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The Graduate School

2007

Assessment of Glacier Mass Balances from Small Tropical Glaciers to the Large Ice Sheet of Greenland Todd Hayden Albert

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THE FLORIDA STATE UNIVERSITY COLLEGE OF SOCIAL SCIENCES

ASSESSMENT OF GLACIER MASS BALANCES FROM SMALL TROPICAL GLACIERS TO THE LARGE ICE SHEET OF GREENLAND

By TODD H. ALBERT

A Dissertation submitted to the Department of Geography in partial fulfilment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Spring Semester, 2007

Copyright © 2007 Todd H. Albert All Rights Reserved

The members of the Committee approve the dissertation of Todd H. Albert defended on March 23, 2007.

______________________________ Jim Elsner Professor Directing Dissertation

______________________________ J. Anthony Stallins Professor Co-Directing Dissertation

______________________________ Henry Fuelberg Outside Committee Member

______________________________ Xiaojun Yang Committee Member

The Office of Graduate Studies has verified and approved the above named committee members.

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To my sister, who knew nothing about my topic, but everything about my struggle.

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ACKNOWLEDGMENTS

Countless people have helped me along the way in some way or another. While I can’t possibly acknowledge everyone who helped me complete this project, I will highlight some of the most important ones. First, I must begin with my wife, who has struggled through this process along with me, shared my frustrations, and probably felt like a single parent at many times. I could never have accomplished all I have without her help and support. My children, Sage and Noah, both helped by being supportive and understanding when Daddy had to work instead of play. This work owes much to their patience and flexibility. Luckily for me, support from my family extends far beyond the walls of my home. From my aunt and uncle who continually gave support and advise, to my cousins who understood the difficulties I faced, everyone was there when I needed a shoulder or ear. My parents are the true heros of this story, instilling me with a sense of the great importance and value of education. They are my true inspiration. My sister, Jennifer, to whom this work is dedicated, has helped me through the hardest parts of this Ph.D. She and I shared in the untimely loss of our mother. She also completed her doctoral degree while working and having two kids of her own. She always understood the struggles I was facing, even if she had no clue about the science I was studying. Her best motivation came when she described the feeling of being finished, that feeling of being able to sit on the couch and do nothing without feeling guilty about not working. Looking forward to that feeling helped keep me on track even in my darkest hours. Even my in-laws, Linda and Jay, provided tremendous support and motivation. I never would have started on this track, however, were it not for some of the great iv

teachers and professors that I met along the way. The first teacher who had a great influence on me was my 12th grade English teacher, Mrs. Hurley. She helped me see value in my writing and taught me that teachers can be your friend. In college, it was in Ellen Martin’s Introductory Geology class that I first learned about ice cores and about Ellen Mosley-Thompson and Lonnie Thompson. Having met Peter Waylen, Micheal Binford, Joann Mossa, and Cesar Caviedes, I had already decided that being a Geography professor was the life for me. Mike Binford, in particular, helped me to see just how cool Geography could be and the many great places it could take you. He also showed me the best way to teach a GIS or Remote Sensing class. Pete Waylen taught me that there is always time for your students, a lesson that was strongly reinforced by Lonnie Thompson later on. Ellen and Lonnie taught me much about the environment, the interconnected nature of the Earth system, and how to be a scientist. They also turned me on to the Quelccaya Ice Cap, a large focus of my research today. In Colorado, Jason Box, Nicholas Cullen, and Sandy Starkweather paved the way and taught me to conduct field work and taught me how to make it as a Ph.D. student. I owe a great debt of thanks to Jason for taking me under his wing and helping me become a field researcher and Greenland specialist. Koni Steffen gave me tremendous opportunities to conduct field research and turned me on to the Greenland Ice Sheet, a second focus of my research. Tad Pfeffer taught me more about snow and ice than I ever imagined there was to know. Roger Barry is a walking reference library of climate research. He sets high standards of what one person can learn and accomplish. Tom Chase taught me to be critical of every piece of science I encounter. Mark Williams taught me to clearly delineate my research while still listening to good music. Peter Blanken helped me to strike a balance between research, teaching, advising, and parenting. At Florida State, I could never thank Tony Stallins enough for his tremendous support and the work he put in to helping my edit my final draft. Jim Elsner helped me with everything from my statistics to my disc golf game while modeling how to drive my own children to do their best. He always had a quick answer to my frequently emailed questions. Xiaojun Yang gave me great encouragement to finish and helped build my self-worth. Henry Fuelberg also was a great asset as the outside member of my committee. v

Finally, I must acknowledge the tremendous support I have always gotten from my friends, both life-long and new, and from the communities I have lived in and been a part of. Most recently, the Cornerstone Learning Community, where I taught for three years, has offered much love and support throughout. I thank you all!

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TABLE OF CONTENTS List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Acronyms and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

II. BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

III. RECENT HISTORY OF DEGLACIATION ON THE TROPICAL QUELCCAYA ICE CAP, PERU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

IV. MEASURING MASS BALANCE ON THE GREENLAND ICE SHEET . . . . . . . . . . . . . 51

V. MODELING MASS BALANCE ON ICE SHEETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

VI. SUMMARY AND FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

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LIST OF FIGURES

1.1

Base map of Peru . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2

Map of Greenland Automatic Weather Station network . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3

Annotated diagram of Smart Stake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4

Photograph of servicing Automatic Weather Station by helicopter . . . . . . . . . . . . . . . . . . 9

1.5

Photograph of Swiss Camp in 1991 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6

Map of Pâkitsoq Ablation Region, Greenland . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.7

Photograph of refrozen meltwater ponds in Greenland . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1

Satellite image of the Quelccaya Ice Cap and its location in Peru . . . . . . . . . . . . . . . . . . 34

3.2

Satellite-derived ice-extent history for the Quelccaya Ice Cap . . . . . . . . . . . . . . . . . . . . 44

3.3

Map of the spatial pattern of retreat on the Quelccaya Ice Cap from 1962-2001 . . . . . . 46

4.1

3-D map of the Pâkitsoq region and entire elevation profile for Greenland . . . . . . . . . . 58

4.2

Scatterplot of measured density profiles and calculated water equivalent depths . . . . . . 61

4.3

Annotated surface height record for JAR2, a typical ablation zone site . . . . . . . . . . . . . 64

4.4

Greenland station mass balance histories arranged by increasing elevation. . . . . . . . . . . 66

4.5

Elevation profile of mean mass balance components for Greenland . . . . . . . . . . . . . . . . 67

5.1

Diagram of the time and space domains of influences on ice sheet mass balance . . . . . 71

5.2

Mean monthly PDDs for ablation zone sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.3

A flowchart of the SNTHERM model operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.4

Measured versus modeled surface lowering using various ice densities . . . . . . . . . . . . . 84

5.5

Measured versus modeled mean hourly surface energy fluxes . . . . . . . . . . . . . . . . . . . . 86

5.6

Diagram depicting idealized layers in a melting snow pack . . . . . . . . . . . . . . . . . . . . . . 96

5.7

General cases of idealized snow surface profile considered in the SOSIM model . . . . 100

5.8

Partial surface height record for JAR 2 with model time domain highlighted . . . . . . . 107

5.9

SOSIM model output for Test Case 1, JAR 2 2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.10

Comparison of modeled ablation in Case 1 between SOSIM and other models . . . . . . 109

5.11

SOSIM model output for Test Case 2, ETH 1999 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.12

Comparison of modeled ablation in Case 2 between SOSIM and other models . . . . . . 111 viii

LIST OF TABLES

3.1

List of satellite scenes used and their attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2

Summary of results of ice-area determination and error estimates . . . . . . . . . . . . . . . . . 44

4.1

Manufacturers reported weather instrument accuracies . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1

Albedos of snow and ice surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.2

Roughness lengths of snow and ice surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

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LIST OF ACRONYMS AND ABBREVIATIONS

ASTER

Advanced Spaceborne Thermal Emission and reflection Radiometer (remote sensor on the Terra satellite launched in 1999)

AW S

Automatic weather station (station designed to operate autonomously on a glacier and monitor the atmospheric pressure, radiation balance, profiles of temperature, wind speed, and humidity, and changes in surface height on a glacier; many stations transmit data hourly via satellite)

BPRC

Byrd Polar Research Center (cryospheric sciences center at The Ohio State University)

CIRES

Cooperative Institute for Research in Environmental Sciences; a joint institute between NOAA and CU

CP1

Crawford Point AW S station; CP2 was a second nearby station installed for a short period

CU

Univeristy of Colorado

EBM

Energy Balance Model

EGIG

Expedition Glacioloqique Internationale au Groenland; refers to mass balance experiments conducted over a transect on the Greenland Ice Sheet during 1959 and 1967 or to the transect line itself

ELA

Equilibrium line altitude (the elevation where mass gains and losses are equal on a glacier)

ENSO

El Niño - Southern Oscillation (refers to the atmospheric and oceanic teleconnection in the tropical Pacific Ocean which impacts global climate)

ETH

Refers to the Swiss Camp or the Swiss Camp AW S station; named for the Swiss Institute of Technology

ETM+

Enhanced Thematic Mapper Plus (an enhanced version of the TM sensor with an additional highresolution panchromatic band; part of the Landsat satellite program)

GC-Net

Greenland Climate Network (a network of automatic weather stations, AW S, on the Greenland Ice Sheet, maintained by NASA through the PARCA program)

GIS

Geographic Information Sciences/Systems

GLIM S

Global Land Ice Measurements from Space (an international group of scientists collaborating to monitor all of Earth’s ice from space)

GT

Global temparature

IPCC

International Panel on Climate Change

IRS

Indian Remote-sensing Satellite

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ISODATA

Iterative Self-Organizing Data (unsupervised remote sensing classification algorithm)

ITCZ

Inter-Tropical Convergence Zone

JAR

Jakobshavn Ablation Region refers to the lower portion of the ice sheet in West Central Greenland near the Jakobshavn outlet glacier; JAR1, JAR2, and JAR3 refer to AW S located in that region extending from Swiss Camp (ETH) near the equilibrium line (ELA) down toward the coast

LIA

Little Ice Age (a period of prolonged cold conditions from 1700 - 1850)

MEI

Multivariate ENSO Index (a combined measure of the strength and magnitude of the ENSO cycle)

MSS

Multi-Spectral Scanner (the original multi-spectral scanner of the Landsat satellite program)

NASA

National Aeronautic and Space Administration (the US Earth and space sciences agency)

NDSI

Normalized Difference Snow Index (a band-math remote sensing classification algorithm for snow and ice)

NOAA

National Oceanic and Atmospheric Administration

PARCA

Program for Arctic Regional Climate Assessment (a NASA program to monitor climate in the Arctic, with a special focus on the mass balance of the Greenland Ice Sheet)

PDD

Positive Degree Day; refers to the sum of positive average daily temperatures in °C

SAM

Spectral Angle Mapper (a supervised remote sensing classification technique)

SGI

Swiss Glacier Inventory

SM S

Smart stake (a less-expensive alternative to an AW S, designed to monitor temperature, wind speed, humidity, and changes in surface height on a glacier)

SOI

Southern Oscillation Index (one measure of the strength and magnitude of the ENSO cycle)

SOSIM

Semi-analytical One-dimensional Snow and Ice Melt model developed for this study

SPOT

Satellite Pour l'Observation de la Terre; a series of French multi-spectral satellites sensors

TM

Thematic Mapper (a multi-spectral sensor; part of the Landsat satellite program)

UTM

Universal Transverse Mercator (map projection)

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ABSTRACT

A combination of field work, modeling, and remote sensing was used to determine mass balances for the Quelccaya Ice Cap in Peru and for parts of the Greenland Ice Sheet. A 40-year history of deglaciation on Quelccaya derived from satellite is presented. Automatic Weather Station and snow pit data throughout Greenland were utilized to determine a mass balance profile for the ice sheet which will serve as a baseline for future comparison. Finally, a series of models were tested in west-central Greenland for their ability to accurately simulate measured melt conditions given hourly observations of the surface meteorology. A new analytical melt model, SOSIM, was developed and tested for this study.

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I. INTRODUCTION

FORWARD My interest in glaciers were first ignited in an undergraduate geology course. The instructor was explaining how scientists use ice cores to study past climates. We spoke after class about Ellen and Lonnie Thompson, a husband and wife team that gather ice cores from the polar regions and the tropics, respectively. I contacted them immediately and was soon working on my Masters degree under their supervision. My research on ice cores quickly led me to the realization that these important climate records are quickly disappearing along with most of the ice on Earth. My research interests shifted from paleoclimate to modern climate change, using glaciers as means to study it and remote sensing as one of my primary tools. This research path relies on an understanding of how glaciers respond to climate and on accurate methods for studying how the glaciers are changing. For my Master’s research, I applied remote sensing techniques to study the historical changes on a well-known tropical glacier, the Quelccaya Ice Cap. After my Master's degree, I worked for several years at the University of Colorado, Boulder, under the supervision of Konrad Steffen, the principal investigator on a NASA initiative to study the climatology of the Greenland ice sheet. Under his supervision I was awarded a graduate research fellowship from NASA to model melt near the margin of west-central Greenland, an area where many measurements were already being made. My research interests never shifted away from the tropics, yet they did expand to include the Greenland Ice Sheet.

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OBJECTIVES The objectives of this research are born of the need to understand contemporary changes in glacier extent. Following my own research path, this project begins in the tropics on the Quelccaya Ice Cap in southern Peru, a well-known ice cap in the tropical Andes, thought to be highly representative of glaciers in the region. My first objective is to present a methodology for studying montane glacier systems using remotely sensed data and introduces a history of ice extent on Quelccaya from 1962 to 2001. I develop a clear, repeatable methodology for studying changes in ice extent of montane glaciers, and present a modern history of ice extent changes on the Quelccaya Ice Cap. This aspect of the research will provide a unique history of glaciation in a region that is highly dependent on glacier melt runoff and where past climate changes have had tremendous societal implications . Although satellite remote sensing is a common methods for assessing changes in the morphology of a glacier, my specific analytical techniques (see Albert, 2002) are applied here to a series of images of the Quelccaya Ice Cap to develop the first historical snapshot of this tropical glacier. While these methods are appropriate for smaller glaciated areas, the great ice sheets on Greenland and Antarctica defy these methodologies due to their sheer size. Imagine studying the evaporation of a small puddle of water by taking successive digital photos of it from above. Observable changes in the small puddle would be indicative of the evaporation rate. Now imagine using those same methods to try to study evaporation from a large lake. The amount of evaporation from the lake would likely not be as easily observable as changes in the size of the lake. Furthermore, those changes would be difficult to capture using a digital camera. So, while visible satellite data are an ideal tool for studying montane glaciers, other methods must be employed on larger ice sheets. My objective in the second half of this dissertation focuses on the mass balance of the Greenland Ice Sheet as it will likely be the most important factor which will influence climate and sea level over the next century. The remote sensing methods used to study Quelccaya are not appropriate for the larger ice sheets. Accordingly, methods for studying the large ice sheets often focus on the flow speed of the glaciers or the mass balance over the surface of the glacier. No single, consistent method is appropriate for studying the cryosphere because it occurs in a wide variety of 2

forms on a wide range of scales. Furthermore, individual ice fields exhibit unique responses to climate forcing as the sensitivity to climate perturbations varies from glacier to glacier. A classic method for determining changes in the mass balance on a glacier involves making mass balance measurements over an elevation profile on the glacier and comparing contemporary measurements to those made previously. In a warming climate, more accumulation is generally expected at higher elevations on a glacier, while more ablation is expected at lower elevations. Therefore, we expect a steepening of the mass balance profile in a warmer climate, as has already been observed on many glaciers around the world (Dyurgerov and Dweyer, 2000). As no such profile previously existed for Greenland for comparison, an initial mass balance profile is created for the Greenland Ice Sheet using recently recorded mass balances over the largest elevation profile ever created on a glacier. These measurements are combined with in situ observations of snow depth and density. Means of measuring these changes in the field are discussed, and a dense network of monitoring stations that has been established on the west-central ablation area of the Greenland Ice Sheet is described. These stations record hourly observations of surface height changes which may be related directly to changes in surface mass balance. While this new mass balance transect provides a useful baseline for future comparison, the downside of it being the first measurement is that there are no profiles to compare it to, and thus, a determination of the trajectory of the ice sheet, whether it is shrinking or growing, cannot be made. Accordingly, my closing objective is to discuss and evaluate methods for modeling changes in surface mass balance in this region. More specifically, I seek to evaluate a series of melt models to determine their applicability to the melt zone in west-central Greenland. A common statistical model, the positive degree day (PDD) model, is a simple empirical model which uses easily obtained temperature measurements to predict the melt at a site on the glacier. The model makes several assumptions of homogeneity regarding the relationships between melt, temperature, and elevation, and neglects or rejects several known feedback mechanisms which can enhance melt on a glacier. I present the results of statistical tests on the soundness of the assumptions made by the PDD model. These tests are conducted by applying the model to the measured temperature and mass balance profile on the Greenland Ice Sheet. A direct comparison is made between modeled melt and

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measured surface lowering to statistically test the validity of the underlying assumptions of the PDD model. For studies of the spatial variability of melt, this simple model fails. Attention is then turned to a common numerical model, SNTHERM. This model was developed by the U.S. Army to find tank tracks in snow using thermal imagery. Unfortunately, the model fails when there is solid ice beneath the snow. Finally, a simpler, analytical model, SOSIM, is created using energy balance methods, but its results do not end up offering any advantage over the PDD model.

RATIONALE Ice is among the most valuable resources on Earth as it is the largest source of fresh water. Montane glaciers and snowpack provide 80% of the freshwater used on Earth. By 2025, the demand on water in developing regions will expand greatly. Arid and semi-arid regions face water scarcity as climates change and demand increases. It is projected that much of this scarcity will be focused on rapidly expanding urban areas. Concerns in these areas will not only include water scarcity, but water quality (Vorosmarty et al., 2000). The management of this resource may be an important future political issue and may rely on observed and predicted changes in the volume and distribution of ice on Earth. Mass-balance estimates may prove useful in determining the capacity of glaciers to store and release fresh water and the variations that can be expected (Paterson, 1994). These predictions, along with estimates of the life-span of these glaciers, may be utilized in decisions regarding the careful allocation of water resources today and in the future (Martinson et al., 1998). This will become increasingly important as urban populations grow and the glaciers supplying their water shrink. As ice on Earth is such a crucial resource and has extremely important ties to the Earth system, especially to our climate, and our climate is currently undergoing rapid and dramatic warming (0.13°C per decade since 1960; IPCC, 2007), it is essential to gain a better understanding of how ice behaves in and influences our climate. Accordingly, this research will focus on the Earth's changing ice cover and ways to better study and understand it.

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FIELDWORK Since a standard academic chapter would not convey the extreme investment in effort of completing the field work associated with this research, this section will deviate from the normal academic nature of the dissertation in an attempt to describe the arduous nature of the work, what was accomplished, and also outline specifically what field work, development, instrument deployment and other work was done by the author. Glaciers are almost always located in extreme environments, so working in these conditions requires skill, equipment, and patience. My field experience in Peru at high elevations was cut short by an unusual storm, thus the description of that work is much shorter than the description of the several months I spent in Greenland over two field seasons.

Peru Expedition Quelccaya is the world's largest tropical ice cap and is located far off the beaten path in the high Andes mountains (Fig. 1.1). From the summit of the ice cap, one can nearly distinguish the great Amazon rain-forest just off to the east. My interests in Quelccaya stem from earlier work on Andean ice extent with Lonnie Thompson and Ellen Mosley-Thompson (Albert, 2000). This research spurred a later multi-disciplinary trip to the ice cap funded by a grant from CIRES, a join institute between NOAA and the University of Colorado (CU). Being in the tropics, Peru's climate is dominated by a huge annual shift in precipitation between an ultra-arid dry season (May to November) and the extreme wet season (December to April) when precipitation occurs in almost daily convective thunderstorms. In the high Andes, this precipitation typically falls as snow, accumulating on mountain tops and refreshing existing glaciers, ice caps, and snow fields. This daily refreshing of the albedo, or surface reflectivity, reflects much of the solar insolation and insulates the underlying ice, both of which work to minimize melting.

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According to the climate, any field work must be done during the dry season, once the ephemeral snowfall has melted off. My proposed visit to the ice cap was carefully scheduled in the height of driest time of the year. The intentions of the visit were to drill holes in the ice cap using a light-weight hand-powered ice corer and then install metal stakes in the holes which could be

Figure 1.1: Base map showing the location of the Quelccaya Ice Cap and nearby cities. Shaded areas are above 3500 m elevation.

surveyed annually to determine the amount of surface accumulation and melting, the two major components of the surface mass balance. Nonetheless, the field expedition was thwarted by an unprecedented 16-day long blizzard which made international news and resulted in the death of thousands of domesticated alpaca and llama. My expedition, when it made it out of the blizzard by crossing a 6000 m pass in meter-deep snow, had to return to the nearest city, Cuzco. 6

Greenland Expeditions My studies of the cryosphere took me from the Andes of Peru to the large dome-shaped ice sheet in Greenland. It did not take long to realize that the simple methods used to study tropical glaciers could not be applied in a meaningful way to an ice sheet, which is more continental in scale. Rather, in situ measurements and some modeling seemed to be appropriate methods to study changes on the larger ice body. Accordingly, I took on the task of creating cheap and robust autonomous weather and surface monitoring stations which could be deployed along side, but in greater spatial density than the existing network of autonomous weather stations (AWS) installed on the ice sheet as part of NASA's Greenland Climate Network (GC-Net; Figure 1.2). With assistance from a trusted colleague (Box, pers. comm.), I created a design for NASA's new Smart Stakes (SMS), depicted in Figure 1.3. SMS are a compromise between the expensive and robust AWS and a much simpler ablation stake. They record hourly measurements of surface height, monitoring changes in snow accumulation and ablation (mass loss), temperature, wind speed and direction, and relative humidity (Figure 1.3). While these stations are not as exhaustive as the AWS, which measure snow temperatures along a depth profile, two levels of air temperature, wind speed and direction and relative humidity, station pressure, and in-coming, outgoing, and net radiation, they are much less expensive to build and far easier to maintain. By far, the greatest expenses of each station is maintenance and retrieval of the data. Some of the AWS transmit the data hourly via satellite and need only to be visited biannually. The satellite transmission time is a tremendous yearly expense. Other stations need to be visited more frequently to retrieve the data, and all stations must be maintained, at a minimum, lowering the stations in the ablation zone, where the annual melt leaves the stations situated high above the surface, and raising the stations in the accumulation zone, where annual snowfall threatens to bury the stations.

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Figure 1.2: Map of the Automatic Weather stations (AWS) on the Greenland Ice Sheet. These stations, along with the Smart Stakes (SMS) described in the text, are part of NASA’s Greenland Climate Network (GC-Net).

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Figure 1.3: Annotated diagram of a Smart Stake (SMS) station.

Figure 1.4: A helicopter and pilot wait while J. Box and T. Albert (photographer) service an AWS at Crawford Point (CP1) on the Greenland Ice Sheet. 9

Raising or lowering each AWS required the better part of a day, working in sub-freezing temperatures, often in very windy conditions. The stations are spread across the ice sheet in some of the least accessible and least hospitable areas in the northern hemisphere. To reach some stations, we need to charter a Twin Otter (DHC-6), a dual propellor airplane equipped with skis for landing on snow, and a pilot qualified to make the flights and landings. In some cases, we are dropped off at a station with our tools, food, a stove, and a tent, and the plane returns the next day. In other cases, the pilot waits in the plane and our work is rushed. Other stations are reachable by helicopter (see Figure 1.4), or by LC-130 (often using JATO – jet-assisted take-off – rockets when taking off from snow), a large cargo plane used by the military. One area of the ice sheet has been established as a focus for NASA's PARCA program (Program for Arctic Regional Climate Assessment). This area, located in west-central Greenland, near the famous Jakobshaven outlet glacier, begins at the equilibrium line, where, on average, annual accumulation and ablation totals are equal. In 1991, a group from the Swiss Institute of Technology (ETH), lead by Atsumu Ohmura, established a research camp on the equilibrium line in this area. This camp has served as a base of operations for much of NASA's field work on Greenland. The camp was originally designed to be temporary (and above ground; see Figure 1.5), but after ETH finished with it, Konrad Steffen, now affiliated with CIRES and CU, bought it from ETH for 1 $US,

Figure 1.5: Photograph of Swiss Camp in 1991, prior to being covered by drifting snow. 10

and the camp is now the base for GC-Net operations. Since taking over the camp, Steffen's group has established a relatively dense AWS network from the Swiss Camp down toward the ice margin. The intentions of this part of the GC-Net is to study the processes which affect ablation on the ice sheet. This region was dubbed JAR, which stands for Jakobshaven Ablation Region, and the AWS below the equilibrium line were named JAR1 (closest to ETH) through JAR3 (closest to the ice margin). The AWS located at Swiss Camp is referred to as ETH. Figure 1.6 depicts the locations of the AWS and SMS in the JAR area. The inset map shows the location of the region within Greenland.

Figure 1.6: Map of the GC-Net station locations used in this study. The inset map shows the relative location in Greenland and the extended elevation profile up to the Ice Sheet Summit referred to later in the text.

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With a set of four newly designed SMS, I took my first trip to Swiss Camp in the spring of 2001. In the ten years since the camp was built, snow drifts had buried the camp, and the only way to access the indoors was through a hatch in the roof. Since the camp was left in the previous spring, the summer melt season had flooded the camp with approximately 1 m of water. Over the winter, that melt water froze into a solid block of ice. My first week at Swiss Camp was spent chipping 12 metric tons of ice out from the work tent and kitchen tent (leaving the former sleep tent filled with ice) and hauling the ice up through hatches in the roof and away from the camp. We also spent time staging our equipment, setting up Scott tents for sleeping, and each day also involved a regiment of cooking, cleaning, and gathering and melting snow for water. Once the camp was ‘opened', the science began. GPS units were installed along an elevation profile extending up and down from the camp. My primary task was to calibrate the instruments for the SMS. Sometime in our third week at the camp, we loaded up snow mobiles and sleds with a steam drill, tents, stoves, tools, food, and other gear, for a journey down into the ablation region. The steam drill burns propane to heat water and pump it through a metal bit at the end of a long hose, using the steam to cut small holes down through the ice. These holes, which remain filled with water if you manage to avoid finding a crack in the ice, quickly refreeze once the drill is turned off. This allows us a few moments to install a long mast, typically made of aluminum, deep into the ice. Instruments and other equipment mounted on the mast become AWS or SMS (see Figure 1.3). Journeying into the ablation zone is risky business. If one manages to avoid falling into a crevasse, some of which are large enough to swallow a large building, the next most serious danger is to be there when the melt season begins and the snow surface transforms into large sheets of rushing water in which no snowmobile can operate and no human can stay dry and warm. The traverse down into the ablation zone allowed us to first visit each station and download the past year's data. Once making it down to JAR3, we then retraced our tracks, lowering and maintaining each station on the way up. Maintenance consists of syncing the clocks on the station data loggers, replacing any broken or failing instruments, and then lowering each station to account for the previous year's ablation. Lowering is done either by lowering the boom arms with the instruments and cutting the top of the mast off, or, more commonly, by cutting the station down, 12

adding a long extension to the mast, drilling a deep hole in the ice with the steam drill, and then reinstalling the station. In several cases, the first hole drilled would drain, despite locating them in depressions, and a second hole would need to be drilled, a slow and tedious process. On our traverse, we saw the earliest signs of melt (see Figure 1.7). Since Swiss Camp was established in 1991, no one had witnessed melt water ponds forming that early in the season. This hastened our preparations for our second traverse, on which I installed the four SMS. These SMS enhanced the spatial and elevational resolution of the mass-balance profile. The profile, shown in Figure 1.6, extends from JAR3, near the ice margin, up to ETH, on the equilibrium line. Adding the existing Crawford Point stations, CP1 and CP2 located at approximately 2000 m elevation, and the Summit AWS, at approximately 3200 m elevation, makes this the largest elevation profile existing on a glacier.

Figure 1.7: Photograph of refrozen meltwater ponds on the ice surface near the coast (coastal mountain range is visible). The existence of meltwater ponds in this area is common later in the season, but in early May, when this photograph was taken, they are indicative of an early oncoming melt season.

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On subsequent trips to Greenland, the SMS were serviced and their data were collected. These data, along with the available AWS data, are used in this research report to evaluate the present mass balance on Greenland and to evaluate surface melt models. A mass-balance profile for west-central Greenland is presented in Chapter IV. When I first applied to the University of Colorado, and throughout my time there, my passions lied with tropical glaciers like Quelccaya. After my first semester, however, my advisor had directed my studies to the Greenland Ice Sheet. Long before I ever set foot in Greenland, he suggested that I undertake a project to model the melt on the western margin of the ice sheet. My experience with remote sensing and my studies in glaciology and tropical climates did little to prepare me for a modeling project on the Greenland Ice Sheet. My new project, now funded by a NASA Graduate Research Fellowship, began with a steep learning curve about models, the types of models that exist, and an evaluation of the existing models that could be useful for this project. I looked at statistical, analytical, and numerical models.

CONTRIBUTIONS TO GEOGRAPHY This dissertation contributes to the fields of Geography and Glaciology in several ways. My research in Peru provides a method for determining ice area from satellite imagery when groundtruth data are not available, and also provides a 40-year history of tropical deglaciation on the Quelccaya Ice Cap. This history suggests that the recent deglaciation likely began in the late 1970s and was punctuated by two periods of limited retreat in 1992-1993 and 1998-2001. My research in Greenland provides the first mass balance profile on the Greenland Ice Sheet, the largest mass balance profile ever created on a glacier. Comparisons with future mass balance profiles will help determine the health of the ice sheet. Finally, my research turned to melt modeling in Greenland. I point out some problems with the most common melt model, the positive degree day model, and I developed a much more effective, albeit data hungry model. Future versions of this new model may be coupled with the Polar MM5 or other atmospheric models to help model the future development of the ice sheet.

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II. BACKGROUND

GLACIERS IN THE CLIMATE SYSTEM Climate fluctuates on all time and spatial scales, and these fluctuations are reflected in the continually varying distribution of ice on Earth (Paterson, 1994). In turn, these changes in ice cover affect global sea level. Ice presently covers about 3% of the Earth's surface and contains nearly 75% of its fresh water (Martinson et al., 1998). Glaciers are important on regional scales as reservoirs of water for drinking, hydroelectricity, and irrigation, and can effect humans through sudden events like ice dam collapses, or through glacier advances which can threaten human structures. On a larger scale, glaciers, and especially ice sheets, can modulate sea level and effect climate through the albedo feedback and by affecting the thermohaline circulation. The great ice sheets even affect climate by posing as a barrier to atmospheric circulation. The importance of understanding the relationships between climate and glacial activity has long been recognized. Accordingly, the International Commission on Glaciers (now called the International Commission on Snow and Ice) was founded in 1894 (Dyurgerov and Meier, 2000; Forell, 1895), and the Global Land Ice Measurements from Space (GLIMS) initiative began recently to monitor the world's glaciers using satellite-borne sensors (Abrams, 2005; Kääb et al., 2002b; Paul et al., 2004; Kargel et al., 2005). Evidence from ice cores suggest that CO2 levels in the atmosphere may have topped 1000 parts per million by volume (ppmv) 50 million years before present (yBP) during the Eocene epoch, even higher than they are today (Kennedy and Hanson, 2006). At that time, sea level was 50 m higher. The larger ocean basins allowed for greater populations of marine organisms that fix CO2 15

through photosynthesis.

This increased photosynthetic activity drove down greenhouse gas

concentrations, driving down the Earth's temperature. By 30 to 40 million yBP, ice sheets began to grow on Antarctica. By 3 to 4 million yBP, CO2 concentrations fell below the pre-industrial levels of 290 ppmv, allowing great ice sheets to form in the northern hemisphere. Since that time, cycles of glaciation and inter-glacial stages have dominated the Earth's climate cycle, and temperature, CO2, and sea level have all fluctuated in step, but inversely with Earth's ice cover. At no time in the past 10 million years, however, have CO2 levels been as high as today's concentration of 380 ppmv and rising. To look for a climatic analogy for our future climate, some scientists fear that we must look to the Eemian around 125,000 yBP, where temperatures on Earth were much warmer, there was scarcely ice on the planet, and, consequently, sea levels were much higher. In that climate, plants thrived, eventually squelching much of the excess CO2. Over geologic time scales, the Earth undergoes a rhythmic pattern of climate change whereby the Earth naturally cools and freezes over tens of thousands of years and then naturally warms, far more rapidly, causing the ice to melt and a return to a warmer, more mild, and less variable climate. These warm periods, called interglacial stages or stadials, punctuate the longer glacial stage conditions where great ice sheets cover much of the northern landscape and sea level drops 70 m or more. With a lower sea level, much of the Earth's land area is, relative to sea level, higher in the atmosphere where the air is colder and there is more ice. This helps the ice sheets continue to expand and the cycle to perpetuate. This saw-toothed pattern of slow cooling and rapid warming only occurs, to our knowledge, during ice ages, times when there is ice on Earth. The present ice age has persisted for the last 40 million years (Imbrie and Imbrie, 1979). These climate cycles are driven by a complex interplay within and between several spheres of the Earth system, and may be influenced by external factors as well. As climate cools, heading into a glacial stage, ice advances displacing plants which normally take up carbon dioxide (CO2). Also, sea level is lowered, and the smaller ocean basins have less surface area to absorb CO2 from the atmosphere. These changes on land and in the oceans cause the atmospheric greenhouse gas (GHG) concentrations to level out or slowly rise. After thousands of years, these concentrations reach a critical threshold, the Earth begins to rapidly warm, the ice sheets disintegrate, and sea-level rebounds. This cycle has aligned itself with the Earth's astronomical (Milankovitch) cycles, which 16

some claim (Hays et al., 1976; Imbrie and Imbrie, 1979; Muller and MacDonald, 1997) is the primary cause of the glacial-interglacial cycles. The dramatic warming events, and other such abrupt shifts in climate, are exhibited by the Earth's climate system at multiple scales. At the glacial-interglacial scale, we see these shifts at the end of the glacial stage when GHG levels increase to a critical level and the climate changes relatively quickly to interglacial conditions. The ice quickly retreats – we are now witnessing ways in which deglaciation can reinforce itself on a large ice sheet, such as melt water penetrating to the base and lubricating ice flow (Zwally et al., 2002;), and sea-ice edge effects (Li et al., 2005). Plants return quickly – we are witnessing how quickly this occurs in Peru as glaciers retreat and plants return to the newly uncovered soil within a few years. Also, sea levels quickly rebound. The rising sea level helps reinforce the warming by effectively lowering the land and the remaining ice to lower portions of the atmosphere where it is warmer. In all, the change to interglacial conditions is far faster than the slow progression to glacial conditions. We also see equally dramatic shifts in climate that occur much more rapidly and punctuate this regular cycle (Rial et al., 2004; Seager and Battisti, accepted). A classic example of such a rapid shift occurred at the end of the last glacial stage as we headed into the Holocene interglacial. As the Earth was warming about 12,800 years ago, the climate suddenly shifted back to glacial conditions. This shift took less than a decade. This event, the Younger Dryas, lasted nearly 1500 years and then ended as abruptly as it started, causing temperatures in Greenland to rise approximately 20°C in 10 years or less. These changes in climate are all reflected in the Earth's changing ice cover. Careful observation and analysis of changes in the extent and volume of ice may contribute to the reconstruction of past climates and aid in the understanding of current and future climate changes. Changes in the mass balance and morphologies of glaciers and ice sheets provide insight into changing climatic conditions on various spatial scales and temporal scales.

SMALL GLACIERS Tropical montane glaciers provide critically important resources to many montane and low-lying areas. In arid and semi-arid areas, mountains provide up to 100% of the available 17

freshwater to the surrounding lowlands (Meybeck et al., 2001), while these environments are among the most sensitive to environmental change (Diaz et al., 2003). The high relief and high gradients found in these environments make mountains profoundly sensitive to extreme precipitation events and to slight changes in temperature. Many societies rely on glacial melt water as a source of drinking water, irrigation water for agriculture, and as a crucial source of hydroelectric power (Mark and Seltzer, 2003). The populations dependent on these resources may be severely affected by the response of glaciers to climatic changes (Francou et al., 2003). In temperate regions, where the snow-pack is close to melting conditions, a small increase in temperature may have a significant change on the local mass-balance, and therefore the meltwater runoff. With enhanced warming, temperate regions will experience an increase in the frequency of rain, and the snowline will rise by an expected 150 m/°C of warming (Beniston, 2003). Accordingly, tropical glaciers have received much recent attention as their importance as water resources and as early indicators of climate change have recently been recognized (Georges, 2004). Changes in glacier melt runoff in a warming climate do not vary linearly with climate. Instead, they depend also on the size of the glacier, the rate of temperature rise, and other factors which influence the glacier mass balance, including changes in precipitation rates and type with elevation, changes in the elevation temperature profile, changes in the seasonality of temperature and precipitation, and the mass balance distribution with elevation. Typically, however, as climate warms and glaciers retreat, the runoff tends to increase at first, but then decrease as the size of the retreating glacier diminishes (Ye et al., 2003). On all glaciers, volume tends to exhibit the most significant change in a warming scenario. Smaller glaciers with higher runoff peaks tend to exhibit the most variability in runoff and retreat more quickly than larger glaciers. Also, the faster the temperature rises, the runoff peaks become earlier and higher (Ye et al., 2003). Throughout the 20th century, observations confirmed a general thinning and retreat of glaciers globally (Dyurgerov and Meier, 2000; Francou et al., 2003; Fujita et al., 2006; Kaser et al., 2004a; Paul et al., 2004; Ramirez et al., 2001; Thompson et al., 2002; IPCC, 2001; Meier et al., 2003, Thompson, 2004), although glacier studies are highly biased toward rapidly changing glaciers, and many glaciers respond to other physical parameters, including isostatic rebound of continental 18

crust, Milankovitch cycles, and climate teleconnections including the El Niño – Southern Oscillation (ENSO). Furthermore, each glacier is located in a unique climate regime and has a unique response to environmental changes. Accordingly, there is considerable variability in the mass balance of glaciers. While many glaciers are retreating, some exhibit growth or expansion (Dyurgerov and Meier, 2000; Paterson, 1994). The growth of glaciers in Scandinavia and in parts of the former Soviet Union has been attributed to the increase in snow accumulation at higher latitudes in the late 20th century (Popovin, 1996). Glaciers in the Caucasus Mountains of the former Soviet Union are predicted to grow through 2025 for this same reason (Kunakuhovitch and Sokalskaya, 1996). Although glaciers and ice caps contain a small fraction of the total ice on Earth, they may have a much larger impact on the rise of sea level over the next one hundred years than the large ice sheets (IPCC, 2001; Oerlemans and Fortuin 1992). This is attributed to their rapid rates of mass accumulation and ablation (loss), and because many of the smaller glaciers will likely disappear completely by the end of this century (IPCC, 2001). Glaciers and small ice caps (henceforth GSICs) outside of Antarctica and Greenland comprise only 0.7% of the Earth's ice, yet they play a significant role in the global hydrologic cycle, particularly the transfer of freshwater to the oceans (Williams and Hall, 1993). The total volume of GSICs is 180,000 km3, and the estimated maximum GSIC contribution to sea level rise is 0.6 m. Most of this volume is found in small glaciers with extents of 100 to 1000 km2. These smaller glaciers are potentially the most vulnerable and susceptible to climate fluctuations. Smaller, thinner glaciers are thought to respond much more rapidly to changes in climate, and frequently, these changes may even be observed in the field (Jóhannesson et al., 1989; Williams and Hall 1993). Changes may occur so rapidly that a short-term climate forcing such as a volcanic eruption may halt or reverse the retreat of the terminus of a glacier. During the last glacial maximum (18,000 yBP), the volume of glacier ice was two and a half times the present volume and the surface area covered by ice was three times the present area. This generated a much higher surface albedo, causing the Earth to cool radiatively. Surface albedo can have a strong positive feedback on ice cover and global temperatures. This effect contributes dramatically to the energy balance of a glacier, which, along with mass gain due to accumulation, determines the mass balance of the glacier (Oerlemans and Fortuin, 1992). Albedo varies greatly 19

with time, even seasonally, and through space, even on a single glacier. In general, albedo decreases with a decrease in altitude (down a glacier), and decreases during the melt season. Modeling the contribution of glacial retreat to sea level rise for various future climate scenarios would be possible given the sensitivity of the glacier to climate. The sensitivity should include the effect of meteorological variables on the mass balance and its components, and the feedback of the ensuing changes on the glacial system. Currently, the sensitivity is unknown, but can be estimated using knowledge of past glacier volume change with observed climatological fluctuations (IPCC, 2001). Further complicating the issue is the idea that most glaciers in the world may not be in equilibrium, and have not been since the Little Ice Age. This impedes the calculation of the initial boundary conditions which are necessary to compute the sensitivity. Furthermore, GSICs may be divided into high-latitude glaciers and tropical and sub-tropical glaciers. Although there is significantly more ice volume in high-latitude glaciers, tropical glaciers exist close to melting conditions, and are therefore extremely sensitive to changes in climate. Having a greater sensitivity to climate, tropical glaciers should respond most quickly to changes in climate. This makes them exceptional indicators of recent environmental changes, and their effects on natural systems (IPCC, 2001; Oerlemans, 1994; Oerlemans and Fortuin, 1992). The determination of climate change by glacial response is inhibited by the varying response and sensitivity from glacier to glacier (Oerlemans, 1994). Compounding this is the fact that glacier mass balance is not only affected by temperature, but may have a greater dependence on precipitation and cloud cover (Kaser et al., 2004a; Oerlemans, 1994; Oerlemans and Fortuin, 1992; Kaser and Osmaston, 2002). According to research by Oerlemans and Fortuin (1992), glaciers in moister regions are more sensitive to climate fluctuations than those in more arid areas. This is attributed to the large mass flux of these glaciers which often extend to lower elevations and hence, warmer temperature regimes. The fraction of wet precipitation on these glaciers is comparatively high and is expected to increase with an increase in temperature. This will increase the rate of melting and the length of the melting season, an effect that is much less significant for arid glaciers. Additionally, the albedo feedback increases with higher precipitation rates.

20

Significant increases in precipitation will probably not compensate for the increased melting on tropical and sub-tropical glaciers. Therefore, if the climate warms as expected, GSICs, particularly those in low-latitude, moister regions, will likely retreat rapidly (Oerlemans and Fortuin, 1992). This could potentially have tremendous social and environmental repercussions.

ICE SHEETS Recently, interest has steered toward the potential role in sea level of melting of glaciers due to climatic warming (Alley et al., 2005; Cogley and Adams, 1998; Dyurgerov and Meier, 1997; Meier, 1984; Zuo and Oerlemans, 1997). Current studies have focused on assessing the changes that might occur in the coming century due to projected climatic warming (Braithwaite and Zhang, 1999; Dyurgerov and Meier, 2000; Gregory and Oerlemans, 1998; Meier, 1993; Oerlemans, 1993a, b; Oerlemans and Fortuin, 1992; IPCC, 2001; Zuo and Oerlemans, 1997). The vast polar ice sheets have the greatest potential to affect sea level. In a warming climate, melting along the margins of the Greenland Ice Sheet is expected to accelerate, and has done so even faster than expected. The effects of warmer temperatures on Antarctica may partially offset the effects of Greenland as increased accumulation there may result in a lowering of sea level. Still, modern observations neither confirm nor discord these presumptions and both ice sheets' future roles in sea level remain unresolved. Likewise, the most sophisticated global climate models still do not possess high enough resolution to capture the enhanced melting along the ice sheet margins, although they do predict an increase in accumulation over the interiors of Greenland and Antarctica (Wild et al., 2003), and passive and active microwave measurements over the Greenland Ice Sheet demonstrate that this increase in melt is well underway (Steffen et al., 2004). The additional meltwater production at the surface is likely enhancing the basal sliding by percolating and lubricating the base (Zwally et al., 2002). The waxing and waning of the ice sheets is controlled by both long- and short-term forcings (Bradley, 1999; Paterson, 1994). Over short time scales, precipitation over the ice sheets determines their mass balance (Bromwich, 1995; McConnell et al., 2000), whereas over longer time scales, it is a result of the centennial- to millennial-scale climatic and dynamic history of the ice sheet (Reeh, 1999). A change in an ice sheet's mass balance results in a kinematic wave which propagates out 21

toward the margins at rates up to four times the rate of ice flow. The time required for such a wave to reach the margin defines the ice sheet's response time and depends on basal slope, ice thickness and temperature, and overall ice sheet geometry (Nye, 1965b; Paterson, 1994). Generally, larger ice masses respond more slowly to changes in climate. Hence, the large ice sheets act as a low pass filter to climate change, primarily responding to longer-term climate trends. This makes ice sheets exceptional indicators of long-term climate trends, yet they may also seem to behave independently of the present climate due this inherited mass balance and dynamics from previous epochs and from its own influence on the regional climate (Paterson, 1994). Ice sheets, are dynamic systems that gain and lose mass in patterns that vary through space and time on all scales. Ice masses exhibit the most rapid response to shifts in climate of all of Earth's systems (Lowell, 2000). In response to an increased flow of energy to the surface, either by turbulent or radiative transfer, the temperature of a non-ice surface would increase and the surface would emit more energy to maintain its balance. In contrast, the surface temperature of melting ice is fixed, and increased energy is used entirely for further melting (Oerlemans, 1994). In the latter part of this century there has been an abundance of evidence suggesting that 20th-century warming was unprecedented (Andranova et al., 2004; Brook, 2005; Brumfiel, 2006; Thompson et al., 2006) and that 21st-century warming is projected to be much greater than the natural variability within the climate system over the past 1000 years (Santer et al., 1995; Thompson, 2000; Thompson et al., 2000).

Furthermore, it is highly likely that 75% or more of the

post-industrial warming that has occurred is from anthropogenic greenhouse gas emissions (Crowley, 2000). These realizations have been accompanied by an increased awareness of the potential risks of global climate change on human settlements. Perhaps one of the most striking and significant of these possible social impacts is the threat of global sea-level rise as coastal cities already threatened by flooding may be severely affected by a small rise in sea level (Dahl-Jensen, 2000). Studies suggest that the predicted sea-level rise and population distributions could lead to over 150 million environmental refugees by 2050 (IPCC, 2001). Nearly all of the freshwater on Earth is locked in the great ice sheets of Greenland and Antarctica. The Antarctic ice sheet alone contains over 70% of the world's fresh water supply (Thomas, 1993), and exceeds 29 × 106 km3 of water volume (Jacobs et al., 1992). Most of the 22

volume of the ice sheet lies above sea level, making the potential for sea level rise very significant, even for the loss of a small part of the immense sheet. The detection of recent deterioration of the ice shelves on the Antarctic Peninsula, such as Larsen and Wordie, and extensive iceberg discharges from the Flichner and Ross Ice Shelves have drawn attention to the possible collapse of the ice shelves over the coming century (Domack et al., 2005). Since their mass of water has already been displaced, sea level cannot rise from the break-up of floating ice shelves. However, the shelves may control the discharge of fast-moving inland ice streams. These ice streams not only affect sea level, but the stability of the ice sheet itself (Alley et al., 2005). The potential sea level rise if Antarctica were to melt is over 70 m (Williams and Hall, 1993). According to the IPCC (2001), a collapse of the East Antarctic Ice Sheet is highly unlikely, even with the warming predicted by a doubling of CO2. This is attributed to the extremely low surface temperatures over the ice sheet. Some studies have shown that the volume of ice on East Antarctica is increasing slightly with time, and conclude that the ice sheet will help offset some of the predicted sea-level rise (Alley et al., 2005). However, other mass balance studies of the ice sheet suggest that Antarctica is losing more mass than it is gaining, and that the ice sheet is less stable than previously thought to be (Rignot and Thomas, 2002; Alley and MacAyeal, 1994; Jacobs et al., 1992). Mercer (1978) suggested that the West Antarctic Ice Sheet is less stable than the Greenland Ice Sheet, and concluded that its collapse would be sudden and could accompany what otherwise would seem like a modest warming. He foretold that the collapse of the ice shelves around the Antarctic Peninsula would occur first as an early warning to the larger collapse of the West Antarctic Ice Sheet, which itself could raise sea level by 5 m. Domack et al. (2005) found that the recent collapses around the Larsen B ice shelf are unprecedented and represent a response to modern climatic change. Recent observations suggest that the ice sheet's contribution to sea level is positive and accelerating (Thomas et al., 2004), and may be contributing more to sea-level rise than the ice sheets of Greenland or East Antarctica (Zwally et al., 2005). Keller et al. (2005) suggest that considerable reductions in greenhouse gas emissions are needed to avoid the otherwise imminent and potentially costly collapse of this ice sheet. Most of the ice loss on Antarctica is due to iceberg calving (Jacobs et al., 1992), the rate of which is determined by processes involving long response times (IPCC, 2001). A warming event 23

may take many thousands of years to reach the base of Antarctica, and it is therefore assumed that a collapse or decline of the ice sheet would be caused by a warming that occurred 10,000 yBP, rather than a recent (anthropogenic) warming (Alley and MacAyeal, 1994; IPCC 2001). According to Alley and MacAyeal (1994), ice sheets, when basally lubricated, can collapse almost suddenly. It is possible, they propose, that changes that occurred several thousands of years ago could cause a sudden response in the sheet much later on. They, and others (e.g. Jacobs et al., 1992) believe that Antarctica is basally lubricated, and that once lubricated, the ice sheet can decline suddenly, and has in the recent past. Furthermore, the collapse of ice shelves around West Antarctica in particular, may allow the basally lubricated ice streams (e.g. Ice Stream B) to flow more quickly toward the sea. This increased flow rate causes more basal friction which in turn causes more melting and therefore further lubrication resulting in positive feedback. These, and similar proposals are not totally accepted by the scientific community and are a source of uncertainty and debate. Through increased rates of melting and runoff and by changes in net accumulation, climatic warming is likely to have a more rapid effect on Greenland than Antarctica (IPCC, 2001). The increased runoff is expected to overwhelm any increase in accumulation, leading to a rise in sea level.

GREENLAND While the size of a glacier is seemingly important, the annual mass balance amplitude of a glacier, the relative amounts of accumulation and ablation, can play a large role in its sensitivity as well, with higher mass balance amplitudes enabling a glacier to respond more rapidly to perturbations. Therefore, we tend to expect Greenland, which receives nearly a meter of snowfall over most of its surface and experiences large areas of melt annually, to respond more quickly than Antarctica, which is an arid desert with little precipitation and rare melt events. The present size and morphology of the Greenland Ice Sheet is a relic of the Pleistocene, the last glacial stage on Earth which ended when the Holocene, the current interglacial, began approximately 10,000 yBP. The top of the ice sheet consists of recently fallen snow, but if you were to drill down through the top, the layers beneath get progressively older. At the very bottom is ice made from the compaction of snow that fell over 130,000 yBP. In our present climate, the ice sheet 24

would not form, however, it is a perpetuating system; its naturally high albedo reflects sunlight, cooling the surface, while its sheer thickness thrusts the surface up to 3,200 m into the troposphere, causing perpetually frozen conditions over most of the ice sheet's interior. It is the ice sheet's enormous size and high latitude location that has enabled it to persist this long. Evidence suggests that if temperatures around Greenland remain as warm as they are today, or, worse yet, continue to warm as predicted, the ice sheet may not persist in its present form. The Greenland Ice Sheet stretches from approximately 60° N to 80° N, covers an area of approximately 1.7 x 106 km2, accounting for nearly 11% of the global ice area, has an estimated volume of 2.6 x 106 km3, and contains roughly 8% of the volume of ice on Earth (Thomas, 1993). This large ice sheet forms a 2,400 km long dome and reaches a summit elevation of 3210 m above sea level (Haefliger, 1998; Steffen et al., 1993). At the summit, the ice is over 3 km thick. The vast and remote Greenland Ice Sheet is a sensitive indicator of secular changes in climate. It is intricately linked to the climate system of Earth on scales larger than the ice sheet itself. The considerable topography of the ice sheet offers a significant obstacle to Arctic circulation (Ohmura et al., 1991) and the high surface reflectivity and its dependence on regional climate influence the high-latitude radiation budget (Dickenson et al., 1987). The ice sheet also influences global climate through the albedo feedback (Barry and Kiladis, 1982). In turn, the mass balance of the ice sheet is influenced by the local climatic environment, particularly the exchanges of mass and energy between the surface of the ice sheet and the atmosphere. The stability of the Greenland Ice Sheet may be of greater concern than its southern hemisphere counterpart, because it exists at temperatures much warmer than Antarctica where temperatures remain well below freezing throughout the year over most of its surface (Hanna et al., 2005). The relatively warm climate of Greenland already allows for widespread annual melting over its surface (Abdalati and Steffen, 1997). Additionally, the mass flux on the Greenland Ice Sheet is approximately ten times that of Antarctica. This makes Greenland much more sensitive to climate (Oerlemans and Fortuin, 1992). Furthermore, wet precipitation increases with temperature and accelerates the rate of melting, lengthens the melting season and also contributes to the albedo feedback, favoring additional warming. These effects are much less significant in the colder, arid Antarctic regions. Furthermore, it is likely that future northern hemisphere warming will be 25

amplified at high latitude by two to three times the global average (IPCC, 2001; Huybrechts and de Wolde, 1999). Secular changes in climate will manifest in the ice sheet's morphology through the exchanges of energy and mass between the atmosphere and the ice surface as well as through the dynamical response in the ice flow. This linkage suggests that reconstructing a history of climate change is possible through the observed changes in ice morphology (Kruss, 1981). Unlike Antarctica, Greenland experiences large areas of intense melting over the summer. Climatic warming will likely enhance the rate, and expand the area of this melting (IPCC, 2001). The Greenland Ice Sheet has no floating ice shelves, and the net loss is balanced between the runoff of surface melt and iceberg calving. Since an increase in global temperatures is expected to cause an increase in atmospheric water vapor, net accumulation over Greenland is likely to increase. As with Antarctica, there is general disagreement regarding the mass balance of Greenland. According to satellite altimetry, the southern end of the ice sheet has exhibited a rise in elevation since the 1970s (Zwally et al., 1989), but the results of this study have been debated (Douglas et al., 1990; Zwally et al., 1990). In fact, many recent studies have shown that there has been a general retreat of outlet glaciers on Greenland throughout the 20th century, particularly in the south and east. This may have contributed significantly to recent sea-level rise. Kapsner et al. (1995) suggest that the contribution of the major ice caps to sea level rise over the next century may possibly be larger than what has been predicted by the IPCC. Greenland's contribution to sea level is ultimately controlled by its mass balance. If the ice sheet were to melt completely, it would cause sea levels to rise by 7.4 m (IPCC, 2001). Although there is no evidence that this will happen in the future, recent modeling results suggest that the Greenland Ice Sheet may have contributed much more to sea level rise in the Eemian than the great ice sheets of Antarctica (Cuffey and Marshall, 2000), and recent observations suggest significant warming of the lower troposphere over Greenland (Box and Cohen, 2006). Cuffey and Marshall (2000) modeled the evolution of the Greenland Ice Sheet in the changing climate of the last 160kyr by combining the results from recent ice core analyses with a three-dimensional coupled-ice-and-heat-flow model. The model was run through the present to verify that the modern features of the ice sheet including topography, ice volume, and summit 26

position are accurately reproduced. Their results indicate that the Greenland Ice Sheet was much smaller and steeper during the Eemian and may have contributed as much as 5.5 m to the higher sea levels of the period. This suggests that the Greenland Ice Sheet may be a significant contributor to sea-level rise during warm periods on Earth and may be a larger source of sea-level rise in the future than was previously believed. The vast Greenland Ice Sheet traverses multiple climate regimes. Accordingly, there is considerable spatial and temporal variability in its mass balance (Paterson, 1994). While many parts appear to be retreating, others may exhibit growth or expansion. The ice sheet is comprised of two mass-balance zones with overlapping snow-property areas. The region of the ice sheet that gains more mass than it loses on average is known as the accumulation zone and comprises some 82 to 90% of the ice sheet area (Ohmura et al., 1999; Steffen et al., 1993). The remaining area, where mass loss exceeds mass gain, is termed the ablation zone. On the boundary of the accumulation and ablation zones, there is a net mass balance. This is know as the equilibrium line and ranges in elevation on Greenland from 750 m a.s.l. in the north to as high as 1800 m a.s.l. in the southern tip (Ambach and Kuhn, 1985). Figure 1.6 depicts the study area and the transect of weather stations used throughout this text. The general topography of the ice sheet and some of the places referred to in the text are show in the inset. Near Jakobshavn, the equilibrium line altitude (ELA) is approximately 1155 m a.s.l. (Haefliger, 1998). These figures, however, appear to be changing rapidly in the current climate, potentially indicating a response to secular warming. Accumulation occurs primarily through precipitation of snow, although deposition, drift and the re-freezing of meltwater also contribute. Records of accumulation, however, are one of the most easily measured parameters of the ice sheet's mass balance (Munk et al., 2003; Ohmura and Reeh, 1991). Mass frequently collects in distinct seasonal layers. As older layers are buried, the mass above causes densification into firn and eventually into ice. The mass added to the ice sheet in the accumulation zone drives a dynamic flow of ice out toward the margins. At or near the margins, mass is lost through ice-berg calving, melting and sublimation. The mass loss of ice from a glacier is driven primarily by the surface energy budget. Measurements of this are presently being made at 18 stations across Greenland (Steffen et al., 1996) and a new research initiative in the ablation zone near Jakobshavn aims to address the energy balance there in detail. 27

The area where melt occurs on an annual basis is termed the wet-snow zone and consists of a much larger area than the ablation zone. Approximately 65% of the ice sheet experiences some melt. This area partially overlaps the accumulation zone and thus still has a positive mass balance. The remainder of the ice cap, where no annual melt occurs, is the dry-snow zone. This area now covers less than 35% of the surface area of the Greenland Ice Sheet. The boundary between the wetand dry-snow zones ranges from 1650 m a.s.l. in northern Greenland to 3100 m a.s.l. in the south (Steffen et al., 1993). Melt is most extensive in late July and is greatest on the western side and southern ends of the ice sheet (Abdalati and Steffen, 1997). When accumulation and ablation are equal, the ice sheet is said to be in balance. However, this does not imply equilibrium. Equilibrium is attained when the ice sheet has fully adjusted to a climate that has remained stable for at least as long as the ice sheet's response time. It requires that the mass balance remains constant over the entire ice surface for that time (Paterson, 1994). The current theory, developed by Nye (1960; 1961; 1963a,b; 1965a,b), is that the ice sheet exhibits small perturbations from this steady-state equilibrium in response to changes in its environment. The Greenland Ice Sheet is not presently in equilibrium and may not have been so since the last neo-glacial period, the Little Ice Age (LIA). Considering the gentle slope and large area of the ice sheet above the ELA, small changes in climate may yield significant changes in the wet-snow zone area. Between 1979 and 1991, temperatures recorded at coastal stations around Greenland showed a positive trend. As a result, the melt area on the Greenland Ice Sheet grew on average 4.4% per year (Abdalati and Steffen, 1997). Observations and modeling efforts suggest that a warming of 1ºC would cause the melt area on Greenland to grow by 7.3 to 7.9 x104 km2, which is greater than the natural variability observed. Wetting of the snow by melting results in a significantly lower surface albedo. This is attributed to the thin film of water that covers individual ice grains increasing the absorption cross-section of each grain (Warren, 1982). In other words, an increase in snow melt will result in a greater absorption of solar radiation, which in turn will further warm the ice sheet. This, in turn, raises the temperature of the snow pack, causing further melt. Thus the ice sheet is considered a positive feedback mechanism in the climate system and affects regional and even global climate. Further enhancing this feedback is the contribution of clouds. Melting snow may provide a moisture 28

source for cloud production. An increase in cloud cover may result in an increase in incoming long-wave radiation received at the surface which adds additional energy to the surface for melt amplifying the feedback process (Abdalati and Steffen, 1997). Over longer time scales, the surface of the ice sheet may lower and reach down to warmer conditions. This may further intensify the feedback (Huybrechts and de Wolde, 1999). Additionally, meltwater produced at the surface can percolate to the base of the ice sheet, lubricating the base, allowing the rate of flow to the warmer margins to increase (Zwally et al., 2002). All of these changes help to intensify melt conditions. Snow melt is also associated with changes in energy and mass exchanges with the atmosphere. The latent heat required to evaporate water from a wet surface is about 13% lower than the latent heat required to sublimate dry snow. Hence, snow melt affects the surface fluxes of energy and mass associated with the phase-change of water. Snow melt may be responsible for as much as 60% of the mass loss from Greenland (Weidick, 1985) and may be studied remotely through a passive microwave signature (Abdalati and Steffen, 1995). As the surface energy balance determines the melt rate on a glacier, the percent of sunlight that the surface reflects, the surface albedo, plays an important role. Fresh snow has the highest albedo of any natural surface (Oke, 1987). As the snow ages, its albedo decays (Male and Gray, 1981). Exposed ice has a far lower albedo. Accordingly, the accumulation rate on a glacier often has a large influence on melt rates, especially in East and Southeast Greenland (Mote, 2003). Reconstructing the past and monitoring the present extent of ice may not be adequate as it is possible for an ice body to advance laterally while it is thinning vertically and losing mass (Meier, 1984). Furthermore, ice sheet mass balance may have a greater dependence on more difficult to reconstruct climate parameters such as precipitation, cloud cover, and atmospheric circulation than on temperature (Bromwich, 1995; Oerlemans, 1994; Oerlemans and Fortuin, 1992). It is also likely that changes in ice distribution are the result of complex and simultaneous changes in multiple atmospheric variables (Oerlemans and Hoogendoorn, 1989). The Greenland Ice Sheet plays a crucial role in the global climate system. Climate warming will likely have a positive feedback on the ice sheet causing mass to be lost, especially along the margins. This will lead to a net increase in global sea levels posing a threat to coastal cities world-wide. The melting along the margins may be partially offset by increased accumulation in the 29

interiors of the ice sheet and also over Antarctica. Uncertainties in all of these mass fluxes results in an unknown contribution to sea level by the ice sheets in the future.

30

III. RECENT HISTORY OF DEGLACIATION ON THE TROPICAL QUELCCAYA ICE CAP, PERU

INTRODUCTION In studying the Earth's changing climate, it is often difficult or impossible to decipher a signal from the noise of weather and the climate system's inherent chaotic nature. It is therefore preferable to focus climate studies on the tropical regions which are less affected by traveling synoptic patterns than the higher latitudes, and more directly reflect the mean state of the climate. This is due, in part to generally homogeneous thermal conditions that exist in the tropics because of the lack of influence of the Coriolis effect (Pierrehumbert, 1995; Sobel et al., 2001). Additionally, much of the climatic activity that greatly affects humans, such as the El Niño - Southern Oscillation, the Inter-Tropical Convergence Zone, and the Asian monsoon are centered in the tropics (Thompson, 2000). Likewise, tropical glaciers exhibit an extraordinary sensitivity to changes in the mean state of the climate (Kaser et al., 2005). Accordingly, climate change signals are more readily observed in the tropics than elsewhere, and fluctuations on tropical glaciers are an ideal focus for climate reconstructions and for studies of contemporary climate change (Kaser and Georges, 1999). At present, the tropics appear to be warming rapidly and are unequivocally responding to a change in the climate (Kaser et al., 1996; Thompson, 2000; Thompson et al., 2000). As temperature is the single variable that is most homogeneous through the tropics, the large-scale retreat of all tropical glaciers is most likely being caused by a change in temperature (Thompson et al., 2006). The Peruvian Andes are home to the largest collection of tropical glaciers in the world. The glaciers in the Andes, and elsewhere in the tropics, are generally very small. The largest tropical ice 31

body, the Quelccaya Ice Cap, presently covers less than 45 km2. These glaciers respond rapidly to climate forcings, and may exhibit an immediate response to small climate perturbations, such as volcanic eruptions, that is clearly observable in the field. The eruption of Mt. Pinatubo in 1991, for example, is clearly seen in the history presented in this chapter. Tropical glaciers are exceptional indicators of environmental changes and the effects of these changes on natural systems (IPCC, 2001; Oerlemans, 1994; Oerlemans and Fortuin, 1992; Thompson, 2000). Careful monitoring of these ice fields may help reveal small climatic changes that may otherwise go undetected.

TROPICAL GLACIERS Tropical glaciers cover an estimated area of 2.5x103 km2, or 0.16% of the total world ice cover (WGMS, 1989). Over 70% of tropical ice cover occurs in the Andes of Peru (Kaser et al., 1996). Up to 23 cm of sea-level rise is expected from the melting of glaciers and ice caps outside of the polar regions during this century (Church et al., 2001). While significantly more ice exists at higher latitudes, tropical glaciers are temperate, generally existing closer to melt-threshold conditions and, accordingly, relatively small climate changes may significantly affect their mass balance (Martinson et al., 1998). The glaciers of Peru provide critical water resources to the hyper-arid coastal lowlands and altiplano and are also the source of glacier-related avalanches and floods that have leveled towns and caused over 35,000 recorded deaths (Williams and Ferrigno, 1999). A significant and accelerating deglaciation trend has been reported for recent decades from the high Andes and elsewhere in the tropics (Dyurgerov and Meier, 2000; Francou et al., 2003; Fujita et al., 2006; Kaser et al., 2004a; Paul et al., 2004; Ramirez et al., 2001; Thompson et al., 2002; IPCC, 2001; Meier et al., 2003, Thompson, 2004). Studies on glacier recession in the tropical Andes have focused primarily on individual glacial termini that are responsive to a variety of factors, making the role of various components of climatic forcing, including the rapid warming of the late 20th century (IPCC, 2001), somewhat difficult to assess. Generally, late 20th century glacier recession has been attributed to global warming (Brecher and Thompson, 1993; Diaz, 1996; Vuille et al., 2000; Thompson 2000; Thompson et al., 2003; Diaz, 2003). Recently, however, detailed monitoring of glaciers at 0.5°S, in Ecuador, and 16°S, in Bolivia, has identified that interannual 32

variability in mass balance is strongly modulated by the El Niño-Southern Oscillation (ENSO) through its influence over moisture variability (Francou, 2000; Wagnon et al., 2001; Francou et al., 2003). This pattern may not apply universally, however, since the influence of ENSO on mass balance is less coherent, though still evident, at 9°S in the Cordillera Blanca of Peru (Kaser et al., 1990) where the influence of ENSO on atmospheric moisture content is weaker (Aceituno, 1988). Furthermore, the effects of global warming on the ENSO cycle are still unclear. The results of the glacier history from 14°S presented here suggest a stronger possible tie to ENSO than to global temperatures. Global temperatures and ENSO are not independent. Trenberth et al. (2002) found that ENSO indicies tend to become more positive, favoring El Niño, given warmer surface temperatures. Tsonis et al. (2005), on the other hand, suggest that it is the trend in global temperature that drives ENSO, favoring El Niño when temperatures are rising, and favoring La Niña when global surface temperatures are falling.

STUDY AREA The largest single ice cap in the tropics, the Quelccaya Ice Cap (13°56'S, 70°50'W, 5670 m above sea level), sits in a remote area 120 km north of Lake Titicaca and only 40 km from the Amazon rain forest (see Figure 3.1). Rimmed mostly by high ice cliffs, in 1983 it had a measured ice thickness of 166 m. It feeds relatively few outlet glaciers and rests upon relatively smooth bedrock on an extensive plateau with gentle topography (Thompson et al., 1979). Quelccaya is located in a tropical region of small annual temperature range yet pronounced seasonal precipitation differences (Vuille et al., 2003a). According to ice-core data, the average annual accumulation on Quelccaya is 1.15 m w.e. / year (water equivalent depth, or the depth of water if the ice were melted; Thompson et al., 1985). Over 80% of the annual precipitation falls in the summer (November through March) when solar radiation reaching the Altiplano is most intense, developing deep convective showers (Thompson et al., 1984). Due to its dome shape, Quelccaya is very sensitive to changes in the height of the 0ºC isotherm (Diaz et al., 2003). Williams and Ferrigno (1999) produced a series of atlases to serve as a base inventory of glaciers in the world. The volume on South America contains a special section on the Quelccaya Ice 33

Cap (Hastenrath and Ames, 1995), and documents the extent of this ice cap from 1962. I have continued this analysis of Quelccaya, a unique indicator of the regional climate, through time until the present and find distinct periods of advance and retreat, which appear to coincide with decadal shifts in the magnitude of the El Niño – Southern Oscillation. These results will be published in an upcoming book, Global Land Ice Measurements from Space, due out in December, 2007.

Figure 3.1: False-color composite satellite image of the Quelccaya ice cap with its relative location in Peru show in the inset map. The only complete published mapping of glacial extent of Quelccaya is presented on topographic maps at 1:25,000 scale based upon photogrammetry of aerial images taken in 1962 (Ministerio de Agricultura, 1972). The largest outlet glacier, Qori Kalis, is a valley glacier on the 34

west side of the ice cap. Terrestrial photogrammetry since 1978 has identified accelerating rates of retreat for Quelccaya's largest outlet glacier, Qori Kalis, and that it responds rapidly to climate forcings (Brecher and Thompson, 1993; Thompson, 2000; Thompson et al., 2000, 2003, 2006, Thompson pers. comm., 2006). These results, however, are difficult to generalize for the entire ice cap. Glaciers of varying aspects, slopes, and elevation ranges should be collectively evaluated to obtain a representative signal in the behavior of glaciers to climate forcing. The Qori Kalis glacier presents a single west-facing outlet-type glacier, which extends below the mean ice margin elevation by over 300 m, and thus experiences considerably warmer mean conditions and a different ablation regime at its terminus than most of the Quelccaya ice margin. If considered in its entirety, however, the Quelccaya Ice Cap presents an especially desirable target for studies of glacier–climate interaction. The margins of Quelccaya incorporate a broad range of topographic gradients, slopes, and aspects, so any changes in ice area that depend on these gradients will be dampened when aggregated for the entire ice perimeter. Furthermore, Quelccaya experiences high precipitation (>1,000 mm yr-1), and compensating ablation primarily by melt occurs near its margins on most days throughout the year. These characteristics suggest that despite considerable inertial stability related to its large volume, the ice cap should be highly responsive to climatic variations.

REMOTE SENSING OF GLACIERS Satellite imagery is an excellent tool for monitoring isolated ice fields as it allows more extensive and frequent observations (Paul et al., 2004). Thus, the response of ice fields to smaller scale climatic perturbations may be modeled. These data provide regional and synoptic scale observations (Gurney et al., 1993) that are otherwise unavailable and offer a less expensive alternative to continuous field monitoring. Satellite data are well dated and may eventually provide a decadal- to century-scale record of glacial extent and environmental change. Satellite imagery also allows for a uniform digital inventory of land ice (Williams and Ferrigno, 1997; Kääb et al., 2002a). Nevertheless, satellite sensors are still limited in their measurement resolution and some variables cannot be observed from these platforms. Therefore, ground-based observations and field research will continue to play an 35

important role in science in the coming years. Rather than eliminating field research, satellite observations offer new ways to address questions and a wider range of questions that may be addressed (Gurney et al., 1993) and aid in more efficient and productive field programs. The changes in glacier area are often used as a first order approximation to the changes in the glacier's total mass. The area of an ice cap may be determined through land-cover classification of a satellite image. Classification schemes rely on the spectral radiant flux signatures of ground features in both short and long wavelengths. Different materials exhibit different spectral signatures which are utilized in grouping features into land cover types. Many techniques have been used to classify remotely sensed imagery. Topographic relief limits the application of certain remote sensors to alpine areas (Dozier et al., 1987), and remote measurements of snow and ice require similar spatial resolution to that of the topographic features, typically tens of meters. Satellite data of this resolution are available from Landsat Thematic Mapper (TM), Enhanced Thematic Mapper Plus (ETM+), from the French SPOT satellites, the Indian Remote-sensing Satellite (IRS), and from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER; Kääb et al., 2002b). Although SPOT imagery has a finer pixel size, TM and ETM+ data have better spectral coverage which is often important for the discrimination of land-cover classes. Snow and ice exhibit extremely low reflectivity in the middle-infrared (Paul et al., 2004) and high reflectivity in the visible. In theory, the unique spectral signatures of snow and ice make them readily distinguishable from other materials. In practice, however, the identification of snow and ice is hindered by surficial dust deposits (Paul et al., 2005). The albedo of a snow or ice surface degrade with age and dust cover. This is most dramatic near the margins where exposed ice becomes dusty. The dust may create a cover over the ice that makes the surface resemble the surrounding glacial moraines. Additionally, snow and ice are not Lambertian; instead, their reflectance is highly dependent on the slope and aspect of the surface, the zenith angle and azimuth of the sun, and the zenith angle and azimuth of the satellite sensor. Since the geometry of the sun and satellite are effectively fixed throughout the recording of the image, additional variation in the reflectance of ice measured by the satellite may be caused by the varying slope and aspect of the surface. Generally, steep ice walls and crevasses become heavily shaded and have lower reflectance values. Shaded ice 36

has a depressed spectral curve that approaches the spectral curve of liquid water. Another factor that confounds the identification of ice is that edge pixels are likely to be combinations of ice and the surrounding surface material, resulting in a mixed signal. Glacier extent mapping from satellite data is not a new idea. Bayr et al. (1994) exploited the spectral reflectance of snow and ice by using a ratio of TM band 4 to TM and 5 to highlight glacier area. Rott (1994) used a similar technique applied to TM bands 3 and 5. Paul (2000) found that the TM band 4 to 5 ratio technique yielded the best results for glacier mapping on Gries Glacier, especially in regions with low insolation, and later estimated this method to be 95% accurate (Paul, 2002; Paul et al., 2002). Unsupervised classification techniques, specifically the isodata algorithm, were used by Aniya et al. (1996) to map the southern Patagonia icefield. This iterative clustering method initially selects candidate clusters and then allows their means to migrate in the spectral domain, optimizing the classification with each iteration (Ball and Hall, 1965). In each iteration, every pixel is compared to each cluster mean and assigned to the nearest cluster. The means are then recalculated and the process repeats until the pixel-to-cluster mean distances are minimized or a pre-defined number of iterations is reached. Gratton et al. (1990) and Sidjak and Wheate (1999) utilized supervised techniques in combination with elevation data to successfully map glacier extents. Supervised classification techniques require the operator to identify pixels of known land-cover classes in the image (Mausel et al., 1990). Fuzzy classification schemes have also been used in glacier mapping by Serandrei-Barbero et al. (1999). Fuzzy image classification uses fuzzy logic to estimate the proportions with which each class occurs in each pixel (Jensen, 1996). Vogel (2002) even used a single, high-resolution panchromatic band to visually delineate snow cover. Paul et al. (2002) surveyed these and other remote sensing and GIS techniques to determine which are best suited at delineating ice extent, finding similar results to Albert (2002). Both studies found that using a ratio of TM band 4 to TM band 5 produced excellent results. Albert (2002) also concluded that the spectral angle mapper (SAM) algorithm, a supervised technique, produced excellent results when the training sets were well defined and the maximum angle was set properly. This algorithm treats each pixel as a vector in n-dimensional space, defining the spectral signature of each pixel by the angle its corresponding vector makes with the axes that define the n-dimensional 37

space of the image. A mean vector for each class is calculated and all pixel vectors are classified based on the angle they make with each class vector (Richards and Jia, 1986). A maximum angle may be defined whereby pixels that are not within that angle of any class are not classified. Albert (2002) also found the isodata algorithm to perform well when it was allowed to run unconstrained. Kääb et al. (2002a) used these methods to derive a detailed inventory of Swiss glaciers for the year 2000. The Swiss Glacier Inventory (SGI) utilized satellite imagery and GIS technology due to the ability to automate and standardize these procedures. Once the satellite data have been properly classified, changes in the area of ice may be studied simply by multiplying the number of ice covered pixels by the pixel area. However, it is possible for a glacier to advance while it is thinning and losing mass (Meier, 1984). Thus, observations of areal extent may not relate directly to changes in mass balance, and observations of changing surface heights (Popovin, 1996) or estimates of the volumetric change of an ice cap may be a better indicator of mass balance changes. New technologies in satellite remote sensing enable researchers to recreate 3-dimensional models of ground features.

These include synthetic aperture radar

interferometry,

shape-from-shading algorithms, and radar and laser altimetry. These and similar methods may be employed to reproduce the surface topography of an ice field at a given time. Using these new techniques, one may, with repeat observations, be able to look at changes in glacier volume. More appropriate may be to investigate the change in mass balance, spatially, over the surface. A definite relationship exists between climate, exchanges of mass and energy, and glacier net balance (Meier, 1965; Paterson, 1981). This linkage suggests that reconstructing a history of climate change from observed evidence of glacial morphology is possible (Kruss, 1981). Secular changes in climate will manifest in a glacier's morphology through the energetic and mass exchanges between the atmosphere and the ice surface as well as through the dynamical response in the ice flow (Meier, 1965). Ice dynamics may be used to describe the adjustments in glacial geometry as a result of changing mass balance (Meier, 1965; Oerlemans, 1986).

38

METHODS Using similar techniques as Albert (2002), a set of images of the Quelccaya Ice Cap spanning four decades were analyzed for ice extent area to create a history of the ice extent. This facet of the research relies on the idea that the area of a glacier is an appropriate proxy measure for the glacier mass balance. To test the validity of this idea on Quelccaya, a careful look was taken at the main outlet glacier of the ice cap, Qori Kalis. Stereo metric photographic pairs were taken of the glacier over a series of years. These photographs allowed for detailed surface models of the glacier to be constructed (Brecher pers. comm., 1999). These surface models were compared to determine the changes in glacier length, glacier area, glacier thickness, and total glacier volume. The purpose of this study was to show that changes in ice extent are representative of changes in the total mass (or volume) of the glacier. While changes in volume were most dramatic, changes in area were well-correlated (r2 = 0.89), which is not unexpected since volume is highly dependent on area. Accordingly, changes in mean ice thickness were compared to changes in ice area, as these two variables are not geometrically dependent. Changes in ice area were not as rapid as changes in thickness on the Qori Kalis glacier, however, they were still highly correlated through time (r2 = 0.78). With a high correlation to ice volume and ice thickness, it was determined that ice area would serve as an adequate indicator for changes in the total mass of the ice cap. A series of images were then collected for the ice cap. All available satellite images of the ice cap were carefully analyzed for the presence of cloud cover or ephemeral snow cover, as each one is capable of obscuring the true ice extent. A total of 9 cloud-free images were collected from 1975 to 2001 (1975, 1985, 1988, 1991, 1993, 1998, 1999, 2000, 2001) and were utilized to construct a history of ice area changes of the Quelccaya Ice Cap. A list of these images and their properties is shown in Table 3.1. Note that most images were chosen in the dry season, May through November, when there is less ephemeral snow cover to obscure the actual ice cap margins. When possible, imagery was selected from the height of the dry season, June through August, when seasonal snow cover has usually ablated away to reveal true ice extent, and snow storms are extremely infrequent.

39

Table 3.1: List of scenes used in this study and some of their attributes.

Scene

Sensor

1962

Aerial photographs

1975

Landsat MSS

1985

No. spectral bands used

Date

Source / Notes

Aug 1962

H. Brecher

3

29 Jul 1975

NASA

Landsat TM

6

25 Jul 1985

NASA

1988

SPOT 4

3

29 Aug 1988

BPRC

1991

Landsat TM

6

31 May 1991

NASA

1993

Landsat TM

6

29 Jun 1993

NASA

1998

SPOT 5

4

8 Aug 1998

BPRC

1999

Landsat ETM+

6

9 Aug 1999

NASA

2000

Landsat ETM+

6

24 Jun 2000

GLIMS

2001

Landsat ETM+

6

14 Aug 2001

NASA

n/a

Also included in the analysis as the base image, or starting point for the ice cap's area, was an ice extent derived by Brecher (unpublished) from stereo aerial photographs taken in 1962. The photographs show little evidence of ephemeral snow cover around the ice margin (Ministerio de Agricultura, 1972; Brecher and Thompson, 1993). The established base area of 55.06 km2 compares well with an earlier estimate of 56.25 km2 by Ames (1989) derived from the same aerial photographs, and the small difference may be attributable to the scale of analyses used in each study. To properly delineate ice from other surfaces the following criteria are desirable: (1) adequate spatial resolution (which depends upon the scale of the ice body being examined), (2) favorable conditions (i.e. relatively clean ice, absence of ephemeral snow cover), and (3) adequate spectral resolution (or number of satellite bands). Objective image processing methods were utilized to determine ice extent, with small manual adjustments applied, when deemed necessary, to compensate for recognized misrepresentation related to the factors listed above.

40

Pre-processing Imagery Each satellite image was subjected to a standard set of pre-processing steps before analysis. First, each image was subjected to a careful visual inspection to determine if any clouds or ephemeral snow cover were present in the scene. All questionable images were discarded. The images mentioned above and listed in Table 3.1 were the images that passed visual inspection. Next, each image was corrected for atmospheric scattering using a standard dark object subtraction (Chavez, 1996). This simple image-based correction is adequate for classification applications using TM data (Song et al., 2001). The data were converted to reflectance values and geometrically corrected by registering them to the UTM coordinate system, zone 19 south, using a 1:25,000 scale topographic map for the most detailed image. Once one image was registered to the map, all subsequent images were co-registered to that image to insure pixel-to-pixel matching of features. During geometric correction, all images were resampled to a common pixel size of 28.5 m by 28.5 m. As a final step before ice area analysis, the images were then cropped to include only the ice cap and immediate environs.

Determining Ice Extent Once each image was in a consistent format and geographic space, ice-area analysis began. Given that the methodology outlined by Albert (2002) represents a set of techniques that are most cost-effective and most frequently employed in ice-area determination, similar methods were applied here. Albert (2002) compared a series of widely used techniques, and some more obscure remote-sensing methods, for accuracy and processing time in delineating the extent of the Quelccaya Ice Cap. The most accurate methods which had the lowest costs in terms of user processing time included a supervised technique called spectral angle mapper (SAM), an unsupervised technique (ISODATA), and two band-math threshold techniques, namely the normalized difference snow index (NDSI) and the TM band 4 to 5 ratio (4/5 Ratio). These results are now widely accepted and utilized (e.g. Paul, 2002; Paul et al., 2004; Kääb, 2005; Kaser et al., 2004b). Albert (2002) also outlines a method for obtaining the best angle threshold to use for the SAM method and the best thresholds for the NDSI and 4/5 Ratio methods.

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For this analysis, four main techniques were used to determine ice area. Hand digitization was used where there was difficulty in using automated techniques (i.e. 1975) or where the hand digitization had already been done (i.e. 1962 and 1985). The second method used is the most popular remote sensing method to date for classifying snow and ice, the band ratio threshold method (Ratio). Being the most successful technique for the Quelccaya Ice Cap (Albert, 2002), the SAM algorithm was also used on any image where spectral resolution was adequate. The final technique chosen was the ISODATA algorithm for its efficiency and accuracy (Albert, 2002). These techniques were applied to the series of satellite imagery from 1975-2001 in order to generate a history of the recent deglaciation on the ice cap. The automated multi-spectral techniques used to determine ice area require adequate spectral resolution to separate snow and ice from other surfaces. Lacking adequate resolution, the 1975 Landsat-MSS images was manually digitized on-screen from an infrared false-color composite of the satellite image to determine ice-area. The number of methods used in processing each image depended on the available spectral bands in each image which is a function of the satellite sensor. When possible, all four methods listed above were used (hand digitization, SAM, ISODATA, and Ratio). In all cases, the ice extents generated from each method were compared on a pixel by pixel basis. Pixels that were determined as ice by a majority of the methods were deemed as ice in the final ice map. Pixels that were determined to be snow or ice by only one or two methods were visually compared to the multi-spectral satellite data and to previous and former geometries of the ice cap to determine if the pixel was likely ice or not. The resulting data are provided in Table 3.2. This table summarizes, for each satellite image or aerial-photograph map, the areas determined by each of four techniques, namely hand digitization, band ratio, SAM, and ISODATA. The mean area and the number of techniques used is also provided along with the standard deviation or error estimate, as discussed below. The final column in the table compares the computed area (mean) to the original ice cap area in 1962. The resulting ice area history is summarized in Figure 3.2. For areas where there was disagreement among methods, visual inspection of each area and the statistics of how many pixels were classified by more than one method, how many methods classified each pixel as ice, and the estimated accuracies of the methods was considered. Ostensibly, 42

the final resulting ice map was somewhat subjective. Albert (2002) estimates that human operators may be as accurate as 99%, and therefore, it is assumed here that the subjective nature of the final analysis only adds to the accuracy of combining the automated methods.

Table 3.2: Summary of results of all methods of ice-area determination and estimated errors. See text for more detailed explanation.

Year 1962 1975 1985 1988 1991 1993 1998 1999 2000 2001

Pixel dimensions (m2) 28.50 28.50 28.50 28.50 28.50 28.50 28.50 28.50 28.50 28.50

Hand Area (km2)

Ratio Area (km2)

55.48 58.85 56.82

55.51 56.82 53.60 50.54 52.14 46.18 46.33 45.79 46.27

SAM Area (km2)

58.60 54.37 51.27 50.23 46.70 48.01 48.41

ISODATA Area (km2 )

55.95 50.92 49.82 48.49 47.24 47.21 47.45

Mean Area (km2) 55.49 58.85 56.53 53.98 50.91 50.73 47.33 46.76 47.00 47.37

St. Dev. or Error Estimate (km2) 0.02 2.00 0.50 0.54 0.36 1.24 1.63 0.46 1.12 1.07

No. of Methods

Percent of 1962 Area

2 1 4 2 3 3 2 3 3 3

100.0% 106.0% 101.9% 97.3% 91.7% 91.4% 85.3% 84.3% 84.7% 85.4%

Estimating Error Each of the four methods was used, when possible, to determine the ice extent for each image. The results of each method were compared and combined to generate a final ice cover map and estimate the error of the ice extent derived from that image. The total area of pixels that all methods did not agree on was compared to the total ice area to create a percent error estimate. When multiple methods were used, one standard deviation of the areas found was used as the estimated error. When a single method was used, an estimate of the technique error from Albert (2002) is provided. In most cases, the error was small as only a few edge pixels were not classified consistently by each method. For areas that all methods agreed on, the final classification was simple, and the calculated error was negligible. As a final check, initial results were evaluated for evidence of over- or underrepresentation of ice area, either from dust-covered surfaces near the ice margin, or more by ephemeral snow augmenting the true ice-area extent. Visual inspection suggested some snow 43

cover in the 1975 and 1985 scenes, and significantly so in 1993. Thus, the objectively determined ice area for these scenes potentially overestimates the actual glacial ice area beneath. The reported area for 1998 has larger error bars because of the lower spectral resolution of the SPOT-4 sensor (only 4 bands), and due to very dry conditions, when ice is often dirtier and therefore harder to classify. In comparison, 1988 has only 3 bands, but the distinction of snow and ice is clearer.

Figure 3.2: Satellite-derived record of ice-area retreat on the Quelccaya Ice Cap. Solid circles represent the mean area determined by all available methods, and the error bars represent the standard deviation about that mean for each point, or, when only one method was used, it is the estimated error from that method (after Albert, 2002). Only the lower error bar is given for 1975 as overestimation is suspected and the true area did not likely exceed the reported value. RESULTS Ice Extent History Analyses of cloud-free satellite imagery from 1975 to 2001 of the Quelccaya Ice Cap reveal for the first time the changing ice extent of the largest glaciated mass in the tropics. The 44

derived ice extents and estimated errors are presented in Figure 3.2 and Table 3.2. The error bars on the graph represent the estimated error for each area determination as explained in the section above. A trend of rapid retreat that began around the mid-1970s resulted in reduction in ice area from 58 km2 to 46 km2 (-20.7%) by 1999. Between 1999 and 2001 the previously accelerating retreat seemed to yield to a state of growth or equilibrium. This ice extent history matches what has been observed in the field by Lonnie Thompson and Henry Brecher since the mid-1970s, including the two periods of limited retreat in 19921993 and 1999-2001. While more recent imagery are not yet available, Thompson and Brecher (unpublished) have witnessed the continued retreat of the Quelccaya Ice Cap and believe that it has continued to accelerate. A slight increase of the 1962 base area is suggested from the first scene analyzed, from 1975, although the course resolution of this Landsat-MSS scene necessitates a fairly a broad margin of error (±2 km2). This Landsat-MSS image has 79-m pixel resolution, limited spectral resolution (4 bands), and some possible ephemeral snow that required slight subjective adjustment to the ice/no ice delineation area. Subsequent scenes indicated a change to a pronounced pattern of rapid retreat that initiated some time between the 1975 and 1985 scenes. Field observations by Thompson suggest that the retreat began early in that period and accelerated. Rapid deglaciation continued until at least 1998, with evidence of interannual variability to the recessional rates. Then, from 1999 to the most recent scene examined, in 2001, the ice cap appears to have stopped retreating, and the analysis results even suggest a slight advance. More recent field observations by Thompson suggest that the ice cap is losing significant area and this loss may be accelerating. Unfortunately, persistent cloud cover hinders obtaining more recent satellite imagery of the ice cap.

Spatial Pattern of Retreat The overall pattern of retreat is not equally distributed around the ice cap. The most significant loss is found on slopes with a west through north orientation (Figure 3.3). This may be a response to insolation variations as a function of aspect, or possibly related to slope angle.

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Figure 3.3: Map of retreat on the Quelccaya Ice Cap from 1962 to 2001. Red areas represent ice areas that have retreated since 1962, and green represents areas that were not classified as ice in the 1962 air photos. These latter areas are likely snow fields that ablate later in the year than when the 2001 satellite image was acquired.

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Western slopes are gradual and the ice thins slowly toward the terminus. It takes less time and energy to ablate this thinner ice than the thick, extensive ice cliffs found on the meandering eastern margin, which understandably show less retreat. Net volume changes as a function of slope cannot be determined in this analysis, since ice thickness change is indeterminable from the available imagery.

DISCUSSION The climate of the Cordillera Vilcanota, the mountain range encompassing the Quelccaya Ice Cap, is dominated by strong seasonality and considerable interannual precipitation variability that have implications for the annual mass balance. Unlike in the polar and temperate regions, tropical glaciers melt throughout the year, but this year-round melt is offset by large accumulations of snowfall. The wet season (November through April) coincides with the austral summer and accounts for most snowfall, which occurs principally from deep moist convection on an almost daily basis (Garreaud et al., 2003). The frequent refreshing of the snow surface maintains high albedo which, along with cloud development during the daytime, limits melt by diminishing the amount of solar radiation absorbed at the surface. The summer wet season is, nonetheless, when melt is also at a maximum, and owes to the combined effects of diurnal maxima rising above freezing promoting a temperate snowpack, along with high radiation receipt despite persistent cloudiness (Wagnon et al., 2001). In the dry season months (May through October), the persistent aridity causes (1) larger portions of available energy consumed by sublimation but largely diminished glacier melt, (2) diurnal minima to be much colder allowing the snowpack to cool, and with the sun now resident in the winter hemisphere, (3) ablation is reduced. The Quelccaya ice-area history corresponds well with the decadal variations in ENSO that regionally dominates interannual climatic variability in the tropics. The linkage between ENSO phase and glacier behavior is now well established for much of the central Andes. La Niña (cooler and wetter in the Cordillera) events promote positive mass balance anomalies that lead to increase in glacial extent, while El Niño (warmer and drier in the Cordillera) events promote rapid ablation, principally through the combination of reduced snowfall and increased 47

solar absorption due to a reduced-albedo melt surface (Wagnon et al., 2001; Francou et al., 2003) and decreased cloud cover. These effects are maximized during the December through March wet season, when wetter or drier than average conditions will foster reduced and much-increased ablation, respectively, and is also the time of year that ENSO phases are typically the most strongly developed. A shift in the mean ENSO state in 1976, from dominant cold La Niña to warm El Niño conditions, has been widely recognized (e.g. Allan, 2000; Francou et al., 2003). This warm epoch culminated with the strong 1997-98 El Niño and has been followed by a shift to more neutral mean conditions. Relative to the 1962 base area, a net loss of approximately 21% was registered during the 22 years of the warm epoch, from ~105% at the onset, to 84% by 1998. The 1976 ENSO shift has been linked to the recent Andean glacial recession though the sustained modulation of glacial mass balance to strongly negative (Wagnon et al., 2001; Francou et al., 2003; Vuille et al., 2003). Accordingly, the shift to more neutral ENSO state after 1998 is synchronous with the abrupt halt in retreat exhibited by the ice cap. The accelerating retreat for Qori Kalis, Quelccaya's principal outlet glacier is reported to have also halted temporarily at the same time (Brecher and Thompson, unpublished). This break from retreat represents a temporary deviation from a longer-term recessional trend, not the achievement of a new stasis equilibrated with the current climatic mode. Since shifts in multidecadal ENSO modes occur with a regularity that suggests that glacial imbalance relative to climate is effectively an omnipresent condition, and due to the persistent global warming trend, the Quelccaya Ice Cap and other glaciers in the Andes won't last long.

Comparison of Results to Similar Studies Monthly mass balance measurements in the nearby Cordillera Real suggest that recent increased ablation rates are not solely a response to the climatic warming of recent decades (Vuille et al., 2003). Instead, the glaciers appear to also be responding to reduced cloud cover and reduced albedo, both leading to increased solar absorption. Surface albedo on tropical glaciers quickly deteriorates between snowfall events. Study of small glaciers in the Cordillera Real reveals stable extents between 1963 and 1975 and slight recession from 1975 until 1983 48

(Finsterwalder, 1987). More recently, rapid and accelerating recessional rates have been measured (Francou, 2000; Francou et al., 2003). Positive monthly mass balance variations were infrequent during the 1990s, and occurred only during La Niña events (Francou et al., 2003). These findings are consistent with the results from Quelccaya reported here. Results of satellite image analyses and glacial termini measurements in the Cordillera Blanca are also consistent with the findings on Quelccaya. Following a period of nearly constant ice extents in the 1960s, slight advances were observed in the first half of the 1970s (Ames, 1998; Kaser et al., 1990). Since then, pronounced and increasing retreat has been documented (Georges, 2004; Hastenrath and Ames, 1995). The retreat turned to slight advances after 1998 in some cases (field observations by the Innsbruck Tropical Glaciology Group; Georges, pers. comm. 2005). The areal loss between the 1970s and the late 1990s amounted to approximately 10% (Georges, 2004), which compares to the 20% loss reported here for Quelccaya over the same period. A value of 20% ice loss for the Cordillera Blanca quoted in the 2001 IPCC assessment requires downward revision, as discussed in Georges (2004). More recently, retreat in the Cordillera Blanca has stagnated, or even reversed to slight advances (field observations by the Innsbruck Tropical Glaciology Group; Georges, pers. comm. 2005). The 2X difference in areal loss by percentage between Quelccaya (~14 ºS) and the Cordillera Blanca (~9 ºS) between the 1970s and the end of the century suggests that glacial change for single mountain range should not be generalized to an entire region. Possible explanations for the observed differences include the terrain morphologies, where lower angled slopes imply a higher glacial sensitivity at Quelccaya, or the more direct mass balance modulation by ENSO towards the Andean Altiplano of southern Peru and Bolivia than further north. To verify the influence of ENSO on the extent of the Quelccaya Ice Cap, two ENSO indexes, the Southern Oscillation Index (SOI) and the Multivariate ENSO Index (MEI) were compared to the ice extent changes for the periods between available imagery. For comparison, the Global mean Temperature (GT) was also compared to changes in ice extent. Average annual values were calculated for each index, and were compared to the mean annual ice extent change between satellite observations. Comparisons were made by simple linear regression. The results of this simple regression model suggest that the recent history of ice extent has been influenced 49

by the dominant ENSO mode (MEI r2 = 0.31; SOI r2 = 0.28) and strength between observations, and has no correlation with global temperature (GT r2 = 0.01; or GT r2 = -0.12 for the partial correlation controlling for MEI). Since ENSO is also correlated to the temperature tendency (dT/dt; Tsonis et al., 2005), direct correlations and partial correlations controlling for MEI were made between the changes in Quelccaya’s ice extent and dT/dt and no significant relationship was found (r2 = 0.08 and r2 = 0.01, respectively). The Quelccaya Ice Cap continues to respond much as it has in the recent past to dominant multidecadal ENSO modes, similarly to other glaciated areas in the central Andes. These findings are consistent with those of other investigators who have demonstrated that the elevated frequency of El Niño versus La Niña events between 1976 and 1998 was the principal factor driving the significant deglaciation trend in the Andes (Vuille et al., 2003; Francou et al., 2003). It is regrettable that anomalous snowfall in the dry seasons of 2002-2004 has compromised the utility of available satellite imagery by obscuring glacial margins, thus preventing this analysis from being extended to the present. New imagery free of snow cover of non-glacial surfaces will hopefully be obtained again in the near future. This would allow for the determination of whether the apparent trend reversal in glacial extent from negative to positive has been sustained, or whether it was merely a short-term perturbation related perhaps to the moderate to strong cold ENSO events of 1999-2000. The lack of snow-free imagery since 2001 suggests that excess snowfall is occurring, and that the current trend is toward positive mass balance. While the results of these analyses suggest that global temperature rise has had no effect on the mass balance of Andean glaciers, this is difficult to reconcile with in situ observations that have verified rapid responses to these glaciers to yearly fluctuations in the mean state of climate. For example, the eruption of Mt. Pinatubo in 1991, which had a discernable cooling effect on the globe, caused a temporary halt to the otherwise rapid recession of the Qori Kalis outlet glaciers, and perhaps the ice cap as a whole (see Figure 3.2).

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IV. MEASURING MASS BALANCE ON THE GREENLAND ICE SHEET

BACKGROUND Models to predict future sea-level rise from various climate change scenarios are now better than ever, yet our understanding of the limitations of these models is also gaining footing. For example, the Fourth Assessment Report (AR4) of the IPCC, due out in April 2007, will highlight the fact that sea level is presently rising much faster than previously predicted. This additional sea-level rise is attributed to the observed dynamical responses of the Greenland and Antarctic Ice Sheets (IPCC AR4, unpublished). Given our present limited understanding of these dynamic responses, their estimated contribution to future sea-level rise has been left out of the current report. Consequently, because the latest sea-level predictions do not include these dynamic responses, they are perhaps conservative in light of the position that scientists increasingly believe that future sea-level rise will be much greater than previously estimated. With a renewed importance, attention is now turned to the Greenland Ice Sheet, and ice sheets in general, to help understand sea-level responses to global warming. In this chapter, I review previous studies of the mass balance of the Greenland Ice Sheet and then demonstrate how an older method may be applied to the Greenland Ice Sheet to provide insight into the present mass balance of the ice sheet.

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Mass Balance Studies of the Greenland Ice Sheet Greenland's contribution to sea level is ultimately controlled by its mass balance, yet there is general disagreement regarding its sign and magnitude. Early studies of mass balance were driven partially by a desire to understand its complex relationship with climate (Ahlmann, 1948). The earliest known long-term mass balance study was launched in 1946 on the Storglaciären in Sweden. This study continues today (Holmlund et al., 1996). The study of glaciers grew rapidly in the 1960s, spurred by the International Hydrological Decade, 1965-1974, and the development of hydroelectric power, particularly in Norway (Collins, 1984). Mass balance is the difference between mass that is added to the glacier, termed accumulation, and mass lost, termed ablation. Accumulation on the Greenland Ice Sheet is primarily driven by precipitation, which varies widely through space and time (Bromwich et al., 1993). The precipitation regime over Greenland is strongly influenced by its proximity to other landmasses, by the Gulf Stream to the south, and by areas of North Atlantic deep-water production to the east and west (Thomas, 2001). Ohmura et al. estimate the mean annual accumulation over the ice sheet to be 297 mm yr-1. The principal source of mass accumulation is precipitation, although precipitation rates over Greenland are relatively small. In fact, today’s rates of precipitation are so small that had the ice sheet not already existed and its accumulation area been so large, it would not exist today (Ohmura et al., 1999). Maintaining Greenland’s ice sheet is extremely reliant upon precipitation in the dry snow zone, the area of the ice sheet which experiences no melt annually. Direct observations of precipitation over Greenland are extremely limited, yet it is the easiest mass balance component to reconstruct from ice core and snow pit data. Approximately 600 km3 of precipitation falls on the surface of the ice sheet each year, nearly 100 km3 of which is lost by wind and sublimation (Box et al., 2004). The remaining mass input of approximately 500 km3 drives deformational ice flow towards the ice sheet margins where an estimated 239 km3 is discharged as icebergs, about 32 km3 is lost to basal melting of floating ice tongues (Reeh et al., 1999), and between 200 and 500 km3 is lost through meltwater runoff (Zwally and Giovenetto, 2000; Box et al., 2004).

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Although the general trend of precipitation over the ice sheet may be explained by large-scale atmospheric circulation and orographic effects near the margins (Ohmura and Reeh, 1991), recent satellite and aircraft altimeter surveys over southern Greenland show significant spatial variability at higher elevations (Davis et al., 1998; Krabill et al., 1999; Zwally et al., 1998). It has been demonstrated that the majority of the spatial patterns of accumulation change, and thus elevation change, on the ice sheet may be attributed to temporal variability in accumulation (Davis et al., 2001; McConnell et al., 2000). Melt on an ice sheet is principally controlled by the turbulent and radiative fluxes of energy at the surface, which vary widely across the ice sheet and throughout the year. Factors that contribute to the surface energy budget include net solar radiation, net longwave radiation, turbulent fluxes of sensible and latent heat, and sub-surface heat flux. The largest sources of energy for melt include incoming longwave radiation, absorbed shortwave radiation and the sensible heat flux. These sources provide approximately 70%, 25% and 5% of the energy for melt, respectively, depending on the location. Together, the incoming longwave and the sensible heat flux account for three-quarters of the energy available for melt, and both of these parameters are highly dependent on the air temperature (Ohmura, 2001b). Accordingly, ablation rates are profoundly sensitive to summer temperatures, especially near the ice margins (Roe, 2002). A mean temperature rise of 1°C can increase the ablation rate by 1 to 2 m yr-1 (Calov and Hutter, 1996).

Methods to Monitor Mass Balance on the Greenland Ice Sheet While satellite imagery provide unprecedented synoptic views of small glaciers and ice caps, the large ice sheets pose much greater technical challenges to satellite monitoring. No remote sensing platform has both adequate resolution to monitor changes on ice sheet margins at appropriate scales and simultaneously offers complete coverage of the entire ice sheet. More importantly, the changes occurring on the ice sheets which are of greatest significance are in the surface mass balance, or the changing thickness at every point over the surface of the ice. This is more directly related to the volume of ice than changes in extent of outlet glaciers. Also of great importance is monitoring changes in the speed of glacier flow towards the margins where the 53

most ablation of snow and ice occurs. While the rapid decline in the extent or length of outlet glaciers surrounding the Greenland and West Antarctic ice sheets are worrisome, the larger pattern of mass balance is of greater concern. Accordingly, alternate techniques which enable the calculation of changes in ice volume are often utilized on the ice sheets. Recent observations have verified that, like in Antarctica, the tidewater glaciers in Greenland have begun to accelerate and are rapidly thinning. Most of the thinning is attributed to basal melting which accounts for as much as 15 m yr-1 since 1997 for the largest outlet glacier on Greenland, the Jakobshavn Isbrae in west-central Greenland (Krabill et al., 1999; Krabill, 2005). In 2003, major outlet glaciers on the east coast began thinning at rates of 25 to 40 m yr-1 (Krabill, 2005), similar to what is found on the Petermann Gletcher in north-western Greenland (Steffen, pers. comm., 2003). Rignot and Kanagaratnam (2006) have observed a widespread acceleration of glacial flow in southern Greenland since 1996, a trend which has been spreading further north in recent years. They found that this increased flow towards the oceans is causing a decrease in the ice sheet mass balance from -90 to -220 km3 yr-1, and warn that as the acceleration spreads further north, Greenland's contribution to global sea level will grow. Zwally et al. (2005) report mass gains of 11 ± 3 Gt yr-1 (-0.03 mm yr-1 sea level equivalent) for the Greenland Ice Sheet from repeat radar altimetry. They also report similar (16 ± 11 Gt yr-1) mass gains for East Antarctica, but a large mass loss from the West Antarctic Ice Sheet on the order of -47 ± 4 Gt yr-1. These combined mass balances, they suggest, contribute +0.05 ± 0.03 mm yr-1 to sea level. The combined mass loss they found for Antarctica is much smaller than the combined mass loss calculated by time-variable gravity measurements made by the GRACE satellites (Velicogna and Wahr, 2006). These measurements suggest that Antarctica is losing mass at a rate of -152 ± 80 km3 yr-1, or a sea level equivalent of +0.4 ± 0.2 mm yr-1. Zwally et al. (2005) found Antarctica to contribute only +0.08 mm yr-1 to sea level. Previous studies have presented estimates of different components of the surface mass balance, such as accumulation (e.g. Drinkwater et al., 2001; Mosley-Thompson et al., 2001) and net mass balance (e.g. Thomas, 2001; Zwally and Giovinetto, 2001), although many studies claiming to give estimates of accumulation are actually providing estimates of net balance in the 54

accumulation zone from ice cores coupled with coastal precipitation measurements near the margins (e.g. Bales et al., 2001; McConnell et al., 2001). These latter studies illustrate the need for a clearer understanding of the surface mass balance near the ice edge. Many mass balance studies rely on measurements of surface elevations from two different times (e.g. Abdalati et al., 2001; Davis et al., 2001), yet surface elevation changes caused by densification, percolation, crustal uplift, ice dynamics, sub-glacial hydrology, and variability in snow depth can be easily misconstrued as mass balance changes and may even be impossible to separate from them. The results of all of these, and other such studies vary widely. Thus far, five major approaches to determine the mass balance of the Greenland Ice Sheet have been applied. These include a comparison of total snow accumulation and total ice discharge, repeat precision airborne laser altimetry surveys, time series of satellite borne radar-altimetry measurements, repeat gravimetric satellite surveys, and point measurements of elevation change in shallow bore holes. The bulk of evidence from such studies suggests that the ice sheet is presently thinning rapidly, especially along its margins, and the retreat appears to be accelerating. This suggests an overall net mass loss from the ice sheet, and a positive contribution to sea level. Most of this mass loss on Greenland is concentrated in channels containing outlet glaciers (Abdalati et al., 2001). This net loss from the ice sheet is enough to account for at least 8% of the total observed rise in sea level (Krabill et al., 2000). Measurements of air temperature over the ice sheet collected in the late 1990s by a series of Automatic Weather Stations (AWS) measured a 2°C warming (Steffen and Box, 2001) as compared to data collected in the 1950s (Ohmura, 1987). Furthermore, melt water production at the surface may cause the rapid acceleration of ice flow to the margins of the ice sheet through the flow of water and energy to the base where basal sliding can increase and additional basal melting can occur (Zwally et al., 2002). It is possibly by these means that the Greenland Ice Sheet experienced rapid melting during the last interglacial (Koerner, 1989) and may cause much faster retreat of the margins from climatic warming than previously modeled by surface ablation alone (Braithwaite, 1990). Additionally, warmer ocean waters at intermediate depths are penetrating further beneath floating ice tongues, especially 55

around Greenland, causing faster basal melting rates. This leads to a retreats of the grounding line of these glaciers (where they change from grounded glaciers to floating ice tongues) and, consequently, the rates at which these glaciers flow out towards and discharge into the oceans (Bindschadler, 2006). Conversely, as the atmosphere warms, increased atmospheric water vapor content could lead to more accumulation over all or part of the ice sheet, partially offsetting the increased melt (IPCC, 2001; Huybrechts et al., 1991; van der Veen, 1987), or even resulting in a more positive mass balance (Wild et al., 2003). Thus, the contribution of the ice sheets to future sea level remains unclear. Gravimetric measurements made by NASA's GRACE (Gravity Recovery and Climate Experiment) satellite have revealed that the mass loss rate on the ice sheet has tripled since 2002 to –239 ± 23 km3 yr-1 (Chen et al., 2006), which agrees remarkably well with a recent estimate made from radar altimetry data –224 ± 41 km3 yr-1 (Rignot and Kanagaratnam, 2006).

In Situ Measurements of Mass Balance Some of the most reliable measurements of mass balance are those made in situ (in the field) and include measurements of surface height change using stakes or acoustic sounders, as are installed on the AWS and smart stake (SMS) stations, or through snow pit or ice core retrievals. Many attempts to quantify the mass balance on Greenland have relied on a combination of such field measurements, particularly of accumulation, and modeling, especially of ice flow. One of the first modern estimates was based on long-line leveling over repeat traverses across central Greenland in 1957, 1958 and 1964 by the Expedition Glaciologique Internationale au Groenland (EGIG transect). This first showed that there was a negative net balance when extrapolated over the entire ice sheet (Bauer, 1966). This estimate corresponded to calculations based on other observations at that time. Seckel and Stober repeated these calculations using an additional traverse in 1968 and claimed that the ice sheet was thickening in the accumulation zone by 0.09 m yr-1 and was thinning in the ablation zone by at least 0.24 m yr-1. Reeh and Gundestrup determined that the ice sheet was thickening by 0.03 ± 0.06 m yr-1 at Dye 3. Along the nearby OSU transect, Kostecka and Whillans computed a mass balance of 0.06 ± 0.14 m yr-1. Their large uncertainty was attributed to accumulation rate measurement 56

errors, flow-line spreading and other possible factors, including ice impurity, which may affect flow. These results agreed well with earlier studies. Along the EGIG transect, Kostecka and Whillans calculated a mass balance of 0.0 ± 0.07 m yr-1. They attributed the differences with previous estimates to their use of longer-term accumulation rates. These studies generally agreed that the accumulation zone had a small positive mass balance while the ablation zone was likely thinning. Most mass balance studies are limited both temporally and spatially (Hannah et al., 2000) and have relied upon traditional in situ stake measurements (Østrem and Brugman, 1991). Unfortunately, measurements at single points or along traverses are limited in coverage and therefore do not give reliable estimates of the mass balance of the entire ice sheet. The advancement of satellite, GPS and laser- and radar-altimetry technologies allows for a more robust and spatially continuous investigation of mass balance (Demuth and Pietroniro, 1999; Favey et al., 1999; Fountain et al., 1999; Rasmussen and Krimmel, 1999; Theakstone et al., 1999). The advantages of remote sensing are especially acute in remote and inhospitable study areas, like Greenland. These methods may be used to derive changes in ice-surface elevation; however, surface height change is related to mass balance through a combination of both ice-flow dynamics and surface mass and energy exchanges (Gudmundsson and Buader, 1999). Although promising, these new technologies are still limited in their measurement resolution and some variables cannot be observed from these platforms. Therefore, ground-based observations and field research will continue to play an important role in science in the coming years. Rather than eliminating field research, these technologies offer new ways to address questions and a wider range of questions that may be addressed (Gurney et al., 1993) and may aid in more efficient and productive field programs.

METHODS Objectives Using a combination of in situ field measurements and measurements recorded by Automatic Weather Stations and Smart Stakes, my objective is to calculate an average mass balance at several points along an elevation transect in west-central Greenland. I have 57

determined the means of the three components of the surface mass balance, accumulation, ablation, and net mass balance, for points along the elevation transect extending from the coast of west-central Greenland up to the ice sheet summit (see Fig. 4.1). This elevation profile provides a base-line record for future comparison and is the largest such profile ever created for a glacier.

Figure 4.1: A false-color composite Landsat image of the Pâkitsoq study area is draped over a DEM to produce a simulated 3-D view of the study area looking toward the northeast. The vertical exaggeration is 20:1. The locations of AWS and newly installed SMS are given. The relative location of the study area within Greenland is indicated by the red rectangle on the inset map. The red dashed line in the main and inset maps represents the elevation profile, extending from JAR3 near the coast up to the ice sheet Summit, as shown in the inset.

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Data The Greenland Climate Network (GC-Net) AWS provide continuous measurements of the near-surface conditions including incoming and outgoing short-wave radiation, net radiation, surface height, atmospheric pressure, and temperature, humidity, wind speed and wind direction at two levels, and snow and ice temperatures at up to 10 levels . Each AWS instrument is factory-calibrated to the accuracy reported in Table 4.1 and is relatively calibrated in situ to ensure relative accuracy of vertical profiles of temperature, humidity and wind speed. Wind speed is recorded at two heights, allowing for the calculation of a wind profile. Temperature is recorded at two heights by passively ventilated, shielded, Type-E thermocouples. The thermocouple data are corrected for solar overheating using a relationship established between overheating and wind speed and incoming solar radiation through the comparison to ventilated temperature instruments as described by Box (2001). It is possible to calculate a sensible heat flux from these profiles of temperature and wind speed using the aerodynamic profile method or the bulk method as described by Box and Steffen (2001). Relative humidity is also recorded at two levels using either CS-500 or HMP-45 instruments. This humidity profile, along with the wind profile, enables the calculation of a latent heat flux using the aerodynamic profile method. The net radiative flux is recorded directly by a REBS Q* 7 net radiometer. The ground heat flux can be estimated from profiles of snow and ice temperature made by a profile string of thermocouples. Together, these data may be used to derive a complete surface energy balance for those points, with any residual energy being available for raising the temperature and melting at the surface. Smart Stakes are a compromise between the AWS, which are more robust but more costly and difficult to maintain, and the simple ablation stake, which records nothing other than cumulative change in the surface height between surveys. SMS combine hourly measurements of surface height change with single-level meteorological measurements to help provide a better spatial resolution to the AWS network in the region. They were designed for and installed in the lower Pâkitsoq region in hopes of gaining a better understanding of the mechanisms and processes involved in ablation and the spatial variations observed in ablation, specifically for this study. During the melt season, the single-level meteorological measurements provide an hourly 59

record of near-surface turbulent fluxes, as the surface can be assumed to be at saturation and at the melting point.

Table 4.1: Manufacturers reported instrument accuracies.

Variable

Instrument

Instrument Accuracy

air temperature

Campbell CS-500, HMP-45 or TypeE Thermocouple

0.1 °C

relative humidity

Campbell CS-500 or HMP-45

3-5%

wind speed (u)

RM Young 05103

0.1 m s -1

station pressure (P)

Vaisala PTB101B

0.1 hPa

surface height

Campbell SR-50

0.001 m

snow temperature

Type-T Thermocouple

0.1 °C

incoming (K9) and reflected (K8) shortwave radiation

Li Cor Photo diode

5-15%

net radiation (Q*)

REBS Q* 7

5-20%

Due to the relatively low cost of SMS, it is feasible to install several in a small area. This allows for a detailed study of the spatial variability of temperature, wind speed, relative humidity, turbulent fluxes, and ablation as well as a look at the influence of factors such as slope, azimuth, and elevation on ablation within a basin. The simplicity and low cost of SMS not only allow more to be purchased, but allow them to be installed and serviced more readily than full AWS. The SMS include a robust set of instruments to monitor wind-speed, humidity, temperature, and changes in surface height. They are each equipped with two 18 Ah batteries charged with a 10 W solar panel and a Campbell Scientific data logger to process and store the data. Each year the data are downloaded in the field and the stakes are lowered to account for ablation. Part of the protocol for maintaining the AWS and SMS network includes digging a snow pit, recording the stratigraphy, and measuring snow densities at each station. All available snow pits (34 in total) density data from 1990-2003 were gathered and the mean densities were

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recorded. These measured densities varied very little from site to site, year to year, and exhibited little relationship with the depth of the snow. Thus, a mean snow density value is used for all first-year snow in west central Greenland with great confidence (rsnow = 365.2 kg m-3). Calculated water equivalent depths and actual measured water equivalent depths from all available snow pits (n = 34) were compared and have a correlation of r2 = 0.93 (see Figure 4.2), suggesting that the mean density of snow in all snow pits, when only including the current annual accumulation layer, is nearly constant for all years and all elevations (from the coast to the summit).

Figure 4.2: Scatterplot of measured snow depths from 34 snow pits across Greenland, measured between 1990 and 2003, and the calculated water equivalalent depth based on the measured density profile from each pit. The strong correlation (r2 = 0.93) suggests that the mean density of snow pits varies little with the depth of the annual snow layer. These measurements were made from one year of snow. Presumably, older snow would be more compact and have a higher density.

Study Area Field data was collected in the lower Pâkitsoq region, defined here as the area that extends from the Swiss Camp (69.573°N; 49.295°W; Fig. 4.1), located on the mean equilibrium line altitude (Ohmura et al., 1991) at 1149 m a.s.l., down to the ice-sheet margin near JAR 3 61

(69.395°N; 50.310°W; Fig. 4.1). At present, there are four automatic weather stations (AWS) in this area, the Swiss Camp AWS (1149 m a.s.l.), JAR 1 (962 m a.s.l.), JAR 2 (568 m a.s.l.), and JAR 3 (323 m a.s.l.), that create an elevation transect through the ablation zone (see Fig. 4.1). Although the meteorological conditions vary widely across the ice sheet, this is representative of a larger region and has been the focus of many earlier studies. In addition, the location of the Swiss Camp on the mean equilibrium line altitude implies that its climate is representative of the overall climate of the ice sheet (Ohmura et al., 1992). In fact, the elevation of the equilibrium line serves as a proxy for the general climate conditions of the ice sheet. This region is presently one of the most intensely monitored portions of the Greenland Ice Sheet and is the major focus of a recent PARCA (NASA's Program for Arctic Regional Climate Assessment) initiative to study the mass balance near the margin of the ice sheet. The study area extends up to the summit of the ice sheet to create the largest elevation profile of a glacier ever constructed (Dyurgerov, 2004 pers. comm.). This area encompasses a network of 11 AWS and SMS along a transect between the ice sheet summit and the margin of the ice sheet just north of the Jakobshavn Isbræ (see Fig. 4.1).

Analysis Paterson (1994) states that in order to study mass balance on a glacier, measurements must be made at a representative set of points. These measurements must include the mass of snow and ice that has accumulated in the previous measurement year in the accumulation zone, and the mass of ice lost in the ablation zone. Since this study is concerned with the detailed mass balance of the ablation zone, these measurements must include the mass accumulated through each measurement year and the mass lost from ablation in each measurement year. In order to study the annual and diurnal cycles of melt, as well as the effects of elevation, slope, aspect and latitude, a network of AWS and smart stakes (SMS), described below, were installed along an elevation transect through the area (Fig. 4.1). The data collected for this study will consist primarily of the AWS and SMS data, snow pit data, and additional data collected in the area. The data collected from a single station, for a single year, is henceforth referred to as a station-year. Forty-five station-years of data from these stations have been supplemented with 62

snow-pit and stake data to yield 62 station-years of accumulation, ablation, and net mass balance measurements from 11 different elevations from near the coast (323 m a.s.l.) up to the ice sheet summit (3254 m a.s.l.). To determine the mass balance components, accumulation, ablation, and net mass balance, several techniques were used, depending on the data available and the surface conditions. These various techniques and the data required for each are elucidated below. The cases of the ablation and accumulation zones will be addressed separately, as they were handled, and special cases will also be addressed. Finally, special attention will be paid to Swiss Camp (ETH) on the equilibrium line, where positive and negative mass balances both occur. All mass balance components are calculated for the mass balance year, defined here as May through April. Generally, in the ablation zone more mass is melting each year than accumulating. An example of surface height measurements for the ablation zone is given in Figure 4.3. Figure 4.3 is further annotated with some of the necessary information and will serve as a basis to discuss how mass balance components were calculated for ablation zone sites. In Figure 4.3, the yearly maximum and minimum surface heights are labeled for the 2000 mass balance year. The previous year's minimum surface height is also labeled. The difference between the yearly maximum and the previous year's minimum represents the snow depth at the onset of melt, as labeled for 2002 in Figure 4.3. The difference between the yearly maximum and the yearly minimum represents the total melt, which includes snow melt and ice melt. Since snow and ice have different densities (rsnow = 365 kg m-3; rice = 917 kg m-3), the total melt cannot be converted directly to a water-equivalent depth (m w.e.) without separating the two components. Thus, the snow depth is needed to determine the ablation as well as the accumulation. The ice melt is calculated as the difference between the total surface lowering and the snow depth. This is equivalent to the difference between the previous year's minimum and this current yearly minimum. This is only valid in the ablation zone, where it may be assumed that all snow was removed from the surface in the previous year (i.e. it melted down to ice). The depths of melt for each surface type were converted to water equivalent-depths by multiplying by the ratio of the density of the material to that of water (rwater = 1000 kg m-3). Snow depths were converted to water-equivalent accumulation depth in the same way. 63

Figure 4.3: Annotated surface height record for JAR2, a typical ablation zone site. Mass balance components are derived from these surface height records from this and other stations, where the difference between the yearly maximum and the previous year’s minimum make up the accumulation record for the year, the difference between the yearly maximum and the yearly minimum is used to derive the ablation for the year, and the difference between the two yearly minimums is used to determine the net mass balance for the year. Average densities for snow and ice are used to convert these heights to water equivalent depths assuming that the year’s accumulation is snow (rsnow = 365 kg m-3) and the difference between the two year’s minimums is ice (rice = 917 kg m-3). In the ideal ablation zone case, the depth of snow on top of the previous year's melt surface is known. For cases where these data are not available, snow depth measurements made in the field or snow pit measurements are substituted when available. While these in situ data are very reliable, they are used only when necessary to remain as consistent and automated as possible, and to demonstrate the ability of the AWS network to determine mass balance components remotely. Where field measurements and AWS measurements of snow depth are 64

unavailable, the mean snow depth was used to estimate the portion of the melt that was snow. These means were never used, however, to determine an accumulation or net mass balance. In the accumulation zone, the surface height trend is upwards, and the major mass balance component is accumulation. Accumulation is simply calculated as the annual change in surface height multiplied by the ratio of snow density to water density. Occasional ablation events are identified, although these are often difficult to separate from redistribution of snow by wind or from compaction. When ablation events are identified, the water equivalent depth is calculated using the mean snow density. For station years where both accumulation and ablation are known, a net mass balance is calculated as the sum of accumulation and ablation.

RESULTS Individual mass balance curves for each station are presented in Figure 4.4. Shown in each graph is the derived record of accumulation, ablation, and net mass balance for any years where data were available. The graphs are arranged in order of elevation. The amount of ablation generally decreases as you progress up the profile. Note the more negative shift over time in all three mass balance components for JAR3, the lowest elevation station. Along the equilibrium line, at ETH, the net mass balance fluctuates between positive and negative. This illustrates that the equilibrium line altitude (ELA) is not fixed, but fluctuates with the given climatic conditions. The overall mass balance of the ice sheet would be greatly diminished by a permanent shift of the equilibrium line to higher elevations. Note that the lowest and highest elevation stations generally exhibit the least variability in the mass balance components, while JAR1 and ETH exhibit the highest variability, especially in ablation and net mass balance. Therefore, these stations may contribute a greater influence on the present mass balance of the ice sheet. Accordingly, future mass balance studies should perhaps focus on and around the ELA. The three mean mass balance components were plotted against station elevation to create the first known mass balance profile for the Greenland Ice Sheet (Figure 4.5). Note that the net mass balance for ETH is slightly negative, suggesting a slight shifting of the ELA to higher elevations, though the error bars include the zero mass-balance line. This would be expected 65

Mass balance (m w.e.)

1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3 1 0 -1 -2 -3

Summit

CP1

CP2

ETH

JAR1 Accumulation Ablation Net Mass Balance

SMS1

SMS2

SMS3

JAR2

SMS4

JAR3

1995

1997

1999

2001

2003

2005

Figure 4.4: Mass balance profiles of automatic weather stations (AWS) and smart stakes (SMS) on the Greenland ice sheet arranged by elevation. 66

67

-3.5

-3.0

0

500

1000

1500

2000

CP1 CP2

ETH

JAR 1

SMS 1 SMS 2

SMS 3 JAR 2

SMS 4 JAR 3

2500

Net Mass Balance

Ablation

Accumulation

3000

3500

Figure 4.5: Mass balance profile of the Greenland ice sheet from the west-central coast, through Swiss Camp (ETH) up to the ice sheet summit. Error bars represent one standard deviation from the mean.

Mass balance (m w.e.)

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

Elevation (m)

Summit

with increased melting over the ice sheet. Looking at the accumulation profile, one can see that accumulation is highest and most variable (see error bars) on and around the ELA. The other mass balance components are also most variable in this area. This higher variability further supports the importance of these elevations to the mass balance of the ice sheet.

Discussion In a warming climate, more accumulation is expected at higher elevations and more ablation is expected at lower elevations. Therefore, we expect a steepening of the mass balance profile in a warmer climate, as has already been observed on many glaciers around the world (Dyurgerov and Dweyer, 2000). There are no adequate historical data to create a mass balance profile to compare with the modern data presented here, yet none of the observations suggest an increase in accumulation anywhere on the ice sheet. The climate of the equilibrium line can be considered representative of the ice sheet as a whole. As climate warms, the equilibrium line can shift to a higher elevation. The sensitivity of the ELA to temperature was determined by Ambach (1985b) and Ambach and Kuhn (1985) using altitudinal gradients of air temperature, accumulation and net radiation, obtained during the 1959 and 1967 EGIG (Expedition Glacioloqique Internationale au Groenland) experiments. They estimated that the ELA would shift by +77 m °C-1 at constant cloudiness, and -4 m per 1/10th cloudiness at constant temperature. They found the most important parameter to be air temperature, as it influences the intensity and duration of the ablation period. The estimated shift of the ELA from Figure 4.5 is +45 m, or approximately 0.58°C warming (although the range of error could even include cooling) between 1990, when the station was installed, and 1995-2002, the period the average net mass balance was calculated over. This assumes that the station was indeed installed at ELA and that the one could linearly interpolate net mass balance between stations, in this case ETH and CP2. Each new year of weather station data collected in Greenland since 1992 yields a temperature record that is warmer than all previous years. Satellite data confirm that larger areas on the ice sheet are melting now than have been observed in the last 25 years, and that the margins of the ice sheet are now thinning rapidly. Snow acts as a thermal insulator and provides 68

a high albedo surface. Both of these factors limit melt intensity or delay the onset of melt, therefore, increases in snow-free areas would lead to greatly increased ablation. Although the net ablation along the margins of Greenland is increasing, records of melt recorded at individual stations in west-central Greenland vary widely in space and time and may not necessarily reflect the overall trends. For example, when complete years of record between 1990 and 2005 are considered, the lowest recorded total annual melt from within the lower Pâkitsoq region was recorded in 1998 at Swiss Camp, on the equilibrium line. That year, the surface melted by only 0.18 m w.e. there, while the next closest station recorded a melt of 1.3 m w.e., the second largest melt ever recorded at that station. The largest melt recorded at JAR1 occurred in 2002, when 1.67 m w.e. of ablation was measured. The nearby ETH station measured 0.59 m w.e. of ablation that summer, which is unremarkable when compared to the melt seasons of 1996 and 1999, when the surface melted by over 1 m w.e. Conversely, in 2001, the JAR2 station recorded a surface melt of 2.92 m w.e., while SMS4, an even lower elevation site, recorded less ablation (2.79 m w.e.). These variations cannot be explained by variations in temperature alone, and therefore any model seeking to capture the variability in melt from site to site needs to include more than just temperature, which varies almost linearly with elevation, as is commonly done in positive degree-day (PDD) models. These models are addressed in the next chapter.

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V. MODELING MASS BALANCE ON ICE SHEETS

Computer models are often employed in Earth sciences because of their ability to simulate natural processes and speed up the time domain. They allow scientists to better understand the processes controlling various parts of the Earth system by tweaking inputs and physics in the model, and they are the best tool scientists have for forecasting future conditions. In the case of ice sheets, models are frequently employed to simulate the surface mass balance in order to understand past, present, and future contributions of the ice sheet to global sea levels. Mass balance modeling involves a wide range of temporal scales, ranging from the microscopic processes which ripen the snow and turbulent eddies which transfer mass and energy between the atmosphere and the snow, to hourly changes caused by atmospheric circulation, all the way up to changes in ice dynamics that may require centuries. Figure 5.1 is a Stommel diagram depicting the time and length scales of the general processes effecting the surface mass balance of the Greenland Ice Sheet. With these varied space and time scales, it is difficult for any single model to incorporate all of the factors contributing to surface mass balance. Accordingly, a diverse array of models has been developed. Among these, three types are the most commonly utilized. These model types include statistical, analytical, and numerical models, each type with increasing complexity and capable of operating at a variety of temporal and spatial scales. In this study, each of these three major types of models were investigated for modeling ablation in the lower Pâkitsoq ablation region, from ETH down to JAR3, where the surface typically begins with a layer of fresh as snow in the spring, which melts off, along with some ice, and ends as bare ice in the fall. A single model was chosen to represent each model type. The 70

goal of each of modeling experiment was to accurately simulate the measured melt rate at the surface over a single melt season given hourly observations from an AWS. While the true relationship between climate and melt is not yet fully understood, these models aim to capture the primary influences and general fluctuations.

Figure 5.1: Stommel diagram depicting the time and space domains that different factors influence the surface mass balance of the Greenland Ice Sheet.

Each of the models is scrutinized for its applicability to melt modeling on the Greenland Ice Sheet, an important component missing from even the best available models (Box, pers. comm.). By testing several types of models, it is hoped that an appropriate model or 71

parameterization scheme could be coupled with a mesoscale model like the Polar MM5 model to accurately simulate mass balance on the ice sheet. The model chosen to represent the statistical models was the PDD (positive degree day) model, the most commonly used of all the models. The PDD model makes several assumptions about the relationships between air temperature, elevation, and melt. These assumptions were tested and the results presented below. Overall, the model is quite simple, has the fewest data requirements, and performs well, however, its assumptions preclude it from being used in any studies requiring the spatial variability of melt. The numerical model chosen was the SNTHERM.89 model developed by Jordan (1991). This commonly used snow-melt model has the most data requirements, and while all of these requirements were met, the model failed to accurately simulate melt on a glacier. The original design and intentions of the model were to simulate melting snow over soil, and while the model has been successfully run over a glacier before (Rowe et al., 1995), it required significant rewriting for its application there. Rowe et al. no longer had the code used to model melt on a glacier, so these rewrites could not be investigated in this study. Several attempts were made to parameterize the model to enable it to run over a glacier, but none produced adequate results. Some of these parameterizations are described below. Finally, attention was turned to physically-based analytical models. The goal of an analytical model is to capture the main physical phenomena that will effect the resulting melt and include those in the model. While true numerical modelers often refer to simple analytical models as ‘toy models’, their utility lies in their ability to sort the most significant physical processes from those which play a secondary role and their ability to allow researchers to see the results of changing one parameter in the model on the output. For this model type, I chose to develop a new analytical model based on the surface energy balance, the main contributor of energy for surface melt, and the bulk subsurface snow processes. The subsurface snow processes included the warming of the snow to the melting point, the melting of the snow, the percolation and refreezing of the meltwater, and the eventual melting of ice. The model operates in one spatial dimension, the vertical, so no mass or energy is transferred up or down slope. A future

72

generation of the model could include such transfers. The theory and development of this new model is described below, as are the results a sensitivity study and the actual modeling results.

PROBLEMS WITH EXISTING MODELS One simplifying assumption that is common to many of the models is that all melt water produced at the surface will eventually run-off to the oceans and contribute to global sea-levels. In reality, a large number of factors influence the final discharge of water to the ocean. Among these are processes within the snowpack, firn and ice, which capture a significant portion of the melt water and retain it within the glacier. On the ice sheet, some of the melt water refreezes within the snow or firn and does not runoff. This mass and energy is not directly lost to the ocean as is often assumed. Models that neglect these processes may overestimate the contribution of increased melting on the Greenland Ice Sheet to future sea level rise by as much as 5 cm over the next 150 years (Pfeffer et al., 1991). Meteorological measurements of precipitation, often used as inputs to climate models, contain errors, notably the underestimation due to capture failure caused by wind-field deformation above the instrument. On average, this error is approximately 18% for Greenlandic stations (Dethloff et al., 2002), but varies based on the particular instrument and wind shield used, the wind regime of the station, and is especially large for snowfall. Furthermore, published precipitation data for Greenland do not distinguish between rain and snow, hampering our ability to correct for oversampling. Moreover, point measurements of precipitation in the complex topography of coastal Greenland are not likely to be representative of a larger area, even as small as a 50 km by 50 km model grid cell (Dethloff et al., 2002). These problems hinder the ability to accurately initialize models over Greenland, and retard our attempts to validate or evaluate models using in situ measurements. A large array of stakes coupled with multiple ice cores in the area around Summit revealed that the mean annual accumulation rate can vary by a factor of 2 within 200 km (Bolzan and Strobel, 1994). When ice core accumulation records are used to determine precipitation, large uncertainties are caused by a lack of knowledge of evaporation and snowdrift. Even current measurements of evaporation on the ice sheet are rare and have been mostly restricted to the 73

summer months and the central portions of the ice sheet. Furthermore, to derive time series of snow accumulation from ice core records, the evolution of the depth-density profile must be simulated. This relationship is sensitive to the precipitation history of the site and assumptions are usually made about precipitation rates from before the ice core record began. In addition, separating the regional accumulation signal from the noise due to spatially and temporal variability is both important and difficult (Kuhns et al., 1997). Still, long-term records of accumulation are one of the most readily reconstructed parameters of the ice sheet's mass balance (Ohmura and Reeh, 1991). Ablation, on the other hand, is driven primarily by the surface energy balance and is more difficult to reconstruct, especially as it leaves no permanent record of itself. Energy balance measurements are being made at 26 stations across the Greenland Ice Sheet. While most of these stations are located in the accumulation zone, nine are located in the ablation zone of the lower Pâkitsoq region.

METHODS To study and better understand the variations and differences in ablation seen on a glacier through time and from glacier to glacier, we need to utilize models which best convey these complexities. The models themselves need not be complex, but must describe the physical processes and factors which contribute to the spatial and temporal variability in ablation rates. These factors might include variations within the atmosphere, snowpack, at the ice/snow and snow/air boundaries, within the ice, or the slope and aspect of the surface. The results of such models may be verified with measurements of surface height changes from AWS, SMS, snow pits, or stakes. If AWS and SMS are used, these stations should be fixed in the ice or firn, as they are in the GC-Net, rather than be tripod-type stations which move up and down with the surface, as tripod stations do not allow for measurements of surface height changes. In attempt to investigate the various model types, their assumptions, and their performance in modeling melt on the Greenland Ice Sheet, one model of each type was chosen and was fed actual measurements of meteorological conditions as input. The desired output of the model was an accurate simulation of the surface melt. Modeled surface melt was directly compared to actual measurements of surface lowering made in conjunction with the measured 74

meteorology. Comparisons were then made between the actual surface lowering and the modeled surface lowering. Evaluations of the performance of the models is discussed below. First, two popular existing models were examined, a statistical model and a numerical model. The numerical model failed to accurately reproduce the melt record over the study area and the statistical model was unable to capture the spatial variability of melt due to model constraints which are discussed below. Accordingly, a third model was then developed. The theory behind the model is described in detail and the model is tested against the other two models. While this model is able to accurately reproduce melt at some stations, it offers little benefit over a simpler energy balance model (EBM) or the simpler statistical model (PDD).

THE PDD MODEL, A STATISTICAL APPROACH The first model tested was the simplest and most commonly-used model, a statistical model called the PDD (positive degree day) model. Since it is often difficult to derive all of the energy terms in a physical model, we frequently turn to statistically-based parameterization schemes. Temperature-based or degree-day models are statistical models which rely on the strong statistical relationships between measured air temperature above the ice surface and the rate of melt of the snow or ice surface. These models may be solely based on mean summer temperatures (e.g. Ohmura et al., 1996), although Braithwaite (1995b) argues that positive degree days are a better predictor for melt. Ohmura (2001a) argues that the reason temperature-based models are so effective is that the air temperature is transferred to the surface not only through the sensible heat flux, but, more importantly, through the longwave radiation emitted by the atmosphere. Braithwaite and Olesen (1990b) related ablation to air temperature using a linear regression, and were able to show that sensible heat could explain approximately 50% of the temperature response of ablation. The relationship between air temperature and ablation was further investigated using a positive degree-day factor by Braithwaite (1995b). As air temperature and surface melt are both the integrated result of the total surface energy balance, the success of temperature-based models is not surprising. Temperature-based methods are frequently employed because temperature data are more readily available than

75

radiative and turbulent flux data, the parameterization schemes are simple yet relatively accurate, and temperature data are easily interpolated between sites (Ohmura, 2001a). The most common of the temperature-based approaches used in ablation modeling is the positive degree-day (PDD) model. The sum of daily average temperatures above 0°C at a site is the cumulative PDD value. Since these values are well correlated with ablation at all sites and daily average temperatures are easily obtained, this empirical approach is both useful and popular. The simplest version of the PDD model uses a constant PDD factor (e.g. 0.006 m water equivalent °C-1 day-1) that is multiplied by the cumulative PDD value to obtain the ablation. Added complexity is often included by allowing for different PDD factors over snow (e.g. 0.003 m w.e. °C-1 day-1) and ice (e.g. 0.008 m w.e. °C-1 day-1), and/or by allowing the temperature to vary with elevation by an elevation lapse rate. These PDD factors are site-dependent and should be calculated or estimated for each site or glacier and each year. The success of the PDD model, is due to a statistical correlation between cumulative PDDs at a site and the cumulative melt there. This correlation is then applied to other locations assuming that the correlation will hold. This assumption is among the multiple weaknesses in the PDD approach. Kuhn (1987) describes conditions when air temperatures are below freezing, yet melting can readily occur, and conditions when air temperatures exceed 0°C when melt will not occur. This illustrates a second weakness of the PDD approach, specifically that it assumes that temperatures above 0°C will always cause melt and temperatures below will never cause melt. Moreover, a day with widely varying temperatures can have an average daily, or even average hourly temperature that does not exceed the melting point, while instantaneous temperatures did exceed 0°C during the day. Furthermore, PDD models require tuning of the PDD factor for every location and thus are not transferable to other glaciated areas. The results of the PDD model are very sensitive to the PDD factor, k, which is not actually a constant like it is treated in most PDD models. Instead, varying surface conditions and meteorological conditions cause variations in k through both space and time. Therefore, while PDD methods are capable of capturing the overall patterns of

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ablation, they are not effective in explaining spatial variations in melt and the large inter- and intra-annual differences in ablation rates at a point.

Application of the PDD Model to the Pâkitsoq Ablation Region Since the AWS and SMS provide values of temperature and surface lowering at points along an elevation transect, these data are ideal for testing the assumptions of the PDD model. There are two primary assumptions which were tested here. Namely, these are that the PDD factor, k, is assumed to be constant through space and time, and melt will occur always and only when PDDs exceed zero (i.e. there is no offset in the linear model). A subset of the AWS and SMS data described above were analyzed to establish whether melt varies linearly with the PDD sum through time and over the elevation transect of the glacier, and whether the assumption that the relationship between PDD and melt is linear without any offset. Only the stations at or below the equilibrium line were included since these sites are where the most significant melt occurs. The mean monthly PDD sums for four ablation-zone AWS are provided in Figure 5.2.

Figure 5.2: Mean monthly positive degree days (PDDs) for four ablation zone sites in Greenland.

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Testing Whether an Offset is Needed When comparing PDD values to melt, the time frame become important. Daily PDD values showed nearly no relationship with melt, while monthly PDDs and melt values show a significant positive correlation (r2 = 0.51). Annual melt values showed a non-linear relationship with melt. A logarithmic relationship (MELT = 1.0578 ln (PDD) - 2.7363) had a stronger relationship for annual values (r2 = 0.94). The -2.7 intercept here may suggest that some amount of PDDs are needed to warm the non-isothermal ice before melting can occur. In other words, the very cold ice surface (typically -10°C) would not begin melting immediately upon the first days where temperature rose above freezing. Instead, warmer temperatures first go to warming the ice to 0°C and then further heat is used to melt the ice. This value may vary further depending on the temperature of the snow or ice pack. These results call into question the assumption of the PDD model that melt occurs only and always when the PDD sum exceeds zero. This is represented by the lack of an intercept in the model. Regression models of PDD and melt sums were compared using no intercept or allowing a single intercept. In all but a few cases, the model with a zero intercept, or no intercept, had a higher confidence of regression. This suggest that an offset is not likely needed in the model and that this assumption is generally valid.

Testing Whether the k-Value is Independent of Elevation Since the data here represent a large elevation range over a single glacier, the monthly regression coefficient was tested to see if it varied with elevation. It appears that lower elevation sites (300 - 800 m) appear to have a lower, and more constant k value (r2 = 0.69). For the higher elevation sites (900 - 1100 m) the relationship continued, but became more variable (r2 = 0.05). A linear value for k is likely not the best way to model melt over the Pâkitsoq region of west-central Greenland, and this calls into question the validity of the model as applied to

78

glaciers elsewhere. The value is sensitive to the elevation of the site and may also vary with the temperature of the snowpack or ice and other surface and meteorological conditions.

THE SNTHERM MODEL, A NUMERICAL APPROACH Numerical models range in spatial coverage and resolution from global general circulation models to one-dimensional models which model snow melt at a single point, such as the SNTHERM.89 model (Jordan, 1991). General circulation models typically have a horizontal resolution on the order of many kilometers and calculate broad meteorological fields. Such resolutions are inadequate to resolve the ablation zone on the Greenland Ice Sheet and seldom include the ability to calculate albedo distributions over snow or ice (Ohmura and Wild, 1995). Regional climate models, such as the Polar MM5 and the HIRHAM4 models, are more easily able to resolve atmospheric changes at higher spatial and temporal resolutions than general circulation models (GCMs) which operate at much lower resolutions (Meesters et al., 1994). Still, regional models often use boundary conditions derived from GCMs, including the ECMWF and the NCEP/NCAR reanalysis data. For regional models to add to the driving model output, however, they must be able to simulate local atmospheric feedbacks and describe the interactions between the large-scale forcing and the small-scale processes adequately at all time scales (Christensen et al., 2001).

About the SNTHERM Model SNTHERM.89 (Jordan, 1991) is a numerical model based on the physics of the ice, water, and air matrix existing in snow utilizing numerical solutions of Darcy’s equations. The model uses an initial snow profile and hourly meteorological observations to determine the hourly snow melt. This model, designed for use on snow over soil, could not be properly tuned to handle snow over ice for the Pâkitsoq region. SNTHERM.89 (henceforth SNTHERM) is a one-dimensional heat and mass balance model initially designed for predicting temperature profiles within a snowpack and its underlying soil. The model solves a set of mass and energy balance equations for the snowpack, and uses meteorological observations as the upper-boundary conditions, and the assumption of a steady79

state at the lower boundary. In addition to predicting temperature profiles, SNTHERM also simulates the transport of liquid water and water vapor in the snowpack, snow accumulation, ablation, compaction, metamorphosis, and the resulting changes in the thermal and optical properties of the snow. A flowchart of the model operation is given in Figure 5.3. The model physics are based on the work of Anderson (1976). Snow and soil layers are divided into horizontally infinite control volumes, whose initial properties are given as input to the model. A numerical solution is found for the governing equations of heat and mass balance for each of the layers. Since only the thermal processes are considered for the underlying soil layers, all water which reaches the soil surface is artificially drained. This is a major weakness of the model which limits its application to glacier surfaces where percolating meltwater often refreezes when it reaches the snow-ice interface. In order to handle snow densification and metamorphosis, layer thicknesses are free to change throughout the simulation. This is not generally allowed in models, however, here it is computationally efficient, and the snow layers remain coincidental with the altering snowpack stratigraphy. As layers thin or thicken, the mass of liquid water and ice are assumed to remain constant, while air and water vapor are permitted to escape. Although SNTHERM is intended for use in seasonal snow covers (Jordan, 1991), it is highly adaptable to a full range of conditions, and has been used successfully in glacial environments, including the ETH site used in this study (Rowe et al., 1995). Rowe et al. (1995) were able to accurately simulate the height and mass of the snow pack at the ETH site in 1990 using a modified version SNTHERM. They found that the evolution of the profiles of temperature, density, and liquid water content met their expectations for the site during melt. The testing of SNTHERM on the Greenland Ice Sheet was limited to one melt season, in a year with a positive net balance, and therefore is not a rigorous test of the model. In the proposed study area, a positive net balance is not likely to occur at any of the sites. The success of Rowe et al. (1995) was due, in large part, to modifications that they made to the model, which remain unpublished, and because they were only concerned with melting snow, as ETH is on the mean equilibrium line. They were also able to overcome the model’s inability to handle water pooling on the ice surface by considering the ice to be soil with no dry soil 80

MASS BALANCE BEGIN

HEAT BALANCE

Add mass to top node from snowfall or rain

Update thermal parameters

Calculate compaction rate of snow cover

Set past fluxes and variables

Calculate solar heating of snow layers

Solve energy balance equations using

Initialize variables

Open input parameter files

tridagonal matrix algorithm

Calculate surface boundary fluxes

Calculate and initialize initial parameters

Calculate the mass of water leaving each node using gravity flow approximation

BEGIN LOOP Read or generate meteorological input

Calculate heat flux for each node

FINAL STAGES Adjust liquid water variables and melt state

Calculate sublimation and diffusion of water vapor within snow layers Start of basic time unit (hour)?

No

Convergence criteria met?

Yes Adjust snow grain-sizes

Update, for all nodes, snow density, mass, and node thickness

Subdivide basic time interval and interpolate meteorological data

No

Reduce time-step and reset variables

Yes Output flux and meteorological data

Divide thick nodes and combine thin nodes

Output data for this time step

Figure 5.3: Flowchart illustrating the basic structure of the SNTHERM.89 model (adapted from Jordan, 1991). 81

component. The model automatically eliminates all water that reaches the snow / soil interface. If the ice is also to be allowed to melt, it must be considered a snow layer, rather than a soil layer. In this case, melting which occurs quickly enough to deliver meltwater to the snow / ice interface faster than it can refreeze will cause the model to crash. Testing of SNTHERM demonstrated that it is not suited to run over ice, and must be adjusted to handle the conditions found in my study area. The model consists of any number of layers of material, each with any number of sublayers, referred to as nodes. The nodes are generally made to correspond to actual layers observed in the snowpack, so that the assumed homogeneity of each node is more realistic. Mass and energy fluxes can occur between nodal boundaries, and the nodes themselves can compress to account for snow compaction. Model nodes are each composed of a fractional mixture of dry soil, dry air, liquid water, water vapor, and ice, denoted henceforth by the subscripts d, a, l, v, and i, respectively. The partial (or bulk) density, gk, of each constituent, k, is taken as the product of its intrinsic density, rk, and its fractional volume, qk, such that gk = qk rk For the study of surface ablation on an ice sheet, the ice may be treated as a snow layer with no dry soil parameter, a density of 917 kg m-3, and a grain-size of 0.0, which allows the grains to be most compact and most similar to glacier ice. The initial state of the snowpack is defined by user-supplied profiles of temperature, density, and grain-size at the beginning of the simulation period, and physical characteristics of the layer types (i.e. snow, ice, soil) are given. During the initialization, necessary program parameters are first read in from a file, constant parameters are established, and initial values are computed. Meteorological data are then read from an input file at a base sampling rate (usually hourly), and are interpolated between those periods for intermediate time steps. The mass and energy balances are then calculated, incorporating any known snow or rain fall during each time step. SNTHERM is driven by external meteorological data and initialized with information about the snowpack and underlying surface material. The mass and energy balances within the snowpack are driven by surface mass and energy fluxes. The surface fluxes are determined from 82

user-supplied meteorological data which include air temperature, humidity, wind speed, precipitation, and incoming and outgoing shortwave radiation, and incoming longwave radiation. If any radiation data are unavailable, SNTHERM is capable of modeling these based on solar geometry and cloudiness. Solutions for the mass and energy balances are obtained sequentially for each time step. Fluid flows are calculated first, and then are coupled to the energy balance equations.

Application to the Pâkitsoq Ablation Region SNTHERM was run for one station year that represented relatively mean conditions in the area through space and time. This initial modeling effort was done with the objectives of learning the operation of the model, testing the feasibility of running the model in the given conditions of the study site, and with the GC-Net data sets. Additionally, some model sensitivity tests were performed to determine how the model reacts to varying boundary conditions, and to ascertain the accuracy needed for each input parameter. Since saturated flow is not permitted in SNTHERM, the density of the ice layers must be set below 917 kg m-3. At densities above 900 kg m-3, all tested versions of the model crashed. Accordingly, model runs were aimed at establishing appropriate densities for the ice, and at studying the sensitivity of the annual ablation to the ice density. SNTHERM was found to be less sensitive to ice density in terms of mass balance, but more sensitive to it in terms of model operation. The model was run with identical forcing data, but with different ice densities and consistently terminated prematurely due to the saturation of the underlying ice and exceeding the maximum density. Repeated runs with different versions of the model ended in the same results. Figure 5.4 shows the results of several model runs of SNTHERM using several different densities for ice compared to the actual surface lowering measured by the station. Notice that in this set of model runs, the model crashed before reaching the end of the melt season unless the density was set to 810 kg m-3 or below. Even at these lower densities, the model greatly over-estimates the actual surface lowering (7.5 m modeled ablation compared to 3.5 m measured). As the density of the ice is lowered, the model is able to continue longer and longer. At an ice density of 810 kg m-3, the model is able to run without crashing, yet 83

Figure 5.4: Measured surface lowering at JAR2 in 2001 (red) compared to modeled surface lowering from several runs of SNTHERM with various ice densities (as shown). When run with ice densities greater than 810 kg m-3, SNTHERM crashed before reaching the end of the melt season. The actual density for ice is 917 kg m-3. Green shaded areas indicate where major melt events were captured by the model. These runs are a small but representative sample of the many model runs. this density differs greatly from the actual density of ice (917 kg m-3). As the meltwater percolates into the underlying ice and refreezes, the density of the ice increases. Seemingly, as the density reaches that of water, no additional meltwater can percolate and the model fails and crashes. 84

Comparisons of SNTHERM modeled surface lowering to that measured by the station yielded some evidence that the timing of melt events, which are driven by the same meteorological data that drive the model, correlate well with the measured values, yet the magnitude of the melt is off by a considerable amount. In Figure 5.4, two shaded boxes illustrate two examples where major melt events were suggested by the model results, although the magnitude of the events was off. Since the model is driven by actual meteorological data, comparisons were made between the model output fluxes and those derived from the station data using the aerodynamic profile method (Oke, 1987). The mean hourly net radiative fluxes derived by SNTHERM were generally larger than those measured by the AWS. This discrepancy occurred whether incoming solar radiation data were directly fed into the model or were calculated by the model, and likely account for the differences in magnitude of the modeled melt. Figure 5.5 compares fluxes modeled by SNTHERM with fluxes measured by the AWS or derived using the aerodynamic profile method from AWS data. Note the discrepancies between modeled and measured net radiation. The latent and sensible heat fluxes calculated within the SNTHERM model are also, on average, higher than those calculated using the aerodynamic profile method using the same meteorological data. Accordingly, the fluxes into the surface during melt are too large, and the predicted annual ablation far exceeds what is measured. Furthermore, micro scale processes that are included in SNTHERM (e.g. molecular diffusion and sublimation between snow grains) may be much less important than larger-scale processes that are not included in the model (e.g. blowing snow, redistribution through drift, and wind compaction). Also, if all of the micro-scale processes are not properly handled and initialized in the model, including them can cause the output to be less accurate. Much of the physics that is included in SNTHERM is difficult to initialize with actual measurements, and instead, parameters need to be tuned in the model. The documentation for the model indicates some likely ranges of these parameters, and, in some cases, indicates the range of values that produces reasonable results over warm soils, the conditions for which the model was developed. SNTHERM has been used to simulate snowmelt over ice for one ablation season, on the equilibrium line, but was modified significantly by the authors in order to achieve 85

Figure 5.5: Mean hourly fluxes of sensible heat, latent heat, and net radiation from the melt season derived from measurements and the aerodynamic profile method are compared to those derived from the same data using SNTHERM. this. Also, they were unable to melt ice with the model, but had no need to for the equilibrium line study.

THE SOSIM MODEL, AN ANALYTICAL APPROACH As the objectives of this chapter include simulating melt over a cold glacier surface and to evaluate the importance of processes acting to melt the snow and ice, an analytical model may be better suited for such process studies than a deterministic model like SNTHERM. SOSIM was applied to the Pâkitsoq ablation region in order to simulate snow and ice melt over the area. This model considers the heat and energy transfer between the atmosphere and surface, using an initial snow depth, average snow density, average snow temperature, and hourly meteorological 86

observations to drive advancing wetting fronts, snow surfaces, and ice surfaces. By developing a model which contains only the most relevant physics, the model itself will hold part of the answer that is sought; namely, what are the dominant processes that drive melt. In some instances, the model faithfully recreated the hourly surface height changes measured in the field. In other cases, the model could not reproduce measured changes of surface height with any reliable accuracy. The model developed here is given the name SOSIM, a Semi-analytical One-dimensional Snow and Ice Melt model. It combines a semi-analytical approach to determine the advancement of the wetting front through the snow, the melting surface, the growth and decay of a superimposed ice layer above the snow / ice interface, and the melting of the ice surface once the snow has ripened and melted.

Rationale Most of the work relating glacier mass balance and environmental parameters has relied upon regression techniques (e.g. Günter and Widlewski, 1986; Letréguilly, 1988; Martin, 1978) and empirical models (e.g. Jóhannesson et al., 1995). Although significant correlation is generally found between glacier morphology and climate, studies of the effect of climate change on ice bodies should be based on physical laws rather than on statistical relationships (Oerlemans and Hoogendoorn, 1989). Such arguments lead to the use of physical models. Models of mass and energy exchange and ice dynamics have been developed and utilized on a limited number of glaciers. For example, Allison and Kruss (1977) estimated net balance histories from the terminus records from the Carstensz and Meren Glaciers, Irian Jaya, Indonesia using a glacier flow model. A climate forcing history was then derived from the mass balance variations. Oerlemans (1986) used a one-dimensional ice flow model to simulate the observed terminus history of the Nigardsbreen Glacier, Norway. King et al. (1996) combined field measurements at Halley, Antarctica with an energy balance model of the ice surface to compute energy exchanges at the surface. The most common type of analytical model used in ablation modeling is the energy balance model. Energy balance models (EBMs) generally use hourly measurements of 87

meteorological variables and have internal calculations for albedo or use direct albedo measurements (Greuell and Konzelmann, 1994; van de Wal and Oerlemans, 1994). These models may operate at measurement points or over small regions. Surface energy balance studies over the Greenland Ice Sheet first began with energy balance modeling work by Ambach (1960; 1963; 1977; 1985a). Ambach obtained energy balance measurements during the 1959 and 1967 EGIG (Expedition Glacioloqique Internationale au Groenland) expeditions. The primary objective of those expeditions was to obtain an understanding of the heat balance in the ablation region of the Greenland Ice Sheet. He found that the ablation was driven by the radiation balance, and that the sensible and latent heat fluxes were nearly equal in magnitude and opposite in sign, and thus, the net turbulent heat flux at the site was close to zero for the period (Ambach, 1960). Braithwaite and Olesen (1990b; 1990a; 1990b) further investigated the relationship between temperature and ablation by using an energy balance model approach over two glaciers in southwest Greenland. They used simple daily climate data from field stations close to the glaciers as input into an energy balance model. The modeled ablation was then compared to stake measurements on the two glaciers. They found that incoming solar radiation accounted for approximately 70% of the energy for ablation at both sites, and sensible heat accounted for the additional 30%. Latent heat fluxes varied between strongly negative and strongly positive, but on average were close to zero.

Model Theory The exchanges of energy between the surface and the atmosphere occur within a constant flux layer within the atmospheric boundary layer where Monin-Obukhov (MO) similarity applies. MO similarity theory is a widely accepted description of the surface layer over uniform, flat terrain, and almost all energy balance and numerical models utilize it. The surface energy balance may be defined as the sum of all energetic fluxes toward and away from the surface. Using the principles of energy conservation, the energy available for melt, QM, may be found through the energy balance equation QM = Q* - (QE + QH + QG) 88

where Q* is the net radiative flux, QE is the turbulent flux of latent heat, QH is the turbulent flux of sensible heat, and QG is the conductive heat flux from within the ice. Each of these fluxes is measured by the AWS or may be modeled with AWS data. QG is very small in the ablation zone during summer and is the most difficult component to measure or model. It is also the smallest and most stable of the fluxes. Accordingly, it is not included in most energy balance models, and is not included in the model presented here. The derivations of each of the fluxes that comprise the energy balance, the instruments used to measure individual components, and the handling of these fluxes in the model, are all addressed further below. Net radiation is the dominant energy flux in most snowmelt situations (Male and Granger, 1981). According to a modeling study by Braithwaite and Olesen (1990b), radiation accounts for approximately two-thirds of the mean ablation over the southern Greenland Ice Sheet for the summer months while the turbulent fluxes account for the other third. In fact, Kuhn (1987) demonstrated that under extreme radiation conditions, snowmelt could occur at temperatures well below - 10°C. Snow and ice surfaces have unique properties that effect the energy balance at the surface. Both have extremely high broadband reflectivities when compared with most natural surfaces, and therefore have unique energy budgets. This high albedo has significant effects on shortwave radiation which, is the major energy source at the surface over the entire ice sheet (Braithwaite, 1995). Since the positive sensible and negative latent heat fluxes nearly cancel, the energy from radiation is mainly used to raise the temperature of the snow and ice to the melting point and then goes into melting (Konzelmann and Ohmura, 1995). The mean summer incoming solar radiation at the ETH Camp on the Greenland Ice Sheet, 288 W m-2, is among the highest recorded values in the world. Still, because of the large albedo values for this site (seasonal mean is 0.77), the absorbed solar radiation at the surface is only 65 W m-2 (Ohmura et al., 1994). The net radiation at the surface is strongly influenced by not only the changing albedo of the surface (Nolin and Stroeve, 1997), but by the changing cloud conditions (Konzelmann and Ohmura, 1995). The albedo of ice is several times lower than that of snow allowing it to absorb much more radiation at the surface. Table 5.1 provides means and ranges for albedos of different snow and ice surfaces. Furthermore, the albedo of snow is highly dependent upon the grain-size, 89

roughness, density, and the liquid water content. Thus, as natural densification of the snowpack occurs, the albedo decreases. During melt, the albedo of a snow surface is effected more than that of ice. Snow and ice are also semi-transparent and, thus, some radiation penetrates beyond the surface. The transmission of short-wave radiation in snow and ice affects the radiation balance in numerous and complex ways. At any depth within the snow or ice, radiation can be either transmitted, reflected or absorbed. The absorption of radiation occurs within a volume, rather than at a surface. Ice is much more transparent than snow, and thus, radiation will penetrate much deeper in glacier ice than in snow. Unlike shortwave radiation, long-wave radiation is almost completely absorbed by snow and ice surfaces alike. For most studies of radiative fluxes at the surface, the surface is assumed to be opaque, that is radiation is either absorbed or reflected at the surface, and the components of the radiative flux budget can be separated accordingly. For snow and ice surfaces, the assumption of opacity is incorrect, particularly in regards to shortwave (visible and ultraviolet) radiation, where penetration may occur to depths of up to 10 m (Oke, 1987).

Table 5.1: Albedos of snow and ice surfaces (Paterson, 1994).

Range

Mean

Dry snow

.80 - .97

.84

Melting snow

.66 - .88

.74

Firn

.43 - .69

.53

Clean ice

.34 - .51

.40

Slightly dirty ice

.26 - .33

.29

Dirty ice

.15 - .25

.21

Debris-covered ice

.10 - .15

.12

90

The decay of shortwave radiation with depth follows an exponential curve described by Beer=s Law: K9z = K90 @ e-az where K9z is the incident shortwave radiation at depth z, K90 is the shortwave radiation incident at the surface, and a is an extinction coefficient (units m-1) that depends on the wavelength of radiation and the properties of the medium, such as particle size, water content, and density. Strictly speaking, Beer=s Law is applicable only to individual wavelengths transmitting through a homogeneous medium, but it has been successfully applied to wider wavelength bands, especially the visible portion of the spectrum (Oke, 1987). The extinction coefficient of snow is greater than that of ice and, thus, radiation will penetrate deeper in ice than snow. In Antarctic snow, approximately 10% of K90 reaches a depth of 25 cm and 1% reaches a depth of 1 m (Weller and Schwerdtfeger, 1970). In glacier ice, 1% of the radiation penetrates to 2 m (Paterson, 1994). Further complicating the radiation balance is the presence of foreign matter in the snow or ice pack. For example, dust or organic matter present in the snow or ice will have a tremendous effect on the local extinction coefficient, and hence the transmission (Male and Gray, 1981). This is especially complicating when trying to make measurements with instruments below the surface, although it is assumed negligible for the study area where the ice is extremely clean. The penetration of shortwave radiation within the snow pack has very little effect on snowmelt for deep snow packs because very little radiation reaches the underlying surface (Male and Gray, 1981; the snow ice interface in the case of the Greenland Ice Sheet). Yet when the snowpack is shallow, solar radiation may reach the underlying surface where it may be absorbed, causing the surface below to warm. This additional energy may be transmitted to the snowpack through conduction or absorption of re-emitted long-wave radiation. This additional energy may go into warming the snowpack or to additional melting. In the case of shallow snowpacks, the albedo of the underlying surface can also effect the radiation balance and may need to be considered (Simpson et al., 2002). In the case of underlying glacial ice, it is unlikely that the radiation penetrating to the ice surface would significantly alter the net balance of energy 91

available for melt within the snowpack, as it could for an unfrozen organic soil layer beneath a shallow snowpack like what is described by Simpson et al. (2002). The turbulent transfer of energy to the surface depends upon the stability of the atmosphere which is controlled by vertical profiles of wind speed and temperature, and on surface parameters like temperature, moisture availability, and roughness. Table 5.2 provides some roughness lengths for different snow and ice surfaces.

Table 5.2: Roughness lengths of snow and ice surfaces (m) (Paterson, 1994).

Surface

Roughness length (m)

Smooth ice

.00002

Fresh snow

.0001

Fine-grained melting snow

.0007

Ice in the ablation zone

.001 - .006

Coarse snow with sastrugi

.011

The turbulent fluxes are directly proportional to the transfer coefficients. In general, the turbulent transfer coefficients of ice are larger than those of snow by up to two times (Paterson, 1994). This can lead to differing turbulent fluxes over the surfaces by a factor of two with all other things equal. The Richardson number is a means of categorizing atmospheric stability and is used to derive the dimensionless stability parameters. From Oke (1987), the Richardson number, Ri, is given as

92

where g is the acceleration due to gravity (9.81 m s-1), mean wind speed in layer

is the mean temperature and

is the

.

The Obukhov length, L, is a surface-layer scaling parameter that is physically related to the surface layer in that it is proportional to the height above the surface at which buoyant factors begin to dominate over mechanical turbulence (Stull, 1988). For unstable conditions, Ri = z / L The relation given for the non-dimensional stability factor, (FM FH), is (FM FH) = [1-15 Ri]-½ for unstable conditions. In relatively stable conditions, FH and F M are assumed equal. Here, in the unstable case, following Oke (1987), we assume that F H = F M2 And thus, FM = [1-15 Ri]-1/6 and FH = [1-15 Ri]-1/3 From similarity theory, the sensible heat flux, QH, may be calculated by the bulk aerodynamic profile method as

where cp is the specific heat of air at constant pressure, ra is the air density, k is von Karman’s constant (0.4), and FH is the thermal stratification, or the dimensionless stability function for heat (Oke, 1987). Similarly, the latent heat flux may be found

where q is the specific humidity. Another component of the energy balance over snow and ice is the energy involved in melting at the surface. Once melt initiates, meltwater percolates into the snow and either 93

refreezes, adheres to the surface of snow grains by capillary forces, or percolates. Meltwater transport through snow is an important source of energy for raising the snow temperature to the melting point. During melt, the temperature above the surface is less affected by the atmosphere since the surface remains at 0°C. Additional energy absorbed at the surface is used for additional melting. Thus, during melt, the atmosphere is abnormally decoupled from the surface. Snow is a good insulator. Heat moving through the snow will result in temperature gradients which initiate vapor diffusion within the snowpack. In a snowpack, temperature and moisture gradients, even on microscopic scales, cause vapor diffusion and redistribute the heat through latent heat exchange. This is many times more efficient than molecular conduction between ice grains. The addition of water, either by rain or meltwater percolation into the snow, will cause a rapid metamorphism where smaller ice grains evaporate and recondense on to larger, more spherical particles due to the difference in the saturation vapor pressures of individual grains. This is analogous to the Bergeron process in clouds. The specific heat capacity of dry snow and ice is assumed to be similar since the contribution of air in the pore spaces is negligible. Still, the pore spaces in snow become extremely important means of transferring energy through vapor diffusion and meltwater percolation. In a snow matrix, temperature gradients can cause vapor diffusion from higher temperature grains, across the pore spaces to lower temperature grains through sublimation and deposition. Since ice has an extremely high thermal conductivity, up to 100 times that of air (Male, 1980), convection within the pore spaces is unlikely and vapor diffusion will dominate. This cannot occur in a significant way within ice where the pore spaces have been closed off and compressed. Energy available at the surface of a sub-freezing, dry snowpack will first go into raising the temperature of the surface to the melting point (0°C) and then subsequent energy, M, will go into melting and liquid water will begin to accumulate in the snow matrix. As melting continues, liquid water will begin to percolated downwards and will refreeze as it comes in contact with sub-freezing snow layers beneath the surface. The release of the latent heat of fusion during refreezing raises the temperature, T, of the surrounding snow and reduces the porosity, ö, which 94

is the ratio of pore volume to total volume. This propagating meltwater is the primary energy source used to raise the temperature of the sub-freezing snowpack (Tseng et al., 1994). The refreezing of meltwater is limited by several factors including (1) the snow temperature cannot exceed 0°C, (2) the rate at which the cold snow pack is able to absorb latent heat from the meltwater, (3) the availability of meltwater, and (4) available pore space in the snowpack. In a simplified model with a one dimensional, uniformly propagating wetting front, once one of these factors has been exceeded, water is available to either remain in the layer by capillary forces or percolate downward, advancing the wetting front. Capillary retention of water is determined by the irreducible water amount, Swi, which ranges at the ETH Camp on Greenland from 0.08 to 0.15 (Greuell and Konzelmann, 1994), and available pore space. After percolating water has been refrozen and stored as capillary water, raising the temperature to the melting point, the wetting front may advance. This process is known as snow ripening. The above description accounts for a moving wetting front boundary between the wet snow zone, an isothermal mixture of snow, water and air at 0°C extending from the surface down to the 0°C isothermal layer, and a dry snow zone, a sub-freezing layer of snow, beneath. Figure 5.6 provides a basic diagram of a ripening snow pack. In reality, there typically exists, at least on a microscopic scale, a non-equilibrium zone where liquid water is found in sub-freezing snow. This is where the refreezing takes place and the snow temperature is raised to the melting point (Pfeffer et al., 1990). The non-equilibrium zone is separated from the wet snow zone by the 0°C isothermal layer and from the dry snow zone by the wetting front, which may advance slightly ahead of the 0°C isothermal layer (Tseng et al., 1994). This zone exists only if the rate of accumulation rate of film water on snow grains in the matrix is greater than the rate of freezing of the film onto the snow grains. As water is added to the system, the 0°C isotherm will advance as the wet zone grows, and the wetting front will advance as water reaches further into the dry snow zone. Hence, the non-equilibrium zone thickness is a complex function of the flow rate and amount of percolating water and the rate of freezing of the water on the surface of sub-freezing snow grains (Pfeffer et al., 1990).

95

Figure 5.6: Diagram depicting the idealized snow layers in a melting snowpack. On a microscopic scale, the wet snow zone is not in thermodynamic equilibrium. Wet snow metamorphism still actively increases the grain size, allowing larger grains to grow at the expense of smaller grains. As smaller grains disappear, some of the capillary water is released (Colbeck, 1978; Colbeck, 1986). In applications to heat and mass transfer, however, this zone can be considered isothermal since the small-scale temperature gradients will average to zero (Pfeffer et al., 1990). According to Pfeffer et al. (1990) the critical processes in each of the three zones can be described by a separate set of equations. In the wet snow zone, the process of water flow through a porous medium is often described by Darcy’s law (e.g.Pfeffer and Humphrey, 1998; Pfeffer et al., 1990; Tseng et al., 1994). Darcy’s law relates the capillary pressure gradient, M pc / M z, and the acceleration of gravity, g, to the volume of water flowing per unit time and area, u:

96

where kl is the permeability of liquid water, ml is the water viscosity, and z is the vertical coordinate (Male, 1980). Pfeffer et al. (1990) use the following form of Darcy’s equation:

where K is the hydraulic conductivity of the snow, krw is the relative permeability of the snow with respect to water, y is the total head, q is the volume of water content, and t is time. This equation does not include temperature which is assumed to be 0°C throughout the zone. For the dry snow zone, no water is present, so only the temperature equation applies:

where ks is the effective thermal conductivity, rs is the density, Cs is the heat capacity, and T is the temperature of the snow. This equation describes the temperature conduction across individual snow grains. In the non-equilibrium zone, both flows of heat and water are important, but the processes differ from those in the other zones. An additional sink term is added to Darcy’s equation to account for the freezing of water:

where mi is the mass of water lost to freezing per unit volume of snow. Since the temperature change of the snow in the non-equilibrium zone is due almost exclusively to latent heat released by the refreezing of meltwater, the conduction component becomes negligible and the temperature equation for the non-equilibrium zone becomes:

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where Lf is the latent heat of fusion. Here, the temperature change of a grain is determined solely by the rate of refreezing of meltwater onto that grain, which is determined by the temperature gradient in the grain and the rate of water percolation to the grain. Other complicating processes occur within the snow matrix including channel flow and fingering of the wetting front, metamorphism of the snowpack structure due to resettling of the grains and grain coarsening, condensation, sublimation and evaporation within the snowpack, hysteresis effects due to freezing and melting, freezing point depressions on and between snow grains, osmotic and chemical potentials, transfer of momentum between phases due to frictional forces and viscous effects, ice lenses, melt channels, and the convection of water liquid and vapor. Meltwater percolation may be locally obstructed by ice layers, but will eventually develop vertical drainage channels, allowing more of the water to run off. Over ice, the behavior of water will depend on the slope of the ice surface and its temperature. Perfectly horizontal ice surfaces will build up water if it cannot remove latent heat fast enough to refreeze it. Highly sloped ice surface may refreeze some water, but will also promote the development of slush flow. Typically, an ice surface is neither perfectly horizontal or highly sloped and falls somewhere between. Snow cover is a unique medium with properties that can vary greatly in time. Continual densification and metamorphism can affect the optical properties of the snow including albedo and shortwave transmission. Furthermore, the melting, refreezing and percolation of liquid water greatly alter the properties of the snow. These changes are typically irreversible. Ice, on the other hand, changes much less rapidly and on small time-scales can be thought of as having constant properties aside from the deposition of debris or snow on the surface. Snow is also greatly affected by the deposition of debris, but can be less affected by the deposition of fresh snow in comparison to ice. Uncertainties in the energy balance result primarily from instrument accuracy or from the lack of measurement of parameters assumed to be negligible or too difficult to measure. Other uncertainties include the energy delivered to the surface by rain which is not measured due to the deficiency of automated precipitation gauges capable of operating in these environments, the 98

inability to measure melt directly, the uncertainness of the paths that melt water takes before running off of the ice sheet and how much is stored within the glacier, and error introduced in modeling the fluxes. Surface roughness can easily vary by two orders of magnitude which corresponds to a change in calculated fluxes by a factor of two (Calanca et al., 1998). Similar errors can occur from extrapolating temperature and humidity profiles to the surface during nonmelt conditions. Unventilated temperature and humidity measurements in low wind and extreme insolation generate overheating of the instruments up to 5 °C (Box, 2001). This leads to an overestimation of the temperature and the saturation vapor pressure which in turn lead to biases in the Richardson number, air density and latent heat of vaporization. The relative humidity measured in the warm radiation shield may be under or overestimated. Further measurement problems can occur within the snow or ice. When installing instruments to measure ground heat fluxes or sub-surface temperatures, the instrument is likely to absorb transmitted radiation at a rate different of that of the medium, thus measuring its own response rather than what it was intended to measure.

Developing the Model The model is driven at the upper boundary by hourly measurements of wind speed, air temperature, relative humidity, and net radiation. The model is initialized with snow depth, bulk snow temperature, density, and irreducible water amount, and bulk ice temperature. Profiles of snow temperature are measured at the beginning of the melt season, and data from other years may be used when pits were not dug as the model is not sensitive to the temperature of the snow. The ice temperatures are measured by thermocouple strings, at intervals of 1 m into the ice, at the AWS. For non-AWS sites, the ice temperature profile of the closest station is used. As with the snow temperature, the model is insensitive to the ice temperatures, especially since thermal diffusion is not presently considered. QM is the boundary condition for the snow and ice melt model. The model is run in onedimension. Using a semi-analytical approach, the model tracks changes in the height (above the ice surface at the model initiation) of the snow surface, the wetting front, the saturated snow front, the superimposed ice front, and the ice surface. Four general cases are considered in the 99

model. These cases are (1) the advancement of the wetting front, (2) the pooling and refreezing of percolating meltwater, and (3) melting of superimposed and glacier ice. These three cases are illustrated in Figure 5.7 and are detailed below.

Figure 5.7: General cases of idealized snow surface profile considered in the SOSIM model. In Case 1, the wetting front advances as meltwater percolates and energy is used to bring the dry snow up to melting temperatures. In Case 2, meltwater continues to percolate and pools at the ice surface. Energy from the meltwater is lost to the underlying ice and the meltwater refreezes creating a layer of superimposed ice. In Case 3, the snow has melted revealing the superimposed ice layer and underlying glacier ice.

Case 1 – Advancement of the Wetting Front Initially, when snow is present, the modeled snow will consist of three layers. These will consist of a dry snow layer with initial density and temperature profiles, an isothermal snow layer at 0°C and with a water content equal to the irreducible water content, and an ice layer. This is illustrated in Figure 5.7, Case 1. The isothermal layer will begin at the snow surface, and, initially, will have no thickness. From the energy balance model, we determine that meltwater is produced at the surface at a rate of M (kg m-2 s-1), where 100

Since the isothermal layer advances more rapidly than the melting surface, this energy may all be used to melt snow. Still, mass is also exchanged with the atmosphere through evaporation, sublimation, deposition, and sublimation. This mass exchange occurs at a rate of E (kg m-2 s-1), where

where L is either the latent heat of sublimation or vaporization, depending on the surface temperature. Thus, the surface lowers at a rate dzsfc/dt (m s-1), where

Ahead of the lowering surface, the wetting front advances, leaving isothermal snow and a water content equal to the irreducible water amount, si, above. The wetting front will advance at a rate dzwf/dt (m s-1), where

As the wetting front advances by dzwf, the amount of mass in the layer increases by M over dt (seconds). Thus, the snow density at time t is

Case 2 – Pooling and Refreezing of Percolating Melt Once the wetting front progresses through the entire dry snow layer and reaches the ice surface, the dry snow layer disappears. The meltwater will begin to pool above the cold ice surface. As energy is lost to the colder ice, the meltwater refreezes creating a later of superimposed ice as illustrated in Figure 5.7. The superimposed ice layer is initially at the ice 101

surface with a thickness of zero. As additional water percolates through the isothermal snow, it hits the cold ice layer beneath and begins to fill in the pore space of the snow. At the same time, some of the water is refreezing at the ice surface, increasing the temperature of the ice (steepening the ice temperature profile). In the SOSIM model, two simplifying assumptions are made. The first assumption is that all percolating water to reach the ice surface will refreeze. No water is allowed to pool or runoff. The second assumption is that only a shallow layer of ice will be warmed, uniformly, and the rest of the ice temperature profile will remain unchanged. In reality, the rate that the superimposed ice surface advances is a ‘Stefan problem’, as it involves a moving surface between two phases of water (Carslaw and Jaeger, 1959). The Stefan problem is non-linear, so special solutions must be determined. One solution, applicable to our situation, is a modification of the Neumann solution presented by Carslaw and Jaeger (1959). One simplifying boundary conditions is that the saturated snow (liquid) must be at 0°C. The top of the superimposed ice layer will also be at 0°C, and its temperature will decrease down to the same temperature as the top of the underlying ice. Furthermore, at the superimposed ice front, the heat liberated by advancing the front must be equivalent to the latent heat of fusion of that mass and must be removed by diffusion. Thus, the rate of propagation of the superimposed ice front is dzsif/dt, where

where Kice is the thermal conductivity of the ice. Using these boundary conditions to simplify the solution is presented in Carslaw and Jaeger (1959) yields that the temperature in the ice at depth z and time t is

where kice is the thermal diffusivity of ice, and l is determined numerically from

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The temperature in the superimposed ice at depth z and time t may also be found from the above equation for Tice(z,t). The position of the superimposed ice front, zsif, at time t is found to be

It is assumed here that the density of ice and water are equivalent. In the simplified SOSIM model, no numerical solutions are required. Instead, all percolating meltwater that reaches the ice surface is refrozen, and a thin layer of ice at the ice surface is warmed by absorbing the latent heat released when the superimposed ice forms.

Case 3 – Melting of Ice Once the superimposed ice front reaches the surface, the process of warming and melting the ice begins. The only requirements to melt a layer of ice is to raise the temperature of the layer to 0°C, and to add enough latent heat to melt. Thus, the surface layer of the ice, whether superimposed ice or not, will lower at a rate of dzice/dt, where

This does not account for thermal diffusion into the ice which would normally be handled numerically using a finite differencing scheme, nor is mass conserved. Instead, it is assumed that all melt water runs off of the impermeable ice surface.

How Is SOSIM Different? The SOSIM model is based on the surface energy balance, and therefore is very similar to an energy balance model (EBM) with a few notable differences. There are a few main physical differences between the EBM and SOSIM. The first difference is that SOSIM requires that the cold content of the snow and ice be met before they are melted. Since the amount of energy required to melt a given mass of ice or snow is much greater than the energy required to raise its temperature, even by a significant amount, and because the snow always ripens and becomes isothermal faster than it melts, this first difference may not add significant value to the SOSIM model. 103

Additionally, SOSIM calculates the changing mass and density of the snow as the wetting front advances and the snow ripens, and includes water retained in the snow by capillary forces. Again, since the wetting front propagates faster than the melting surface, this feature also does not add any direct benefit over the EBM, but may be used in the accumulation zone to estimate the depth of percolation. One further difference in the physical formulation of SOSIM is the growth and melting of a superimposed ice layer. Snow pit observations at stations in the lower Pâkitsoq region each Spring confirm the existence of a superimposed ice layer, although no observations are available later in the melt season that measure the maximum thickness of the superimposed ice. Furthermore, detailed mass balance modeling of the ice sheet requires knowledge of the position and thickness of this layer, especially in the lower accumulation zone. The growth of superimposed ice in the SOSIM model provides advantages over the EBM and PDD models in that, given an initial snow depth measurement, other models assume that there is still snow present at the surface as long as that depth of snow or ice has not yet been melted. SOSIM, on the other hand, accounts for the earlier appearance of ice at the surface and provides an estimate of the maximum thickness of the superimposed ice layer. In addition to the physical handling of the subsurface snow layers in SOSIM, the model also calculates an evaporative and condensive mass flux based on the turbulent flux of latent heat. The modeled surface in SOSIM is allowed to grow and decay based on evaporation and condensation in addition to the surface lowering from melt. Snow fall events occur during the melt seasons which also affect the surface height and the surface composition. In all other models, once the snow has been melted off, only ice can exist at the surface. SOSIM allows the addition of snow, even after the seasonal snow pack has been melted off and only ice exists at the surface. No reliable measurements of precipitation are available on the ice sheet, as previously discussed. The surface height data from the AWS provide some indications of snow accumulation, however these data are a cumulative integration of a wide number of processes and, on a daily basis, the signal to noise ratio is too low to allow for reasonable estimates of even daily snowfall. Furthermore, it is intended to use the surface height measurements to validate the 104

results of the SOSIM model, and accordingly it is not advisable to use these measurements in any way to produce the model results, if possible. Instead, 6-hourly snowfall predictions from a special high-resolution run of the Polar MM5 model, running in 36 h forecast mode (Box et al., 2004) were used. The precipitation estimates from the Polar MM5 are perhaps the best available for the Greenland Ice Sheet. According to Box et al. (2004), however, the predicted snow amounts are about 10% too high. Thus, the snowfall used here is adjusted to 90% of the Polar MM5 output.

What’s Missing from SOSIM? Although SOSIM is more complex than a simple EBM or PDD model, it still has many simplifying assumptions and ignores several physical processes. Included among these simplifications is the lack of a non-equilibrium zone between the wetting front and the wet snow above. To include a non-equilibrium zone, the model would need to be solved numerically, and it is believed that the inclusion of this often microscopic layer would add little or no benefit to the model. A more significant exclusion from the model is the ability for water to pool more rapidly than it is refrozen when percolating meltwater reaches the underlying ice. Pooled water could quickly saturate the overlying snow, lowering the albedo, and creating slush, which would ultimately run off down the slope, removing mass from some areas more rapidly than predicted, and potentially forming lakes in depressions. As discussed above, the moving phase change boundary between the superimposed ice and the saturated snow is a Stefan problem requiring numerical solutions. A future, numerical version of this model could include this boundary problem in the solutions, as this may have a significant influence on the surface mass balance. Another numerical problem that is not considered in the current version of SOSIM is the diffusion of heat. Thermal diffusion is believed to be a significant energy sink during the melting of ice as the deep, cold ice provides a near-infinite sink for energy. Neglecting this energy component may lead to overestimations of the total ablation at a site. In addition to the above components that are not considered in the model, melt in SOSIM initiates at the surface and is based on the energy budget at the surface. Short-wave radiation, 105

however, penetrates into the snow and ice as discussed above, so that the energy maxima may occur below the surface. SOSIM also neglects this penetration of radiation, which is most significant for direct short-wave insolation.

Model Evaluation Comparing the results of the SOSIM model to those of a simpler energy balance model (EBM) and PDD models allows us to evaluate the model complexity and determine if the added complexity adds value to the other approaches. The SOSIM model was applied using 30 stationyears of data and performed well in almost all cases. Two test cases are discussed below, one of which illustrates the model performance for a typical ablation zone site in a typical melt season, and one illustrates the model complexity and ability to simulate the general surface mass balance pattern at the equilibrium line in a complex melt season where large snow falls occur many times throughout the melt season, often on top of bare ice.

Test Case 1: JAR 2 2001 JAR 2 is one of the lowest stations on the ice sheet with a reasonably long record. The 2001 melt season at JAR 2 was typical of many of the melt seasons throughout the region, where melt initiates in mid-spring and then continues at an almost constant rate of surface lowering until the end of summer. The surface height record for JAR 2 2001 is shown in Figure 5.8. The beginning and ending dates of the model run are indicated by the vertical dashed lines in the figure. The SOSIM model yields the changing position of the wetting front, ice surface, and snow surface through time, as shown in Figure 5.9. The wetting front appears to advance in large steps as melt events occur early in the season. This tends to be the case for all station-years. Once the wetting front reaches the ice surface, superimposed ice builds up. In almost all cases, the superimposed ice builds slowly until melt accelerates, and then there is a sudden rapid growth of the ice layer. This can be seen after day 160 for case 1 (Fig. 5.9). In reality, such a rapid delivery of melt water to the cold ice surface would likely result in water pooling and saturating the overlying ice. Slush would form and could run-off. In this case, when the measured surface 106

Figure 5.8: Partial surface height record for JAR 2 AWS. The 2001 season is indicated in red and the highlighted area represents the time domain of the first test case for the SOSIM model. height curve approaches the superimposed ice curve, there is a sudden drop in surface height, which may indicate a small amount of slush flow leaving the area. Once the superimposed ice is melted, the modeled rate of melt exceeds, at least initially, the rate of measured surface lowering. This may be due to the lack of thermal diffusion in the model as discussed above. Otherwise, the observed surface height changes are well-modeled and the net surface height change is reproduced to within 10%. Comparing the results of the SOSIM model to the other models requires the conversion to water equivalent depth. The water equivalent depth is estimated from the measured surface height record in order to compare with the models. The results of the SOSIM, EBM, and PDD models are shown in Figure 5.10 along with the estimated water equivalent height change from the observations. Generally, the PDD model does not accurately capture the magnitude of melt. In water equivalency, the SOSIM and EBM models are not very different in their timings or 107

Figure 5.9: SOSIM model output for Test Case 1, JAR 2 2001. Modeled surface height changes show accurate timings of most melt events and captures the general pattern of surface mass balance at the site, although ice melt tends to occur at a higher rate in the model than is measured. magnitudes, although for this case, SOSIM more closely models the mass balance magnitude. The difference between modeled and measured ablation cannot be explained by errors in the conversion of the measurements to water equivalency alone. For nearly all station years tested, the SOSIM model overestimates the ablation, but performs better, in general, than any of the other models tested, including SNTHERM (see Figure 5.4 for comparison).

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Figure 5.10: Comparison of SOSIM model ablation to that of a simple EBM, and PDD models. The estimated water equivalent depth from the surface height measurements is given for comparison. Modeled ablation rates from the SOSIM model are similar to those from the EBM until later in the season when snow fall is handled in SOSIM and the cumulative cold content of the ice has caused the curves to diverge. The PDD model underestimates melt.

Test Case 2: ETH 1999 Swiss Camp (ETH) is located on the mean equilibrium line altitude. This higher elevation site experiences much less melt and accumulates much more snow during the ablation season than the lower elevation sites. The 1999 melt season was chosen in this case because of the large snow fall events that occurred throughout the melt season. Accordingly, reproducing the surface height curve for this station year requires an accurate record of the snow fall. Once again, the Polar MM5 output is used for modeled snow fall. 109

The SOSIM modeled surface height record is compared to the measured record in Figure 5.11. Also shown in Figure 5.11 are the predicted records of the wetting front and ice surfaces as well as the cumulative snow fall from the Polar MM5 model. For the first half of the season, the modeled surface height record appears to reproduce the measurements with some skill. A moderate snow event in the middle of the season is missed by the Polar MM5 model, and the modeled and measured surface heights diverge from there. Late in the ablation season, a large snow event is predicted by the MM5 model, but the magnitude is not captured. This results in the model diverging further from the measurements, and the model ends up over-predicting the surface mass balance by almost 50%. The ice surface at the end of the model run had lowered by 1.3 m while the measurements suggest an ice surface lowering of about 55 cm. In comparison,

Figure 5.11: SOSIM model output for Test Case 2, ETH 1999. Modeled surface height changes show accurate timings of most melt events and captures the general pattern of surface mass balance at the site, but Polar Mm5 modeled snow fall timings and amounts are off. 110

the EBM and PDD models predicted larger surface lowerings as none of the other models handled the snow fall during the melt season (Figure 5.12).

Figure 5.12: Comparison of SOSIM model ablation to that of simple EBM, and PDD models. Modeled ablation rates from the EBM and PDD models are greater than those from SOSIM which incorporated snowfall events and more accurately simulated the actual measured ablation at the site.

The generation of superimposed ice in the model may be more realistic at this relatively flat site. The AWS surface height measurements show a definitive change in melt rate once the surface lowers to 50 cm. This change may be indicative of the shift from a snow surface to an ice surface. Since the modeled surface height reached this point earlier, it predicted an earlier exposure of the superimposed ice, and therefore did not allow ample time to completely grow the 50 cm ice layer that the measurements suggest formed. 111

Summary of SOSIM Results The SOSIM model has a demonstrated skill at predicting surface height changes that better represent the actual surface than any other model tested, however little value is added to the simpler EBM when only water equivalent depths are considered. Accordingly, for applications where only the water equivalent melt is needed, the simpler EBM is recommended. When surface height reconstructions are preferred, or when the timing or depths of the superimposed ice or wetting front layers are needed, the SOSIM model offers significant advantages.

CONCLUSIONS SNTHERM, a comprehensive one-dimensional mass and energy balance model of the snowpack, was investigated as a potential snow-melt model for the lower Pâkitsoq ablation region in west-central Greenland. The results of SNTHERM were compared to those of a simpler, analytical snow and ice melt model and a simple statistical model. The analytical and statistical models had significantly fewer data requirements, were more appropriately formulated to perform over and melt underlying ice, and predicted the surface lowering at stations in the lower Pâkitsoq region to within a small fraction of the error found in the SNTHERM predictions. Therefore, the simpler analytical model, SOSIM, and the statistical PDD model were found to each offer advantages over SNTHERM. The popularity of the simple PDD model is certainly justified, but caution should be taken when applying this model to larger glaciers or over heterogeneous conditions. The assumptions made in the model do not apply in every case and must be well understood and tested before this model is applied. This new SOSIM model includes the necessary physics to simulate melt, but does not suffer from some of the weaknesses of SNTHERM. For example, rather than meltwater disappearing at the snow-ice interface, it will pool and refreeze, forming superimposed ice. This phenomena is regularly observed in the Pâkitsoq ablation region and may play an important role in the timing and rate of ice melt. 112

Repeat laser altimetry is utilized over Greenland to assess the present mass balance of the ice sheet (e.g. Krabill et al., 2000). Measurements of elevation change, however, are related to accumulation in complex ways. The elevation change at a point is the sum of the change in local ice-equivalent-thickness (total mass of ice occupying a unit area of bedrock divided by the density of pore-free ice), the change in vertical separation between the surface and the 4-MPa pressure level overburden (deep enough to lie within incompressible ice), and any changes in the elevation of the bedrock at that point due to subsidence or isostatic rebound. Since the divergence of the ice flow field is not known, longer-term (over which this affect may contribute significantly) changes in elevation cannot be evaluated and we must assume this component to be negligible in evaluating shorter-term changes. Roe (2002) demonstrates, however, that ice dynamics are extremely effective at diffusing local accumulation rate variability. Since the SOSIM model is able to reproduce meltwater production and penetration as well as surface height changes, it may provide a useful tool in evaluating future mass balance measurement missions such as the repeat laser altimetry. Additionally, it may be applied to the ice sheet as a whole to provide estimates of melt intensity to couple with melt extent measurements from passive microwave remote sensing.

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VI. SUMMARY AND FUTURE WORK

The work presented here applies and assesses recent methods for studying the constantly changing distribution of ice on Earth. Three studies were performed. The first study uses satellite remote sensing and aerial photography to document the changing extent of the tropical Quelccaya Ice Cap from 1962, when the earliest images captured the complete extent of the ice cap, to 2001, when the most recent cloud-free and snow-free satellite image was captured. The second study here used in situ observations of surface height changes from snow pits, snow stakes, and autonomous instrument stations to determine the mass balance along an elevation profile on the Greenland Ice Sheet from the west-central coast up to the summit. This profile represents the longest such elevation profile currently in existence, and provides a base from the period 1995 to 2005 with which to compare future profiles. It is expected that this profile will steepen in the future as more accumulation is predicted at higher elevations and more ablation is expected along the coast. Finally, this dissertation takes a critical look at melt modeling on the Greenland Ice Sheet. Several models were assessed, including the statistical Positive Degree-Day (PDD) model, a numerical model called SNTHERM, and a new analytical model, SOSIM, developed as part of this research. The assumptions of the PDD model were tested and found to be tenuous at best, despite the popularity of the model and its overall performance in the study area. SNTHERM was unable to adequately model snow melt over a cold ice surface, so a third model was developed. The new model, SOSIM, performed better than the other models tested, but its heavier data requirements limit its utility and in many cases the simpler PDD model would suffice. Future versions of SOSIM may include some of the missing heat transfer functions and 114

be distributed over the surface, allowing melt water to move across the surface as well. Such a model could be coupled with a mesoscale atmospheric model, like the Polar MM5 model, to make melt predictions on the ice sheet. Additional work will always be required as our understanding of the dynamics of these ice bodies and their interrelation to Earth’s climate is constantly evolving. One obvious extension to the Quelccaya work is to continue searching for a more recent satellite image to confirm whether the recent pattern of retreat has continued to accelerate as is suggested by field observations. This history of glacier advance and retreat could be better set in a detailed record of climate. Future studies of the ice cap should include detailed measurements of the local meteorology and changes in surface height across the ice cap. Such measurements pose serious logistical challenges in this area and have heretofore been unsuccessful. Daily thunderstorms during the wet season provide lightning hazards to metal towers situated high above tree-line, near the summit of one of the world’s tallest peaks. Locals may dismantle the towers for the metal. Furthermore, the massive mass balance amplitude on the ice cap poses additional challenges of keeping the tower above the snow in the wet season, and still relatively close to the surface in the dry season. These challenges cannot be ignored, yet many feel that collecting these data is essential. Studies of the Greenland Ice Sheet are on the front-burner of many NASA scientists and other international glaciologists, especially since its recent dynamic responses to secular warming have exceeded predictions. Recent ice core studies have also uncovered evidence of past changes on the ice sheet that were abrupt and monumental. These two factors have drawn much attention to this ice cap which has a sea-level potential large enough to displace 10% of the Earth’s population. Future studies of the northern ice sheet must include a wide array of remotely-sensed and in situ data, as well as modeling efforts. Two promising methods include gravimetric measurements made using the GRACE satellites, and mass-balance profiles made from continuous field monitoring.

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Overall, the present state of rapid climate changes provides an exciting backdrop on which to study the Earth’s changing cryosphere, and it is an especially exciting time to study the interactions between climate and ice.

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BIOGRAPHICAL SKETCH EDUCATION 2005-2007

Ph.D., Department of Geography, Florida State University

2000 - 2004

Ph.D. Candidate, Department of Geography, University of Colorado

1998 - 2000

M.S., Atmospheric Sciences, Ohio State University

1993 - 1998

B.S., Geography, University of Florida

PUBLICATIONS Albert, T.H., Evaluation of remote sensing techniques for ice-area classification applied to the tropical Quelccaya Ice Cap, Peru, Polar Geography, 26 (3), 210-226, 2002. REPORTS Albert, T.H., Measuring and modeling surface height changes on the Greenland ice sheet: Pâkitsoq ablation zone, west-central Greenland, pp. 37, University of Colorado, Boulder, Colorado, 2004. Steffen, K., N. Cullen, R. Huff, S. Starkweather, T.H. Albert, and M. McAllister, Variability and forcing of climate parameters on the Greenland Ice Sheet: Greenland Climate Network (GC Net), pp. 30, University of Colorado, Boulder, 2004 Steffen, K., N. Cullen, R. Huff, S. Starkweather, and T.H. Albert, Variability and forcing of climate parameters on the Greenland ice sheet: Greenland Climate Network (GC-Net), pp. 29, University of Colorado, Boulder, 2003.

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Albert, T.H., A high-resolution ablation study near Illulisat (Jakobshavn) on the Greenland Ice Sheet, pp. 10, University of Colorado, Boulder, Colorado, 2002. Steffen, K., J.E. Box, N. Cullen, and T.H. Albert, Variability and forcing of climate parameters on the Greenland Ice Sheet: Greenland Climate Network (GC Net), pp. 22, University of Colorado, Boulder, 2002. Steffen, K., J.E. Box, N. Cullen, and T.H. Albert, Greenland ice sheet climatology and surface energy balance modeling: Greenland climate network (GC-Net), pp. 24, University of Colorado, Boulder, 2002. Albert, T.H., Investigations of the recent changes on the tropical Quelccaya Ice Cap, Peru, Masters thesis, Ohio State University, Columbus, Ohio, 2000. GRANTS AND AWARDS 2002 - 2003

CIRES Innovative Research Grant, Co-Principle Investigator, University of Colorado, $26,000

2001 - 2004

NASA Graduate Research Fellowship, Principle Investigator, University of Colorado, $70,000

1999 - 2000

Dean's Small Grant, Ohio State University, $1,000

1998 - 1999

PEGS Scholarship, Ohio State University, $4,000

PROFESSIONAL APPOINTMENTS 2004 - 2007

Adjunct Instructor, Tallahassee Community College

2004 -

GLIMS (Global Land Ice Measurements from Space) Steward, Quelccaya ice cap, Peru

2004 - 2007

Lead Teacher and Science Coordinator, Cornerstone Learning Community, Tallahassee, Florida

2001 - 2004

Graduate Research Assistant, University of Colorado

2001 - 2003

Lab and Recitation Instructor, University of Colorado

2002 - 2003

Tutor, University of Colorado, Boulder, Colorado

1999 - 2000

Research Assistant, Ohio State University 143

1998 - 2000

Lab and Recitation Instructor, Ohio State University

1997 - 1998

Research Assistant, University of Florida

1996 - 1997

Tutor, University of Florida

144