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Modeling glacier-rock-climate interactions: Moraine deposition, stagnation events, and supraglacial debris

ProQuest Dissertations and Theses, 2009
Dissertation
Author: David A Vacco
Abstract:
New, quantitative information on past climates can be extracted from observations of glacial deposits through joint interpretation using a new glacier-flow model that simulates debris transport and deposition. Locations of moraine sets in some northern-hemisphere locations including Greenland and North America are consistent with the hypothesis that temperature anomalies associated with millennial cold events occurred primarily in wintertime. Extensive forward simulations show that glacier stagnation is more likely for larger and faster warming, suggesting that glacial deposits can be used to learn the amplitude of abrupt-warming events. Additional data will be required on supraglacial-debris effects before such temperature-change reconstructions are quantitatively accurate for heavily debris-laden glaciers, but existing understanding is sufficient to show that well-defined moraine ridges lacking extensive, homogeneous, hummocky deposits just upglacier represent climatically significant events and not landslide-triggered advances. The first chapter of this work involves the coupling of a dynamic glacier model with a dynamic subglacial sediment package, allowing sediment to be deposited sub- and pro-glacially. The result is a numerical glacier model that deposits moraines based on its terminus position. Experiments were run, varying the climate forcing on the glacier, to observe the resulting moraines and compare them to moraine sets observed in nature. Successful simulation of moraine sets in Greenland driven by ice-core climate records required notable damping of the millennial signal, as required by the hypothesis that millennial temperature fluctuations occurred primarily in wintertime. The second chapter involves testing of the hypothesis that, if the influence of valley hypsometry is controlled for, stagnation of terminal regions of a glacier require warming larger and faster than some threshold, although with some tradeoff between rate and size of warming. Quantitative modeling experiments were run using simplified valley shapes, in order to isolate a cause and effect relationship between hypsometry, climate change, and glacial stagnation. Stagnation was found to be more likely for rougher beds with lower mean slopes, as well as for larger and faster warmings. The results indicate that it may be possible to quantify ancient climate changes based on observations of glacial stagnation deposits. The third chapter expands on the study of glacier stagnation, to include transport of supraglacial debris and its thermal shielding effects on glacial melting. Modern observations and process understanding show that extensive supraglacial debris favors stagnation. The ice-flow model from the first two chapters was expanded to include "point" sources (landslides) and distributed sources of supraglacial debris, transport of the debris, and the thermal effects of the debris. The results show that landslide deposits sufficient to cause notable glacier advance cause stagnation events while remaining widely distributed on the glacier surface, thus producing hummocky topography upglacier of any moraine, such that a single moraine ridge formed without such hummocky deposits represents a climatic event rather than a landslide. Model runs show that if sufficient supraglacial debris is supplied from distributed sources, the glacier will be longer and more-likely to experience stagnation following warming than an equivalent clean glacier. A rich range of behavior is simulated, with sensitivity to some parameters that are not yet well-constrained by field glaciology. Quantitative estimation of the size and rate of warming responsible for the observed pattern of stagnation deposits, or lack thereof, in glaciated valleys in a region remains a realistic possibility, but will require improved understanding of debris dynamics.

TABLE OF CONTENTS

List of Figures...................................................................................................................vii Acknowledgements.............................................................................................................x CHAPTER 1. Modeling dependence of moraine deposition on climate history: the effect of seasonality......................................................................................................................1 1.0 Abstract.....................................................................................................................1 1.1 Introduction...............................................................................................................1 1.2 Model Description....................................................................................................3 1.2.1 Ice Model..........................................................................................................3 1.2.2 Sediment Model................................................................................................4 1.2.3 Sediment Source...............................................................................................5 1.2.4 Subglacial Sediment Transport by Water.........................................................5 1.2.5 Glacial Bulldozing............................................................................................5 1.2.6 Sediment Sink....................................................................................................5 1.3 The Climate Forcing................................................................................................6 1.4 Results and Discussion............................................................................................8 1.5 Conclusions and future work..................................................................................12 1.6 Acknowledgements.................................................................................................13 1.1.7 References............................................................................................................14 CHAPTER 2. Numerical modeling of valley glacier stagnation: toward a new paleoclimatic indicator......................................................................................................17 Abstract.........................................................................................................................17 Introduction...................................................................................................................17 Background...................................................................................................................18 Conceptual Model.........................................................................................................19 Model Description........................................................................................................22 Shallow-Ice approximation.......................................................................................23 Climate parameterization..........................................................................................23 Experiment Design........................................................................................................24 Results...........................................................................................................................26 Response to Instantaneous Warming (ELA Rise)....................................................26 Stagnation as a function of warming rate.................................................................30 Discussion and Implications.........................................................................................33 Topographic Control.................................................................................................33 Stagnation as a climate proxy...................................................................................33 Limitations of our assumptions.................................................................................33 Conclusions and Future Work......................................................................................35 Acknowledgements.......................................................................................................36 References.....................................................................................................................36 CHAPTER 3. Modeling Supra-Glacial Debris.................................................................39 3.0 Introduction.............................................................................................................39

vi 3.1 In prep, to be submitted to Geophysical Research Letters: Effect of Rock Avalanches and Supraglacial Debris on Glaciers.........................................................39 3.1.0. Abstract...........................................................................................................39 3.1.1. Introduction.....................................................................................................39 3.1.2. Thermal influence of supraglacial debris........................................................40 3.1.3. Supraglacial debris model...............................................................................41 3.1.4. Experiment Description..................................................................................42 3.1.5. Experiment results, avalanche effects on glacial dynamics............................44 3.1.6. Discussion.......................................................................................................49 3.1.7. References.......................................................................................................51 3.2 Additional Modeling Experiments of Supraglacial Debris on Glaciers.................53 3.2.1 Introduction......................................................................................................53 3.2.2 Debris source: englacial sediment...................................................................53 3.2.3 Supraglacial debris equation in one-dimension..............................................53 3.2.4 Experiment description, englacial debris source.............................................54 3.2.5 Experiment results and discussion, englacial sediment source........................54 3.2.6 Discussion of results........................................................................................65 3.2.6 References........................................................................................................67 3.3 Conclusions, and Future Work...............................................................................68

vii LIST OF FIGURES Figure page

1.1 GISP2 time series, filtered…………………………………………. 7 1.2 moraine results, ∆t = 15 o C ………………………………………… 9 1.3 moraine results, ∆t = 3.0 o C ……………………………………….. 11

2.1 stagnation cartoon …………………………………………………. 21 2.2 model domain set up ………………………………………………. 25 2.3 contour plot, number of stagnated cases …………………………… 27 2.4 histograms of cases that stagnated ………………………………… 28 2.5 stagnation length over bed slope ………………………………….. 29 2.6 stagnation length contours ……………………………………….. 30 2.7 stagnation length over warming rate ………………………………. 32

3.1.1 experiment initial conditions, avalanche ………………………… 43 3.1.2 Franz Josef experiment, bed elevation set up ……………………. 44 3.1.3 ice thickness snapshots …………………………………………… 45 3.1.4 ice velocity snapshots ……………………………………………. 46 3.1.5 supraglacial debris snapshots ……………………………………. 47 3.1.6 stagnation length over avalanche thickness ……………………… 48 3.1.7 Franz Josef experiment supraglacial debris snapshots …………… 49

3.2.1 ice thickness snapshots, clean ice …………………………………. 55 3.2.2 ice velocity snapshots, clean ice …………………………………… 56 3.2.3 ice thickness snapshots, c = 1.5 kg/m 3 ……………………………. 57 3.2.4 ice velocity snapshots, c = 1.5 kg/m 3 …………………………….. 58 3.2.5 supraglacial debris snapshots, c = 1.5 kg/m 3 ……………………… 59 3.2.6 ice thickness snapshots, c = 4.0 kg/m 3 ……………………………. 60 3.2.7 ice velocity snapshots, c = 4.0 kg/m 3 …………………………….. 61 3.2.8 supraglacial debris snapshots, c = 4.0 kg/m 3 ……………………... 62 3.2.9 steady ice profiles over debris concentration ……………………… 63 3.2.10 supraglacial debris steady distribution over debris concentration... 64 3.2.11 stagnation length over debris concentration ……………………... 65

viii PREFACE

The three chapters of this dissertation are quantitative studies of glacier-climate interactions, already published or to be published in the scientific literature. My modeling experiments are all designed such that the output represents sediments, or sediment locations, that can be compared to observations of natural glacial valleys. The effort of my doctoral research has been to link numerical modeling and field observations, specifically by using controlled numerical experiments to help interpret field data. The results of my dissertation are that we can use field measurements to make quantitative interpretations about climate history, as constrained by my modeling experiments. The ultimate goal, still far in the future, is a valley glacier model containing a complete description of glacial sediment dynamics, such that the model can be used to informally invert observed glacial deposits for the climate forcing that created them. Chapter 1 , the modeling of moraine deposition, is published in the tribute to G.S. Boulton special issue of Quaternary Science Reviews. Committee member David Pollard had previously developed an ice sheet model that included dynamic subglacial sediment transport and deposition. For the study of Chapter 1, I modified Dave’s model to represent valley glaciers, and added processes that allowed the glacier model to deposit moraines. The purpose of this study was to experiment on how varying climate forcings lead to different moraine patterns. I, David Vacco, am the first author of the QSR paper of Chapter 1. My work was to develop the glacier model, including developing a novel, quantitative law for moraine deposition, run the experiments, and author the manuscript for publication. Richard Alley, second author of the manuscript, contributed the main hypothesis tested by the paper, ideas and guidance for my research, and intensive help with editing the manuscript for publication. David Pollard, third author of the manuscript, contributed his formulation of a glacier model based on the shallow ice approximation glacier model with a coupled ability to simulate subglacial-sediment, helped me with debugging my code, provided intensive help and mentoring through my numerical modeling experiments, and contributed edits and comments to the manuscript for publication. Chapter 2 involved quantification of the dependence of glacial stagnation on the bumpiness of the subglacial bed. The experiments found that the observed length of stagnation (along glacial flow) is correlated to the magnitude and rate of warming that triggered glacial retreat. This study concluded that we might be able to use observations of glacial stagnation deposits to determine the magnitude and rate of the corresponding climate change. I am the first author of the manuscript for Chapter 2, which has been submitted and accepted for publication by Quaternary Research, pending editorial approval of revisions. I authored the numerical model code, ran the experiments, and wrote the manuscript. Richard Alley, second author of the manuscript, contributed guidance with the hypothesis testing, conception of the experiments, and intensive help with authoring the manuscript. David Pollard, third author, contributed his formulation for the shallow ice approximation model, and much guidance to me with quantitative hypothesis testing. Chapter 3 was the study of how supraglacial debris affects glacial stagnation. Surprisingly, we have found no previous modeling experiments assessing the ice- dynamical effects of the insulating influence of supraglacial debris on glaciers. The

ix quantitative relationship between debris cover and melt reduction is well known, however. For this study, I implemented a new treatment of supgraglacial debris and coupled it to my shallow-ice glacier model. The experiments indicated that debris cover plays a very strong role in glacial stagnation. I am first author of the work of Chapter 3, including the manuscript to be submitted for publication. I authored the model involving dynamic ice and supraglacial sediment, the coupling, and numerical modeling experiments. Richard Alley, second author of the manuscript, provided me with guidance through my hypothesis testing, and significant help with authoring of the paper. David Pollard, third author, provided me with guidance toward authoring of the model and debugging help, and comments and edits of the manuscript for publication.

x ACKNOWLEDGEMENTS

Thanks to Richard Alley for mentoring, advising, ideas, and guiding my scientific development. Thanks to Dave Pollard for teaching my how to model glacier dynamics, and frequent help with debugging. Thank you to my doctoral committee, including Richard Alley, Dave Pollard, Sridhar Anandakrishnan, Rudy Slingerland, and Derek Elsworth, for comments and questions that improved this dissertation. Thanks to Patrick Applegate, Byron Parizek, Todd Dupont, and many others for discussions that helped me along. Thanks to my Parents and brother for hanging in with me over a 13-year career as a student. Thanks to my friends for being there.

1 CHAPTER 1. MODELING DEPENDENCE OF MORAINE DEPOSITION ON CLIMATE HISTORY: THE EFFECT OF SEASONALITY

David A. Vacco, corresponding author, dvacco@geosc.psu.edu Richard B. Alley David Pollard

Published in Quaternary Science Review: Received 26 September 2007; Accepted 4 April 2008. Available online 12 November 2008.

David A. Vacco, Richard B. Alley, and David Pollard, in press, Modeling dependence of moraine deposition on climate history: the effect of seasonality. Quaternary Science Reviews (2008), doi:10.1016/j.quascirev.2008.04.018

1.0 Abstract A simple shallow-ice flowline glacier model coupled to a model of sediment transport and deposition is used to simulate formation and preservation of moraines. The number, positions, and volumes of moraines formed all are sensitive to the climate history assumed. We drive the model with the GISP2 central-Greenland temperature record, and with reduced-millennial-amplitude versions of that record, to test the hypothesis that the Younger Dryas and other millennial oscillations were primarily wintertime events and thus had less influence on glacier behavior than did the Last Glacial Maximum with its strong summertime as well as wintertime signal. We find that the reduced-amplitude Younger Dryas provides a better match to observed moraines.

1.1 Introduction Glaciers are sensitive to climate (e.g., Oerlemans, 1994). Although ice-dynamical events such as surges (e.g., Kamb et al., 1985) do occur, averaging over several surge cycles or over several glaciers should remove non-climatic effects. Then, glacier extent is primarily controlled by climate. In the simplest interpretation, glacier fluctuations are driven primarily by changes in summertime temperatures (e.g., Oerlemans, 2001; Denton et al., 2005). For an initially steady glacier on which snow accumulation is balanced by melting, a 1 o C temperature rise increases meltwater loss about 35% but increases saturation vapor pressure (hence precipitation, all else being equal) by only about 7%.

2 However, glaciers undoubtedly are influenced by numerous climatic factors, and fluctuations in glaciers can result from changing snow accumulation or other forcings, especially if temperature does not change at the same time. Thus, using glacier-length records solely as summer-temperature records will at least occasionally lead to errors. We thus wish to be able to test hypotheses for changes in glaciers, and to conduct formal inversions to learn what forcings are consistent with an observed glacier-length change. Although historical changes in glaciers are of great interest, proxy evidence is all we have available for most time periods, with ages of moraines especially important. These ice- marginal deposits are classically interpreted to represent near still-stands of the glacier margin, either during retreat or when advance switched to retreat, allowing sediment deposits to build up at the toe of a glacier (Sugden and John, 1976). The sediment that composes glacial moraines is transported to the toe by various processes, including subglacial water transport, subglacial till deformation, glacial bulldozing of pro-glacial sediments, and melt-out of material carried in or on the ice, with subglacial stream transport and till deformation especially important (e.g., Boulton and Jones, 1979; Boulton and Hindmarsh, 1987; Hart and Boulton, 1991; Alley et al., 1997). Because of lags in ice-flow, sediment transport, etc., times of moraine formation and volumes of sediment deposited are not simple functions of climate (e.g., Oerlemans, 2001). Thus, complete testing of hypotheses regarding climatic change in glaciated regions can be improved by driving a moraine-depositing glacier model with the suggested climate history, and comparing modeled and observed moraines. Furthermore, if the model is computationally efficient, inversions or other optimizations can be conducted to help generate hypotheses. To this end, we have coupled a numerical glacier model based on the shallow-ice approximation to a subglacial-sediment transport model. We have incorporated the ability to vary the relative importance of different sediment-transport mechanisms. The climate forcing, glacial domain length, elevation, and shape can all be prescribed within the ranges observed in nature, giving this model the flexibility to simulate important aspects of a great range of natural glacial settings, from large ice sheets to small alpine glaciers. Here we describe the model, and then use it to address the Denton et al. (2005) hypothesis of changing seasonality associated with the Younger Dryas event. Denton et al. (2005) noted that in the well-calibrated central-Greenland ice-core records, during the Younger Dryas mean annual temperatures cooled most of the way to last glacial maximum (LGM) values after a long warming trend. However, in many moraine records and other climate records especially from Greenland and northwestern Europe, the Younger Dryas was much warmer than the LGM and not much colder than the Little Ice Age; in these locations, the Younger Dryas moraines are located not nearly as far downstream as LGM moraines, but are closer to the Little Ice Age moraines. Denton et al. (2005) suggested that this disparity is best explained by extreme wintertime cold during the Younger Dryas, with summers then only slightly reduced in temperature, in comparison to cold temperatures year-round during the LGM. We show here that this hypothesis has implications not only for the relative positions of moraines, but also for numbers and volumes of late-glacial moraines. We have not yet attempted detailed hypothesis-testing for a single moraine set (which will require better calibration of the model to local conditions), but we find robust results

3 from the model that, when compared to available data, support the Denton et al. (2005) hypothesis. We note that use of information from suites of moraines partially offsets difficulties introduced by dating errors, which may be as large as the duration of a climate event of interest (e.g., Gosse et al., 1995, Ivy-Ochs et al., 1999, Licciardi et al., 2004, Rinterknecht et al., 2004, Benson et al., 2005, Schaefer et al., 2006).

1.2 Model Description 1.2.1 Ice Model The dynamic glacier model used for this study implements the shallow-ice approximation in one dimension (Hutter, 1983), following the approach of Schoof (2002, Chapter 2). The shallow-ice model is appropriate for a glacier if it satisfies the condition of small aspect ratio, ε: ε 2 << 1 (1.1)

where ε = [D]/ [L], with [D] the ice thickness scale, and [L] the ice length scale. If we apply scales typical of valley glaciers, [L] = O(10 km). The valley-glacier thickness scale can be calculated as [D] = O(300 m), from assumed steady-state with snowfall rate of O(1 m/yr) and Glen’s power-law creep with strain rate proportional to stress raised to the power n=3 [Paterson, 1994]. Then ε 2 ~ 0.02 << 1. This aspect ratio is sufficiently small that the shallow ice approximation is adequate for our purposes (Schoof, 2002). Applying the shallow ice scaling to the stress tensor yields the planar stress-strain relation where vertical shear is the only important stress to ice flow,

( ) z u z u A dx dH zsg n n xz ∂ ∂ ∂ ∂ =−= − − 1 1 1 1 ρτ , (1.2)

where x is the horizontal axis (perpendicular to gravity), z is the vertical axis, τ xz is the vertical shear stress, s is the ice surface elevation, A is the ice stiffness, taken as 6 x 10 -24

Pa -3 s -1 for temperate ice, H is the ice thickness, and u is the horizontal ice velocity. The mass conservation equation for ice gives us mass transfer over time,

( )txb x Q t D ,= ∂ ∂ + ∂ ∂ , (1.3A)

where D is glacier surface elevation, Q is the vertically integrated mass flux, and b(x,t) is the surface mass budget = snowfall rate – melt rate, in units of length/time (e.g., meters/yr). Once we apply the scaling argument that [D] << [L], we solve equation (1.2) for du/dz, vertically integrate twice to obtain the ice flux, and insert the result into equation 1.3A to obtain:

),(' 1 2 txb x D x D HA xt D n n +       ∂ ∂ ∂ ∂ ∂ ∂ = ∂ ∂ − + , (1.3B)

4 where A’ = A(ρg) n .

1.2.2 Sediment Model To this fairly standard ice-flow model, we couple a dynamic sediment-deformation model following the work of Clark and Pollard (1998), and ice-sediment coupling of Pollard and DeConto (2005). In regions of the domain where subglacial sediment is present, it deforms as a weakly non-linear dynamic sediment layer (Boulton and Hindmarsh, 1987), following the till measurements of Jenson et al. (1995, 1996). Our use of a weakly nonlinear relation may require additional comment. Under sufficiently high stress, applied for sufficiently long time, there is little doubt that till exhibits nearly plastic or frictional behavior (e.g., Iverson et al., 1998; Rathbun et al., in review). However, owing to dilation and perhaps other processes, strains of order 1 or less at stress below the ultimate strength of the material likely yield low-stress-exponent flow laws (Jenson et al., 1996; Rathbun et al., in review). Because of strong non- steadiness in the subglacial environment, the till may never experience strains in excess of order one under sufficiently steady conditions to reach the frictional/plastic behavior (Iverson et al., 1998; Alley, 2000). With these considerations, the stress-strain relation is written as

m sed m m dz du D pc 1 0 1 0 1 tan'               ++= − µφτ , (1.4)

where c is the sediment cohesion, p’ is effective pressure (overburden pressure minus pore-water pressure), φ is the sediment angle of internal friction, D 0 is the reference deformation rate, µ 0 is the viscosity, u sed is the horizontal sediment velocity, and m is the power law exponent, where m ~ 1.5 gives a weakly non-linear sediment. We use equation (1.4) to calculate the subglacial sediment flux via deformation, where τ is a boundary condition imparted on the bed from the ice above, and the sediment velocity at the ice- sediment interface is imparted to the ice flux in equation 1.3B. Equation 1.4 is solved for du/dz, and integrated vertically to obtain the mass flux. We use the result to solve for the dynamic sediment-mass continuity equation:

( ) sedwaterquarry z sed sed Q x Qdzu xdt dh d ∂ ∂ −+       ∂ ∂ −= ∫ 0 (1.5)

where u sed is the basal ice velocity due to sediment deformation, h sed is the sediment thickness, z d is the depth where sediment velocity is zero, Q quarry is the flux of sediment into the domain by glacier bed erosion (explained below), and Q sedwater is the flux of sediment transported by subglacial water (explained below). The resulting system of equations (1.3) – (1.5) is a coupled dynamic ice- and sediment-transport model that can be solved numerically.

5 1.2.3 Sediment Source Sediment enters into the domain via glacial erosion of the bed. Erosion rate is taken to be linearly proportional to the work done by the glacier on the bed,

bedbedquarryquarry uAQ τ = , (1.6)

where Q quarry is the quarrying rate in meters/yr, u bed is the glacial sliding velocity, τ bed is the shear stress exerted on the bed, and A quarry is the quarrying coefficient. A quarry is a parameter that was tuned to match observed quarrying, which often is on the order of mm/yr (Hallet et al., 1996).

1.2.4 Subglacial Sediment Transport by Water Although other mechanisms can be specified, sediment transport initially is modeled for deforming till and in water beneath the glacier. For transport in subglacial streams, we follow Alley et al. (1997), such that,

3 waterwatersedwater QAQ = , (1.7)

where Q sedwater is the mass flux of sediment due to subglacial water, Q water is the flux of subglacial water, and A water is the subglacial fluvial sediment coefficient, which can be calculated from general sediment-transport relations or tuned to a particular situation. Meltwater flux is dominated by surface melt, which we route immediately to the bed, so that Q water is the integrated up-valley surface melt. 1.2.5 Glacial Bulldozing In addition to the sediment transport mechanisms described above, we include sediment transport at the glacier toe by bulldozing. At every time-step in the model, we test for advance of the glacier terminus. In any time-step that the terminus advances, we instantaneously transport all sediment to the toe that was overrun by the recent advance. This mechanism allows advancing ice to “bulldoze” its moraines. In reality, this need not be an instantaneous process, but it can be spectacularly fast (Nolan et al., 1995).

1.2.6 Sediment Sink Glaciofluvial sediment transport is highly efficient in many or most glacial environments, removing most of the sediment from the system so that moraines represent only a small subset of the total glacial transport (e.g., Bell and Laine, 1985; Alley et al., 1997). Our modeling experiments show that, for geomorphically active glaciers, important ice-dynamical effects would be produced rapidly by sedimentation if all of the sediment were retained beneath or just in front of the glacier. For the model runs reported here, we introduced a sediment sink to account for the loss in proglacial streams. We specify instantaneous loss of 80% by volume of the sediment reaching the ice front. We obtain relatively large moraines, and even higher losses probably are appropriate for some glacial settings.

6

1.3 The Climate Forcing Denton et al. (2005) reviewed and extended evidence indicating that millennial- scale climate changes around the north Atlantic during the last ice age should be interpreted differently from the slower orbital-scale changes. In particular, Denton et al. (2005) argued that the millennial-scale oscillations primarily reflected changes in north Atlantic sea ice linked to oceanic and atmospheric circulation with dominant wintertime impacts (Alley, 2007), whereas the orbital-scale changes from Milankovitch forcing included associated Earth-system response with important greenhouse-gas concentration changes, yielding strong changes in summertime as well as wintertime. We thus separate millennial from orbital climate changes for use in our initial experiments, using a digital filter with a 10,000-year-frequency cutoff (Figure 1.1B). (We do not focus here on sub-millennial changes, such as result from El Nino, NAO, volcanic eruptions, etc., choosing to discard this high-frequency information for our initial experiments, Figure 1.1A.) The time schedule of climate changes is taken from the oxygen-isotopic history of the GISP2 ice core, central Greenland (Stuiver and Grootes, 2000). We reconstruct a temperature history with millennial and orbital amplitudes scaled independently. We specify sea-level temperature to give a selected amplitude between LGM and modern in the orbital band. We then add the millennial variations, scaled by an additional factor 0 ≤ α ≤ 1.

7

A.

B.

Figure 1.1. The GISP2 time series through the last deglaciation (Stuiver and Grootes, 2000, blue Dashed line, 1.1A), and smoothed with a 800 yr low pass filter (thick black line, 1.1A). The time-series was seperated into a deglacial signal (1.1B., blue line) using a 10,000 yr low pass filter, and the full signal including the millennial scale variability (1.1B, black line).

Years B.P.

Years B.P.

Fraction, warming LGM-to-Modern

Fraction, warming LGM -to-Modern

8

As discussed below, this additional scaling is suggested by the Denton et al. (2005) seasonality hypothesis. Once sea-level temperature is determined, the temperature at higher elevations is taken from the assumed lapse rate. Hence

Temp (t,z) = L (t) + α YD (t) – γ z, (1.8)

where t = time in kyr, z = meters above sea-level, L(t) is the deglaciation time series, YD(t) is the millennial time series, γ is the temperature lapse rate with elevation = 0.008 o C m -1 , and the strength of the millennial scale signal is controlled by a fraction 0 ≤ α ≤1. Decomposing the temperature record like this allows us to test the effect of weakening the millennial scale signal in GISP2 (termed “weakening the Younger Dryas” for convenience, where, for example, “Younger Dryas = 10 %” means α = 0.1). To calculate mass balance of the model glacier in a simple way from this time-series of millennial and orbital changes, the temperature cycle over a single year is assumed to be sinusoidal about the mean annual temperature with an amplitude of 13 o C. This assumption allows the annual amount of melt at the ice surface to be calculated using the positive degree-day parameterization (Van der Veen, 1999). For simplicity, the ice-equivalent snowfall rate was assumed to be 1.0 m/yr at sea- level. The modeled snowfall rate was allowed to vary with temperature as a function of saturation vapor pressure, where the snowfall rate was modeled to increase 7 % per o C of mean annual temperature increase. Clearly, hypotheses for mass-balance changes driven by dynamical changes in the atmosphere rather than by thermodynamic effects on saturation vapor pressure can be tested in this framework, but are beyond the current contribution.

1.4 Results and Discussion The model output is a plot of glacial till strata labeled by age of deposition (figure 1.2 – 1.3). The results show morphologic and stratigraphic relationships between the tills deposited by the GISP2-driven glacier model. The resulting moraines are correlated with advances in the modeled glacier caused by cold events in the GISP2 deglaciation record. When the temperature forcing includes the millennial-scale signal at full strength, and a 15 o C warming between typical glacial and interglacial conditions (Cuffey et al., 1995), the resulting moraines (figure 1.2A) correspond to the two cold events (24 kyr and 21 kyr) during the time often identified as the LGM, plus the Younger Dryas cold event (12.8 – 11.5 kyr). The Younger Dryas moraine is partially cored by sediments deposited during the pre-Bφlling or Heinrich Event 1 (H1) cold event, ~ 16 kyr. In this case the “Younger Dryas moraine” contains sediments that are older than the Younger Dryas cold event in GISP2. Cosmogenic dates on a moraine with a similar complicated sedimentary structure

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13 kyr,

Full document contains 80 pages
Abstract: New, quantitative information on past climates can be extracted from observations of glacial deposits through joint interpretation using a new glacier-flow model that simulates debris transport and deposition. Locations of moraine sets in some northern-hemisphere locations including Greenland and North America are consistent with the hypothesis that temperature anomalies associated with millennial cold events occurred primarily in wintertime. Extensive forward simulations show that glacier stagnation is more likely for larger and faster warming, suggesting that glacial deposits can be used to learn the amplitude of abrupt-warming events. Additional data will be required on supraglacial-debris effects before such temperature-change reconstructions are quantitatively accurate for heavily debris-laden glaciers, but existing understanding is sufficient to show that well-defined moraine ridges lacking extensive, homogeneous, hummocky deposits just upglacier represent climatically significant events and not landslide-triggered advances. The first chapter of this work involves the coupling of a dynamic glacier model with a dynamic subglacial sediment package, allowing sediment to be deposited sub- and pro-glacially. The result is a numerical glacier model that deposits moraines based on its terminus position. Experiments were run, varying the climate forcing on the glacier, to observe the resulting moraines and compare them to moraine sets observed in nature. Successful simulation of moraine sets in Greenland driven by ice-core climate records required notable damping of the millennial signal, as required by the hypothesis that millennial temperature fluctuations occurred primarily in wintertime. The second chapter involves testing of the hypothesis that, if the influence of valley hypsometry is controlled for, stagnation of terminal regions of a glacier require warming larger and faster than some threshold, although with some tradeoff between rate and size of warming. Quantitative modeling experiments were run using simplified valley shapes, in order to isolate a cause and effect relationship between hypsometry, climate change, and glacial stagnation. Stagnation was found to be more likely for rougher beds with lower mean slopes, as well as for larger and faster warmings. The results indicate that it may be possible to quantify ancient climate changes based on observations of glacial stagnation deposits. The third chapter expands on the study of glacier stagnation, to include transport of supraglacial debris and its thermal shielding effects on glacial melting. Modern observations and process understanding show that extensive supraglacial debris favors stagnation. The ice-flow model from the first two chapters was expanded to include "point" sources (landslides) and distributed sources of supraglacial debris, transport of the debris, and the thermal effects of the debris. The results show that landslide deposits sufficient to cause notable glacier advance cause stagnation events while remaining widely distributed on the glacier surface, thus producing hummocky topography upglacier of any moraine, such that a single moraine ridge formed without such hummocky deposits represents a climatic event rather than a landslide. Model runs show that if sufficient supraglacial debris is supplied from distributed sources, the glacier will be longer and more-likely to experience stagnation following warming than an equivalent clean glacier. A rich range of behavior is simulated, with sensitivity to some parameters that are not yet well-constrained by field glaciology. Quantitative estimation of the size and rate of warming responsible for the observed pattern of stagnation deposits, or lack thereof, in glaciated valleys in a region remains a realistic possibility, but will require improved understanding of debris dynamics.