Age ELA (m) Glacier Modern AAR = 0.66 BR = calculated BR = 2.2 steady-state ELA [ΔELA] (BR) [ΔELA] [ΔELA] (m)* Coleman-Roosevelt 2063 1850 [213] 1801 (3.66) [262] 1895 [168] Deming 2180 1815 [365] 1840 (2.3) [340] 1850 [330] Easton 2080 1785 [295] 1789 (3.5) [291] 1842 [238] Boulder 2105 1755 [350] 1712 (4.7) [393] 1873 [232] Average (m) 2107 1801 [306] 1786 [322] 1865 [242] ΔELA standard deviation (m) 69 58 67

*Determined from long-term mass balance data of the North Cascades Glacier Climate Project. 106

A similar range is provided by the calculated BR: -2.0 to -2.4°C. The lowest

estimates of average temperature change come from an assumed balance ratio

of 2.2: -1.4 to -1.8°C. The calculated average change in summer temperature for

all three approaches ranges from -1.4 to -2.3°C.

Table 3-7 Calculated Little Ice Age ELA depressions for four Mount Baker glaciers, and associated temperature changes from modern using a lapse rate of 0.62°C/1000m.

LIA ELA and associated temperature change Moder ΔELA ΔELA ΔELA n ELA (m, (m, (m, Glacier (m) AAR=0.66) Δ°C BR=calc.) Δ°C BR=2.2) Δ°C Coleman- 2063 -213 -1.3 -262 -1.6 -168 -1.0 Roosevelt Deming 2180 -365 -2.3 -340 -2.1 -330 -2.0 Easton 2080 -295 -1.8 -291 -1.8 -238 -1.5 Boulder 2105 -350 -2.2 -393 -2.4 -232 -1.4 Average 2107 -306 -1.9 -322 -2.0 -242 -1.5 Note: Three ELAs are calculated for each glacier: one using an accumulation area ratio of 0.66; a second for a specific balance ratio determined for each glacier; and a third for a balance ratio of 2.2.

The largest average temperature changes were calculated assuming no

change in winter precipitation. The required temperature reductions decrease as

winter precipitation increases. Examples that illustrate this point are shown in

Table 3-9. The lapse-rate method, assuming no change in precipitation, yields

average temperature changes 0.0-0.3°C higher than those calculated with a 7

percent increase in precipitation and a maximum difference of 0.2°C larger than

those calculated with a 10 percent increase in winter precipitation. The estimates

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derived using Equation 5 and with no change in winter precipitation differ most from the corresponding lapse-rate results.

Table 3-8 Estimates of Little Ice Age temperature and precipitation for changes in ELA, based on methods of Kuhn (1981) and Hooke (2005).

† †† Δh δTa= 0* δbw= 0** δbw= +7% δbw= +10%

δTa δbw δTa δbw δTa δbw δTa δbw (LIA (°C) (kg/ (°C) (kg/ (°C) (kg/ (°C) (kg/ Glacier ΔELA, m) m2) m2) m2) m2) Coleman- -213a 0 1221 -1.6 0 -1.3 202 -1.2 289 Roosevelt -262b 0 1502 -2.0 0 -1.7 202 -1.6 289 -168c 0 963 -1.3 0 -1.0 202 -0.9 289 Deming -365a 0 2093 -2.7 0 -2.5 210 -2.3 300 -340b 0 1949 -2.6 0 -2.3 210 -2.2 300 -330c 0 1892 -2.5 0 -2.2 210 -2.1 300 Easton -295a 0 1691 -2.2 0 -1.9 203 -1.8 290 -291b 0 1668 -2.2 0 -1.9 203 -1.8 290 -238c 0 1365 -1.8 0 -1.5 203 -1.4 290 Boulder -350a 0 2007 -2.6 0 -2.4 205 -2.2 293 -393b 0 2253 -3.0 0 -2.7 205 -2.6 293 -232c 0 1330 -1.7 0 -1.5 205 -1.4 293 Average ΔELAa 1753 -2.3 0 -2.0 205 -1.9 293 ΔELAb 1843 -2.4 0 -2.1 205 -2.0 293 ΔELAc 1388 -1.8 0 -1.5 205 -1.4 293 *No change in temperature. **No change in winter precipitation. †Seven percent increase in winter precipitation. ††Ten percent increase in winter precipitation. a calculated assuming an accumulation area ratio of 0.66. b calculated with a balance ratio determined for each glacier. c calculated with a balance ratio of 2.2.

The lapse-rate method assumes no change in winter precipitation, as well as a precipitation gradient of 1.0 kg·m-2m-1. The Appendix provides results of

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calculations based on different values for the precipitation gradient. The temperature effect increases as the precipitation gradient increases. An increase from 0.0 kg·m-2m-1 to 1.50 kg·m-2m-1 can produce increases in calculated temperature depression of over 1°C for some glaciers.

Table 3-9 Temperature reductions calculated using lapse rate and equation-based methods for a 7 percent and 10 percent increase in winter precipitation for four Mount Baker glaciers. Δ°C for AAR = Δ°C for BR = Δ°C for BR = 0.66* calc. ** 2.2† Glacier LR†† 7% 10% LR†† 7% 10% LR†† 7% 10% Coleman-Roosevelt -1.3 -1.3 -1.2 -1.6 -1.7 -1.6 -1.0 -1.0 -0.9 Deming -2.3 -2.5 -2.3 -2.1 -2.3 -2.2 -2.0 -2.2 -2.1 Easton -1.8 -1.9 -1.8 -1.8 -1.9 -1.8 -1.5 -1.5 -1.4 Boulder -2.2 -2.4 -2.2 -2.4 -2.7 -2.6 -1.4 -1.5 -1.4 Average -1.9 -2.0 -1.9 -2.0 -2.1 -2.0 -1.5 -1.5 -1.4 *Changes calculated assuming an accumulation area ratio of 0.66. **Changes calculated with a balance ratio determined for each glacier. †Change calculated assuming a balance ratio of 2.2. ††LR = Lapse rate-only method.

Discussion

Glacier Reconstructions

Modern Ice Thicknesses and Bed Elevations

Ice thickness calculations are subject to several sources of uncertainty, some of which are difficult to quantify. The most important sources of error are the spreadsheet inputs and assumptions. First, the surfaces of the Little Ice Age glaciers on Mount Baker can only be approximately estimated. Second, a significant shortcoming of the Benn and Hulton (2010) program is that it assumes 109

that glaciers move and change shape only through plastic deformation. A

temperate glacier can also move by sliding over its bed (Paterson, 1994). Hodge

(1974) concluded that basal sliding at Nisqually Glacier on Mount Rainier (Fig. 3-

1) is the main mechanism of glacier flow. Because my calculations do not

consider basal sliding, my ice thicknesses estimates must be considered

maximum values.

Measured and calculated modern ice surface elevations on Mount Baker

are similar. Differences occur mainly near glacier termini, for example on lower

Boulder and Coleman-Roosevelt glaciers, where the ice surface is irregular or

steep. Benn and Hulton (2010) acknowledge that their spreadsheet can yield

erroneous estimates of ice thickness in steeper areas.

Harper (1992) estimated average thicknesses of four glaciers on Mount

Baker. His estimate of average ice thickness of Easton Glacier, made with radio- echo measurements, is 70-80 m. He used an area-volume relation to estimate average thicknesses of the other three glaciers: Coleman-Roosevelt Glacier (44 m), Deming Glacier (45 m), and Boulder Glacier (45 m). In comparison, my estimates for Easton, Coleman-Roosevelt, Deming, and Boulder glaciers are, respectively, 61 m, 52 m, 65 m, and 44 m (Table 3-4). My results are derived from a DEM that was created using scanned and digitized topographic maps made in 1975, whereas Harper’s data are from a combination of 1979 USGS topographic maps and aerial photographs; thus the two data sets may not agree exactly. Also, my glacier areas are 0.1-0.5 km2 larger than Harper’s. Finally,

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Harper (1992) noted that his estimates of volumes could be in error by as much

as 25 percent. Errors of this size would propagate into his thickness estimates.

The results of Harper’s (1992) radio-echo survey of Easton Glacier are informative. The maximum measured thickness was 107 m at an elevation of

1980 m asl. In contrast, the maximum thickness that I calculated was 88 m, at

1870 m asl. The location at which Harper obtained his maximum ice thickness,

however, is west of the glacier centerline, over a possible depression in the

glacier bed. There is considerable across-glacier difference in ice thickness on

Easton Glacier, which makes it difficult to compare the two datasets. Also,

Harper’s original data are no longer available, further complicating comparison of

the data.

Harper (1992) concluded that the thickest ice on Mount Baker is on a

gently sloping area of Deming Glacier between 2130 and 2190 m asl. In contrast,

I calculate that the maximum thickness of Deming Glacier is between 1440 and

1550 m asl, below the icefall. I recognize a second, less-pronounced area of

thick ice much higher on the glacier, between 2050 and 2300 m asl, close to the

area of thick ice inferred by Harper (1992). Harper (1992) also argued that

Easton Glacier is one of the thickest glaciers on Mount Baker, due to its relatively low surface slope. My results indicate that Easton Glacier is nearly as thick as

Deming Glacier, which is consistent with Harper’s (1992) conclusion.

Driedger and Kennard (1986) measured ice thickness at many points on

six glaciers on Mount Rainier. The glaciers they studied range in area from

approximately 3 km2 to more than 11 km2. The point thickness values range from 111

less than 30 m to nearly 215 m. Most of the measured thicknesses are in the 90-

120 m range. These values are larger than the thicknesses I estimate for Mount

Baker glaciers, which is expected given that most? Of the Mount Rainier glaciers are larger than those on Mount Baker.

Little Ice Age Glacier Hypsometries

One way to test whether the area covered by a Little Ice Age glacier on

Mount Baker is accurate is to compute ratios of the areal extents of the present- day and Little Ice Age glaciers (Table 3-5). Grove (1988) concluded that this value should range from 1.5 to 1.9 for North Cascades glaciers. The average value for Mount Baker glaciers is 1.6. Easton Glacier has the largest value, 2.02.

Mount Baker glaciers were, on average, 20-30 m thicker along their centrelines at the maximum of the Little Ice Age than today. I analyzed glaciers with a range of shapes and sizes, thus these results may be applicable to other

North Cascade glaciers with similar geometries.

I calculated shape factors in the ablation areas of the glaciers, but values near the headwalls of the glaciers are more difficult to determine and have larger uncertainties. Errors in the shape factor will impact the results; average calculated thicknesses for a range of shape factors are shown in Table 3-10. If shear stress is held constant at 100,000 Pa, a change in the shape factor from

0.5 to 0.7 results in a maximum thickness change of 30-40 m. Shape factors of

Mount Baker glaciers differ because of the variability in bed and valley walls. It

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thus is difficult to quantify the error associated with my choice of shape factors; it is likely, however, to be of the order of 10 to 20 m overall.

Table 3-10 Average reconstructed Little Ice Age thicknesses of four Mount Baker glaciers using a range of values for the shape factor (f).

Average ice thickness (m)

Glacier f=0.5 f=0.7 f=0.9

Coleman-Roosevelt 86 64 52 Deming 98 72 58 Easton 90 65 51 Boulder 71 52 41 Average 86 63 51

Shear stress also can only be approximated, based on a standard range of values for temperate glaciers. Average reconstructed ice thicknesses for a range of shear stress values, assuming a constant (0.7) shape factor are shown in Table 3-11. The differences are of the order of 20-30 m for a change in shear stress of 50,000 Pa.

Another issue is whether the Little Ice Age glaciers on Mount Baker were in a steady-state condition, which is a requirement for the ELA and palaeoclimate analyses. This condition is likely met, given the length of time that the glaciers must have sat at or near their outermost Little Ice Age moraines. The large moraines at Boulder and Easton glaciers, in particular, were built over at least many decades and probably centuries, indicating steady-state conditions (Long,

1955). I assume, like Meier (1962), that the dimensions of these glaciers

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changed little while they constructed such large moraines, thus the average net

budget during construction would have been near zero. The moraines, therefore,

provide adequate evidence for my assumption of steady-state conditions, at least

for the purpose of this study.

Table 3-11 Average reconstructed Little Ice Age thicknesses of four Mount Baker glaciers using a range of values for the shear stress (τ). Average ice thickness (m) Glacier τ=50,000 τ=100,000 τ=150,000 Coleman-Roosevelt 36 64 91 Deming 39 72 104 Easton 34 65 96 Boulder 27 52 75 Average 34 63 92

The accuracy of my approach cannot be evaluated on the basis of previous reconstructions of palaeo-glaciers and palaeo-ELAs that are far more subjective and fail to consider important methodological details. Previous researchers drew ice surface contours of palaeo-glaciers based on judgment alone. In contrast, I adopted the objective, reproducible method of Benn and

Hulton (2010) that uses present-day surface topography and basic glacier physics. Physically based reconstruction methods such as those used by Benn and Hulton (2010) and Ng et al. (2010) are more rigorous and objective than visually based best-guesses.

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Equilibrium Line Altitude Depression

The differences between my approach and the approaches of previous

researchers are of two main types: (1) the method and data used to determine

the modern steady-state ELA of a glacier; and (2) the method used to determine the former steady-state ELA of a glacier. Thomas (1997) assumed an AAR of

0.65 for Easton Glacier and, based on this value, concluded that the Little Ice

Age ELA was 1760 m asl, 255 m lower than what he inferred to be the modern steady-state ELA. My estimates of ELA lowering at Easton Glacier, based on three objective methods, range from 238 to 295 m. Burbank (1981) used an AAR of 0.60 for glaciers on Mount Rainier and calculated an average Little Ice Age

ELA depression of 160 m. His values, however, range widely for glaciers around

the mountain, from 60 to 300 m. My smallest ELA depression – 168 m at

Coleman-Roosevelt with a balance ratio of 2.2 - is much larger than Burbank’s

minimum value of 60 m for Carbon Glacier.

The three approaches that I used to estimate ELA depression warrant discussion. My AAR and BR values are based on present-day ELAs; I cannot test the accuracy of these values by using the same ELAs as a check. They are, however, based on data specific to Mount Baker and not AARs or BRs from other areas (Furbish and Andrews, 1984; Rea, 2009; Kern and Laszlo, 2010). Having said that, I would have obtained similar results with the AAR method if I had simply used the standard AAR range of 0.5 to 0.8 of Meier and Post (1962).

The similarity in the ELA depressions obtained using the calculated BRs and the assumed AAR values is no coincidence. I calculated BRs using modern

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glacier hypsometry and AARs in a modified version of the Osmaston (2005)

spreadsheet. The spreadsheet requires an ELA value and hypsometry to

determine the BR, and I determined my input ELAs by applying an AAR of 0.66

to each modern glacier. The BR thus was tailored to produce an accumulation

area that constitutes approximately 66 percent of the total area of the glacier.

Of the methods used in this study, the BR method requires the most

assumptions and therefore has the largest potential error, assuming that the hypsometries and modern AAR and BR values are accurate and that these values were similar at the maximum of the Little Ice Age. I do not know if additional assumptions required to use the BR approach are valid, therefore the

AAR method is preferable. The AAR method is also easier to apply and is more easily understood than the BR approach.

Palaeoclimate

Both methods of climate reconstruction used in this study have sources of error, mainly in the glacier reconstructions and associated ELA depressions. The lapse rate method is easy to apply, but the assumption that winter precipitation has not changed since the maximum of the Little Ice Age is probably not valid, regardless of what effect it would have on calculated temperature depressions.

Both precipitation and temperature play important roles in the location of the

ELA. In general, an increase in winter precipitation reduces the temperature lowering required for a given ELA depression. Estimates of temperature change from studies where differences in precipitation are not considered thus are

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maximum values (Porter, 1977). Another potential source of error is the use of regional climate data to calculate the lapse rate on Mount Baker. The highest weather station on Mount Baker is over 1400 m below the summit, thus the local lapse rate must be extrapolated far beyond direct observations.

The method I used to evaluate precipitation and temperature changes also has several sources of error. The variables in Equation 2 (e.g. gamma, length of the melt season) are difficult to accurately quantify, consequently there are possible errors that result from the use of this equation. Assumptions that likely introduce error are that net radiation does not change with elevation and has not changed since the Little Ice Age. The temperature reconstructions for a range of precipitation and radiation values are summarized in the Appendix (Table 5). If net radiation during the maximum Little Ice Age was lower than modern and there was no change in precipitation, the magnitude of calculated temperature depressions decreases by a degree or more. The calculated temperature depressions are even smaller if net radiation decreases and winter balance increases. Such estimates, however, assume that temperature and radiation are independent variables in Equation 2. Net radiation, however, is calculated as a function of temperature, thus the two variables co-vary. An energy balance modeling approach would account for the complex relations between these parameters, but is beyond the scope of this thesis.

Although it is not possible to directly assess the accuracy of my reconstruction, previous work in the North Cascades provides some support and precedent for my approach. Burbank (1982) inferred a precipitation decrease 117

from 1850 to 1978 of only 7 percent, based on long-term climate data and a

lichenometric study. He reported several climate scenarios based on the

techniques and lapse rate reported by Porter (1977). In scenarios in which

precipitation was no more than 20 percent higher at the maximum of the Little Ice

Age than today, Burbank (1981, 1982) argued that his average ELA shift (160 m)

could be explained by a temperature rise of 1°C or less since the beginning of

the nineteenth century.

Temperature reconstructions based on studies of supalpine trees in

western Washington confirm the results of Burbank (1981, 1982). Graumlich and

Brubaker (1986) conclude that mean annual temperature was approximately 0.9-

1.0°C higher during the period 1914-1979 than between 1590 and 1913. This

result is similar to the approximately 1°C rise in temperature since the beginning

of the nineteenth century reported by Burbank (1982). Burbank’s estimate of

temperature change, however, is for summer, not the entire year. The magnitude

of temperature change for a given change in precipitation is consistently larger for summer than for the entire year (Porter, 1977; see also Table 3-1).

My results support the argument made by Burbank (1982) that changes in precipitation must be improbably large to significantly affect conclusions drawn about temperature changes. For example, a precipitation increase of 10 percent at Mount Baker reduces the required temperature change by less than 0.2°C.

My work provides an improved constraint on Little Ice Age climate at

Mount Baker. An implication of the research of Graumlich and Brubaker (1986) is that average ablation-season temperature in the North Cascades during the Little 118

Ice Age was more than 1°C cooler than in the late twentieth century. Burbank

(1982) concluded that accumulation-season precipitation in the region was approximately 7 percent higher at the peak of the Little Ice Age than in the late twentieth century. I eliminated results obtained using a BR of 2.2, because this method yielded inconsistent results. Table 3-12 presents my final results; I assume that the change in precipitation was between 0 and 7 percent, and I used both an AAR of 0.66 and my calculated BRs. ELA depressions of 250-350 m with a 7 percent increase in winter precipitation indicate a mean summer temperature reduction of 1.7°C -2.4°C at the Little Ice Age maximum.

Table 3-12 Maximum Little Ice Age changes in ELA and temperature for four Mount Baker glaciers.

Glacier Δh (m) δTa (°C)* (if δbw= +7%) Coleman-Roosevelt -213a -1.3 -262b -1.7 Deming -365a -2.5 -340b -2.3 Easton -295a -1.9 -291b -1.9 Boulder -350a -2.4 -393b -2.7 Average ΔELAa -306 -2.0 Average ΔELAb -322 -2.1 a = calculated with an accumulation area ratio of 0.66 b = calculated with a balance ratio determined for each glacier. *Temperature reduction for a 7 percent increase in winter precipitation.

Both precipitation and temperature were likely important contributors to the reconstructed Little Ice Age ELA depression. If, for example, the temperature 119

depression is set to 1.0°C, the balance gradient is 1.0 kg/m2m, the melt season is

150 days long, the temperature lapse rate is -0.0062°C/m, and the AAR is 0.66,

precipitation increase at the Little Ice Age maximum above present-day values

ranges from 16 percent at the ELA of Coleman-Roosevelt Glacier to 44 percent

at Deming Glaciers.

Conclusions

Today Mount Baker glaciers are, on average, 20-30 m thinner than at the

Little Ice Age maximum. Little Ice Age glaciers on Mount Baker were, on

average, 1.6 times larger than at present.

Comparison of the AAR and BR methods suggests that the former may

yield more accurate results. The AAR method can be reliably used when glacier

hypsometry is known or can be reconstructed from former glacier extents, and if

local or regional mass balance data are available. A BR of 2.2 produced the least

consistent results, which is perhaps not surprising because this value was

primarily derived from research on coastal Alaskan glaciers (Furbish and

Andrews, 1984). However, it is the most widely used value in this type of

reconstruction, including past research at Mount Baker. The assumed BR

method yields Little Ice Age ELA depression estimates that are too low.

The average ELA depression for four Mount Baker glaciers at the Little Ice

Age maximum is between 300 and 330 m. A coupled increase in accumulation

season precipitation of 7 percent and a decrease in average ablation season temperature of about 2.0°C explains this ELA depression.

120

Comparison of climate reconstruction methods shows that, for ELA depressions of the magnitude that occurred during the Little Ice Age, plausible changes in precipitation would lower reconstructed temperatures no more than

0.3°C. Precipitation should not be ignored, however, when interpreting the relatively small ELA depressions of the Little Ice Age. My estimates of temperature reduction during the Little Ice Age are consistent with the range of values reported by previous researchers, although they are at the upper end of this range because of my relatively large ELA shifts. Most previous researchers, however, used a BR of 2.2, which gives a lower ELA depression and consequently a lower temperature depression than I suggest is appropriate.

121

CHAPTER 4 CONCLUSIONS

Glacier accumulation area ratio (AAR) and equilibrium line altitude (ELA) can be accurately determined from end-of-summer high-resolution orthoimagery and elevation data in a GIS. Using this approach, I calculated the AARs and

ELAs of all 11 glaciers on Mount Baker for the 2009 mass balance year. The ELA cannot be easily visually determined for these glaciers because of the complex distribution of snow and bare ice at the end of the ablation season. The AAR is a more accurate representation of the distribution of snow and ice on a glacier at the time of minimum mass balance.

This approach can be used wherever the National Agriculture Imagery

Program includes photography of glacierized areas. More costly, long-term, field- based mass balance and AAR or ELA measurements supplement photogrammetric AAR measurements. The North Cascade Glacier Climate

Project (NCGCP), which has a program of long-term mass balance measurements for the North Cascades, is exploring this possibility for North

Cascades glaciers, including those on Mount Baker.

Analysis of long-term mass balance data by the NCGCP and the National

Park Service indicates that the steady-state AARs of North Cascades glaciers are between 0.60 and 0.70. Assuming a steady-state AAR of 0.66 and using detailed glacier hypsometric information, I calculated the average area-altitude balance ratios (BR) of Mount Baker glaciers to be 3.4. This value is similar to the 122

BR of 3.7 I calculated for North Klawatti Glacier using long-term mass balance data from the NPS. These values are significantly larger than the commonly used reference BR of 2.2 of Furbish and Andrews (1984). Balance ratio calculations are highly sensitive to the input ELA and hypsometry; even my values, which are only for Mount Baker glaciers, range from 2.1 to 5.5. Due to the large uncertainties in the accuracy of a BR, especially for unstudied glaciers, I recommend that the steady-state AAR be used in its place.

I estimate that Mount Baker glaciers at the maximum of the Little Ice Age were, on average, 20-30 m thicker than today. The maximum Little Ice Age glacier areas were about 1.6 times larger than the glacier areas in 2009.

Comparison of three methods of ELA reconstruction -- steady-state AAR, the BR

I calculated, and an assumed BR of 2.2 -- shows that the reference BR of 2.2 produces the least consistent results and the lowest ELA depressions. Previous studies that have used this value have likely underestimated ELA depression. If I exclude results based on a BR of 2.2, the average Little Ice Age ELA depression for reconstructed Coleman-Roosevelt, Deming, Easton, and Boulder glaciers is between 300 m and 330 m. If a 7 percent increase in winter precipitation is applied, a 300-m ELA depression corresponds to a decrease in summer temperature at the Little Ice Age maximum of approximately 2.0 °C. My results are close to, although slightly larger than, previous estimates of Little Ice Age temperature depression.

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APPENDIX: LITTLE ICE AGE CLIMATE RECONSTRUCTIONS

The tables included in this appendix contain the full range of inputs and

results used to reconstruct temperature and precipitation at the maximum of the

Little Ice Age at Mount Baker. The methods used to obtain these results are

explained in detail in Chapter 3. δTa is a change in summer temperature, δbw is a

change in winter precipitation, δbw/δz is the assumed winter precipitation lapse

rate, and Δ ELA is the calculated shift in equilibrium line altitude. ELA shifts are

calculated using three methods: an accumulation area ratio (AAR) of 0.66 (66 percent accumulation area; a balance ratio (BR) calculated from long-term mass

balance records; and an assumed BR of 2.2.

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Table 1 Little Ice Age climate reconstructions for Easton Glacier.

δb / w AAR = 0.66 BR = 3.5 BR = 2.2 δz (kg/m Δ δT δb Δ δT δb Δ δT δb Method a w a w a w 2m) ELA (°C) (kg/m2) ELA (°C) (kg/m2) ELA (°C) (kg/m2) Lapse rate only N/A 295 ‐1.8 0 291 ‐1.7 0 238 ‐1.4 0

δTa= 0 °C 0.00 295 0 1396 291 0 1377 238 0 1127

δTa= 0 °C 0.50 295 0 1544 291 0 1523 238 0 1246

δTa= 0 °C 1.00 295 0 1691 291 0 1668 238 0 1365

δTa= 0 °C 1.50 295 0 1839 291 0 1814 238 0 1484

δbw= 0% 0.00 295 ‐1.8 0 291 ‐1.8 0 238 ‐1.5 0

δbw= 0% 0.50 295 ‐2.0 0 291 ‐2.0 0 238 ‐1.6 0

δbw= 0% 1.00 295 ‐2.2 0 291 ‐2.2 0 238 ‐1.8 0

δbw= 0% 1.50 295 ‐2.4 0 291 ‐2.4 0 238 ‐1.9 0

δbw= +7% 0.00 295 ‐1.6 203 291 ‐1.5 203 238 ‐1.2 203

δbw = +7% 0.50 295 ‐1.8 203 291 ‐1.7 203 238 ‐1.4 203

δbw = +7% 1.00 295 ‐1.9 203 291 ‐1.9 203 238 ‐1.5 203

δbw = +7% 1.50 295 ‐2.1 203 291 ‐2.1 203 238 ‐1.7 203

δbw= +10% 0.00 295 ‐1.4 290 291 ‐1.4 290 238 ‐1.1 290

δbw= +10% 0.50 295 ‐1.6 290 291 ‐1.6 290 238 ‐1.3 290

δbw= +10% 1.00 295 ‐1.8 290 291 ‐1.8 290 238 ‐1.4 290

δbw= +10% 1.50 295 ‐2.0 290 291 ‐2.0 290 238 ‐1.6 290

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Table 2 Little Ice Age climate reconstructions for Deming Glacier.

δb / w AAR = 0.66 BR = 2.3 BR = 2.2 δz (kg/m Δ δT δb Δ δT δb Δ δT δb Method a w a w a w 2m) ELA (°C) (kg/m2) ELA (°C) (kg/m2) ELA (°C) (kg/m2) Lapse rate only N/A 365 ‐2.2 0 340 ‐2.0 0 330 ‐2.0 0

δTa= 0 °C 0.00 365 0 1728 340 0 1609 330 0 1562

δTa= 0 °C 0.50 365 0 1910 340 0 1779 330 0 1727

δTa= 0 °C 1.00 365 0 2093 340 0 1949 330 0 1892

δTa= 0 °C 1.50 365 0 2275 340 0 2119 330 0 2057

δbw= 0% 0.00 365 ‐2.3 0 340 ‐2.1 0 330 ‐2.0 0

δbw= 0% 0.50 365 ‐2.5 0 340 ‐2.3 0 330 ‐2.3 0

δbw= 0% 1.00 365 ‐2.7 0 340 ‐2.6 0 330 ‐2.5 0

δbw= 0% 1.50 365 ‐3.0 0 340 ‐2.8 0 330 ‐2.7 0

δbw= +7% 0.00 365 ‐2.0 210 340 ‐1.8 210 330 ‐1.8 210

δbw= +7% 0.50 365 ‐2.2 210 340 ‐2.1 210 330 ‐2.0 210

δbw= +7% 1.00 365 ‐2.5 210 340 ‐2.3 210 330 ‐2.2 210

δbw= +7% 1.50 365 ‐2.7 210 340 ‐2.5 210 330 ‐2.4 210

δbw= +10% 0.00 365 ‐1.9 300 340 ‐1.7 300 330 ‐1.7 300

δbw= +10% 0.50 365 ‐2.1 300 340 ‐1.9 300 330 ‐1.9 300

δbw= +10% 1.00 365 ‐2.3 300 340 ‐2.2 300 330 ‐2.1 300

δbw= +10% 1.50 365 ‐2.6 300 340 ‐2.4 300 330 ‐2.3 300

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Table 3 Little Ice Age climate reconstructions for Coleman-Roosevelt Glacier.

δb / w AAR = 0.66 BR = 3.7 BR = 2.2 δz

(kg/m Δ δTa δbw Δ δTa δbw Δ δTa δbw Method 2 m) ELA (°C) (kg/m2) ELA (°C) (kg/m2) ELA (°C) (kg/m2) Lapse rate only N/A 213 ‐1.3 0 262 ‐1.6 0 168 ‐1.0 0

δTa= 0 °C 0.00 213 0 1008 262 0 1240 168 0 795

δTa= 0 °C 0.50 213 0 1115 262 0 1371 168 0 879

δTa= 0 °C 1.00 213 0 1221 262 0 1502 168 0 963

δTa= 0 °C 1.50 213 0 1328 262 0 1633 168 0 1047

δbw= 0% 0.00 213 ‐1.3 0 262 ‐1.6 0 168 ‐1.0 0

δbw= 0% 0.50 213 ‐1.5 0 262 ‐1.8 0 168 ‐1.2 0

δbw= 0% 1.00 213 ‐1.6 0 262 ‐2.0 0 168 ‐1.3 0

δbw= 0% 1.50 213 ‐1.7 0 262 ‐2.1 0 168 ‐1.4 0

δbw= +7% 0.00 213 ‐1.1 202 262 ‐1.4 202 168 ‐0.8 202

δbw= +7% 0.50 213 ‐1.2 202 262 ‐1.5 202 168 ‐0.9 202

δbw= +7% 1.00 213 ‐1.3 202 262 ‐1.7 202 168 ‐1.0 202

δbw= +7% 1.50 213 ‐1.5 202 262 ‐1.9 202 168 ‐1.1 202

δbw= +10% 0.00 213 ‐0.9 289 262 ‐1.2 289 168 ‐0.7 289

δbw= +10% 0.50 213 ‐1.1 289 262 ‐1.4 289 168 ‐0.8 289

δbw= +10% 1.00 213 ‐1.2 289 262 ‐1.6 289 168 ‐0.9 289

δbw= +10% 1.50 213 ‐1.4 289 262 ‐1.8 289 168 ‐1.0 289

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Table 4 Little Ice Age climate reconstructions for Boulder Glacier.

δb / w AAR = 0.66 BR = 4.7 BR = 2.2 δz (kg/m δT δb Δ δT δb Δ δT δb Method Δ ELA a w a w a w 2m) (°C) (kg/m2) ELA (°C) (kg/m2) ELA (°C) (kg/m2) Lapse rate only N/A 350 ‐2.1 0 393 ‐2.4 0 232 ‐1.4 0

δTa= 0 °C 0.00 350 0 1657 393 0 1860 232 0 1098

δTa= 0 °C 0.50 350 0 1832 393 0 2057 232 0 1214

δTa= 0 °C 1.00 350 0 2007 393 0 2253 232 0 1330

δTa= 0 °C 1.50 350 0 2182 393 0 2450 232 0 1446

δbw= 0% 0.00 350 ‐2.2 0 393 ‐2.4 0 232 ‐1.4 0

δbw= 0% 0.50 350 ‐2.4 0 393 ‐2.7 0 232 ‐1.6 0

δbw= 0% 1.00 350 ‐2.6 0 393 ‐3.0 0 232 ‐1.7 0

δbw= 0% 1.50 350 ‐2.9 0 393 ‐3.2 0 232 ‐1.9 0

δbw= +7% 0.00 350 ‐1.9 205 393 ‐2.2 205 232 ‐1.2 205

δbw= +7% 0.50 350 ‐2.1 205 393 ‐2.4 205 232 ‐1.3 205

δbw= +7% 1.00 350 ‐2.4 205 393 ‐2.7 205 232 ‐1.5 205

δbw = +7% 1.50 350 ‐2.6 205 393 ‐2.9 205 232 ‐1.6 205

δbw= +10% 0.00 350 ‐1.8 293 393 ‐2.1 293 232 ‐1.1 293

δbw= +10% 0.50 350 ‐2.0 293 393 ‐2.3 293 232 ‐1.2 293

δbw= +10% 1.00 350 ‐2.2 293 393 ‐2.6 293 232 ‐1.4 293

δbw= +10% 1.50 350 ‐2.5 293 393 ‐2.8 293 232 ‐1.5 293

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Table 5 Mean summer temperature (δTa) reconstructions for a change in net radiation (δR) and winter balance (δbw ) at the Little Ice Age maximum calculated using Equation 4 in Chapter 3.

Glacier Coleman‐ Roosevelt Easton Boulder Deming Average ΔELA (m) ‐213 ‐295 ‐350 ‐365 ‐306

δR δbw = 0% ‐2.72 ‐3.77 ‐4.47 ‐4.66 ‐3.91 (MJ/m2d) if: and δTa = 0 °C δR = ‐1 MJ/m2d ‐1.01 ‐1.63 ‐2.04 ‐2.15 ‐1.71 δTa (°C) if: and δbw = 0% δR = ‐1 MJ/m2d ‐0.63 ‐1.25 ‐1.66 ‐1.76 ‐1.33 and δbw = 10% δR = ‐2 MJ/m2d ‐0.42 ‐1.04 ‐1.45 ‐1.56 ‐1.12 and δbw = 0% δR = ‐2 MJ/m2d ‐0.04 ‐0.66 ‐1.07 ‐1.17 ‐0.74 and δbw = 10%

Note: All calculations assume a winter balance gradient of 1.00 kg/m2m; a ΔELA calculated using an AAR of 0.66, an ablation season lasting 150 days, and an ablation season temperature lapse rate of -0.0062°C/m.

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