Introduction 1 Chapter 1 Thesis Introduction Sea level rise. Tipping points. Global warming. Today, the field of glaciology is irrevocably linked to the study of climate change, from the ivory tower to the network news. However, beyond attempts to quantify ice melting rates and predictions of the lifespans of dwindling glaciers, many aspects of the fundamental physics underlying the deformation of glaciers are poorly understood. Computational modeling of the response of glaciers in Greenland and Antarctica to hydrologic forcing over a timescale shorter than one month is the focus of this thesis. The results presented here are almost completely based on computational modeling but the goal is to explain several field observations of outlet glaciers and ice streams in the published literature. The interaction between ocean tides and ice stream motion (chapters 2, 3, and 4) and the rapid drainage of supraglacial meltwater lakes are the two glacial processes on which this thesis focuses. The introductory section describes the Earth’s cryosphere, focusing on the current scientific interest in glacier dynamics. The next section outlines the classical treatment of ice dynamics—both for general ice masses and the specific case of ice streams. The introduction then summarizes the current understanding of the interaction between the ocean tides and outlet glaciers, specifically over timescales shorter than a month. The next section discusses observations of the tidal influence on outlet glaciers from Antarctica and Greenland. The penultimate introductory section is a brief synopsis of the Introduction 2 finite element modeling methods used throughout this thesis. Last is a short outline of the remainder of this thesis. 1.1 The Cryosphere The term cryosphere refers to all frozen water on planet Earth. While sea ice, river and lake ice, snow, and permafrost all belong to the cryosphere, glacial ice dominates the system. A glacier refers to any mass of crystalline ice that both persists over the course of an entire year and is large enough to flow under its own weight. The largest glaciers on the planet are the Antarctic and Greenland Ice Sheets, which together contain nearly 85% of all the freshwater on the planet (e.g., SMIC Report, 1971; L’vovich, 1979; IPCC, 1990; 1996; Van der Veen, 1999). In the past few decades, the specter of global climate change has driven a renewed interest in the cryosphere, focusing on the fact that water in the cryosphere, primarily in the Greenland and Antarctic Ice Sheets, is equivalent to about 65 meters of sea level equivalent height (e.g., Cuffey and Paterson, 2010; Lythe et al., 2001; Bamber et al., 2001; Meier et al., 2007; Dyurgerov and Meier, 2005). As highlighted by the International Panel on Climate Change’s (IPCC’s) Fourth Assessment Report (2007), the lack of understanding of the interaction between the cryosphere and hydrosphere (i.e., ice sheets and the ocean) is a key piece of missing information that limits the believability of forward, predictive climate modeling. Upwards of 60% of the ice leaving the Greenland Ice Sheet and upwards of 90% of the ice leaving the Antarctic Ice Sheet is carried through a limited number of fast moving outlet glaciers, thus understanding the dynamics of these outlet glaciers is critical to predicting future ice levels (e.g., Cuffey and Paterson, 2010; Morgan et al., 1982; Bauer, 1961; Rignot and Kanagaratnam, 2006). The focus of Introduction 3 the first two research chapters is the interaction of these outlet glaciers and the short-term ocean tides. We use Cuffey and Paterson (2010) as the reference for defining the characteristics of outlet glaciers. The technical definition of an outlet glacier is a fast- moving region of ice bounded by visible rock; an ice stream is a fast-moving region of ice bounded only by slower-moving ice. However following the convention of Cuffey and Paterson (2010), these terms are used interchangeably. The distinction between outlet glaciers and ice streams is generally too strict for practical use as many glaciers transition between ice-ice and ice-rock boundaries over their lengths. Note that while ice streams and outlet glaciers almost always flow into the ocean, the presence of a floating ice shelf or ice tongue is not a defining characteristic. Figure 1.1 shows the locations of all the ice streams discussed in this thesis. As mentioned earlier, the majority of ice leaving the Greenland and Antarctic Ice Sheets travels through outlet glaciers. Direct calving of icebergs and basal melt are two of the primary mechanisms for removal of ice mass (e.g., Jacobs et al, 1992; Vaughan and Doake, 1996; Reeh et al., 1999; Mote, 2003; Wild et al., 2003; Hanna et al., 2005; Box et al., 2006; Krinner et al., 2006; Rignot et al., 2008; Cuffey and Paterson, 2010). Calving occurs when fractures propagate through the ice thickness at the edge of a glacier, resulting in blocks of ice shearing off the main ice body. Usually these new icebergs are carried out to sea, where they eventually melt. Basal melting occurs due to frictional heating along the base of grounded ice, melting due to geothermal heat along the base (e.g., subglacial volcanism, such as in Iceland), and the melting of floating ice shelves due to warmer ocean water reaching the ice’s base. Introduction 4 Over long timescales, changes in the climate system can dramatically impact the response of ice streams to the conditions of the ocean. Increased melting, both on-land and at the grounding line due to higher ocean temperatures, reduces ice in the ice stream system and lubricates the ice stream’s base, further increasing flow speeds. The combination of increased flow speeds and increased basal melt can thin ice streams to the point that any attached ice shelf breaks up. Ice shelf breakup in turn causes increased ice stream speeds due to the removal of the buttressing stress of the ice shelf, as was observed in the 1995 breakup of the Larsen A Ice Shelf and the 2002 breakup of the Larsen B Ice Shelf in Antarctica (Rott et al., 2002; De Angelis and Skvarca, 2003; Rignot et al., 2004, Scambos et al., 2004). Thus, the long-term behavior (and future) of ice shelves is linked to the interaction, and potential feedback, between the cryosphere and the earth’s oceans. However, the loss of ice through outlet glaciers is not the only mechanism for removing mass from the Greenland and Antarctic Ice Sheets on yearly timescales. Surface melt accounts for about 40% of the ice lost from Greenland and about 10% of the ice lost from Antarctica each year (e.g., Box et al., 2006; Krinner et al., 2006; Cuffey and Paterson, 2010). While this mass loss alone is significant, there is evidence from Greenland that supraglacial meltwater, should it reach the glacier’s bed, can increase ice flow rates (e.g., Zwally et al., 2002; Joughin et al., 2008). The potential for such a feedback to cause a dramatic increase in the loss of ice mass with increasing temperatures (and thus melt rates) is not fully established, but modeling suggests that the effect can increase the mass-loss by upwards of a factor of two (Parizek and Alley, 2004). Introduction 5 Ultimately, while this thesis is not a direct study of the interaction of the cryosphere and the global climate system, that connection is the background motivation of this work. The hope is that the research presented here helps to elucidate some of the fundamentals of the response of ice to short timescale forcing. Understanding the hourly and daily dynamics of outlet glaciers requires more study. Through the investigation of tidal forcing of ice streams (chapters 2 to 4) and rapid drainage of supraglacial lakes (chapter 5), this thesis demonstrates some of the modeling concerns of processes that span the gap between very rapid (elastic) response on the order of days and more measured (viscous) response of ice streams on the order of years. The remainder of this introduction focuses on background information related to tidal forcing of ice streams, while the introductory material for the lake drainage problem is deferred to chapter 5 as that background material is unrelated to the remainder of this thesis. 1.2 Ice Stream Dynamics This section provides a brief summary of ice stream dynamics. Information is presented from the introductory textbooks on glaciology by Van der Veen (1999) and Cuffey and Paterson (2010). A discussion of the general deformation of ice sheets and other non- streaming glaciers illustrates the unique nature of ice stream behavior. A description of the general physics in the extreme cases of ice stream geometry follows. Consider a cross-sectional view of an ice sheet, as is shown in figure 1.2. The surface deformation at the location of a longitudinal cross section can be approximated by: = + (1.1) 푢�⃗ 푢�⃗푑 푢�⃗푏 Introduction 6 where the total velocity vector is the additive sum of the internal deformation and 푑 the basal sliding . 푢�⃗ 푢�⃗ 푏 In terms of푢�⃗ internal deformation, we assume that glacier flow is driven by the weight of the ice itself, where the basal driving stress for a vertical profile of the ice is: 푏 = sin( )휏 (1.2) 푏 푖 where is the ice density, is gravitational휏 휌 푔퐻 acceleration,훼 is the ice thickness, and is 푖 the surface휌 slope. Assuming푔 that ice deforms viscously over퐻 most timescales, that 훼 viscous deformation can be expressed using a canonical Glen-style flow law (Glen, 1955; 1958), and that glacier flow is laminar, we find that: 2 = ( ) (1.3) + 1 퐴퐷 푛 푢�⃗푑 휏푏 퐻 The value for the stress exponent n is traditionally푛 chosen to be equal to three based on laboratory stress-strain curves (e.g., Glen, 1955; 1958).