ESS 431 Principles of Glaciology ESS 505 The Cryosphere

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1 MID-TERM November 9, 2015 ESS 431 Principles of Glaciology ESS 505 The Cryosphere Instructions: Please answer the following 5 questions. [The actual 5 questions will be selected from these 12 questions below, or some minor variants of these questions.] Each question has equal value of 10 points. The numbers [in square braces] with each sub-question indicate the points available for that sub-question. This is a closed-book test; however, you are free to use a calculator. To facilitate grading, please start each question on a new piece of paper, and write your name on each page. You have 1 hour and 20 minutes (1:30-2:50). 1. Terminology Give short concise definitions of the following 10 terms. [There may be different terms on the actual test.] constitutive relation thermal conductivity rime ice nucleus firn accumulation area ratio equilibrium line destructive metamorphism depth hoar sastrugi 2. The Cryosphere The cryosphere is composed of ice stored in a variety of reservoirs and forms. Some components may be more responsive to short-lived excursions in seasonal weather patterns than others. (a) Suppose that the event is 5 successive unusually cold and wet winters. [1] Identify a component of the cryosphere that you would expect to change significantly in response to this excursion event. [3] Describe how this cryospheric component would change, and why. Describe how this change in the cryosphere might in turn affect the long-term weather, or the climate. [1] Identify a component of the cryosphere that would not change significantly in response to the above event. Why not? (b) Suppose that the event is 5 successive unusually warm, sunny spring seasons. 1

2 [1] Identify a component of the cryosphere that you would expect to change significantly in response to this excursion event. [3] Describe how this cryospheric component would change, and why. Describe how this change in the cryosphere might in turn affect the long-term weather, or the climate. [1] Identify a component of the cryosphere that would not change significantly in response to the above event. Why not? 3. Physics of the phase diagram Explain in physical terms (related to molecular and crystal structure, and hydrogen bonds) why: (a) [3] Increasing pressure in water decreases the melting point temperature. (b) [3] Increasing curvature of ice surfaces decreases the melting temperature. (c) [4] Water is most dense at 4 o C rather than at 0 o C. 4. Ice in clouds (a) [5] Describe the primary differences in characteristics and relative abundances of cloud condensation nuclei (CCN) and ice-forming nuclei (IN). (b) [5] In a cloud at a temperature of -15 C, explain how the difference in abundance of CCN and IN allows rapid growth of ice crystals to sizes large enough to precipitate. 5. Avalanches Three skiers have arrived at the top of a slope and they are trying to decide whether to ski it. They have dug a snow pit and found a weak layer of buried surface hoar ~1 m below the surface. They have measured the average density of the snow slab above the weak layer (ρ=150 kg m -3 ), the slope angle (θ=38 degrees) and calculated the average down-slope shear stress at the base of the weak layer (ρ g H cos(θ) sin(θ)=750 Pa). They have also used a shear frame to measure the shear strength of the weak layer. They find that it fails at 950 Pa. (a) [6] Give reasons to support why they should or should not ski the slope. (b) [4] Are there more tests that would help in their decision-making? 6. Deformation of Glacier Ice (a) [4] Describe how the structure of ice crystals (atomic arrangement and bonding) allows ice to flow when a stress is applied. (b) [3] Why do imperfect ice crystals deform more easily than perfect crystals? (c) [3] Why is colder ice harder to deform than warmer ice? 7. Advance and Retreat of Glaciers on Mt. Baker Six major glaciers on Mt. Baker, WA, including Easton Glacier, shown below, receded until the early 1950 s, then advanced by several hundred meters from the 1960s through the early 1980 s. The glaciers have subsequently retreated (from Harper, 1993, Arctic and Alpine Research). The 2

3 accompanying figures show average monthly winter precipitation and average summer temperature at Sedro Woolley, in the Skagit Valley near Mt Baker. The red curves are running 8-year means. (a) [4] Explain why the advance and retreat pattern fits scientific expectations. Be sure to discuss the assumptions behind those expectations. (b) [3] Estimate the net ablation rate at the terminus of Easton Glacier, based on its response to climate changes. (c) [3] Do you expect Easton Glacier to advance again soon? Why or why not? 8. Glacier Flow The shear stress at the base of a glacier generally falls in a fairly narrow range near 1 bar (10 5 Pa), with variations of typically less than a factor of 2. Glacier speeds, on the other hand, span a relatively wide range, from 10 0 to 10 3 meters per year. (a) [6] What are the physical causes for these two behaviors? 3

4 (b) [4] Why are their percentage ranges of variation so dramatically different? 9. Deformation in a Glacier We select a coordinate system on a glacier with the x axis running down-slope along the surface, and the z axis pointing downward and normal to the glacier surface. The shear strain rate ε! xz in a glacier (force directed in the x direction, on planes whose normal vector points in the z direction) is related to the shear stress τ by the relation (Glen s Flow Law) 1 du n n! ε xz = = Aτ = A[( ρ g z sin( θ )], 2 dz where z is depth below the surface, u(z) is horizontal velocity, ρ is ice density, g is acceleration due to gravity, and θ ~4 o is surface slope of the glacier. The softness parameter A in Glen s Flow Law for ice near 0 o C is A ~ Pa -3 a -1, for n=3. The glacier is 200 m thick. Fifty years ago, an unfortunate mountain goat of a rare sub-species that stood 1 meter tall at the shoulder fell into a crevasse in the glacier and was buried upright in a standing position. The Burke Museum is interested in recovering this rare specimen; however, the curator is concerned that the specimen may have been distorted too much by shear flow. The goat s depth of burial in the glacier probably varied over the 50-year interval; however, to make calculations simpler, you can assume that it was buried for the entire 50 years at its average depth. (a) [3] Calculate the current height of this specimen at the shoulder (i.e. distance from hoof to shoulder), if its average depth of burial over the 50-year period was 10 m. (You can estimate this by following the change in separation over time for 2 points (e.g. hoof and shoulder) that were originally on a vertical line, and separated by 1 meter.) Show your work, and list and explain your assumptions. (b) [2] Calculate the current height of this specimen (i.e. distance from hoof to shoulder), if it was buried on average at a depth of 100 m. (c) [2] Is the specimen museum-worthy after this time? Why or why not? (d) [3] If the goat was on average 10 meters below the surface, how far has it moved from the location where it fell into the crevasse? (Be sure to mention your assumptions about basal sliding.) 10. Glacier Surge (a) [3] Describe how a surge-type glacier changes through a complete surge cycle. Include changes to the glacier profile and the timing of those changes. (b) [2] Does the fast flow in a surge result from sliding or from internal deformation? Briefly outline 2 lines of evidence to support your answer. (c) [3] The surge of Variegated Glacier stopped on July 4. Why do surging glaciers tend to pick up speed slowly, but stop abruptly? Be sure to consider the basal water system. (d) [2] How does the tidewater glacier cycle differ from the surging-glacier cycle? 4

5 11. Glacier Flow (a) [2] Explain the difference between velocity vectors and flowlines. (b) [2] Sketch the flow pattern on the surface of a simple (no tributaries) steady-state glacier, by making a map outline and using flow vectors (use at least 12 vectors spread over the glacier surface) to represent the flow direction and relative speed at different points on the surface. Your map should show: How the along-valley component of the flow changes along the glacier and from margin to center-line. How the cross-valley flow component differs in the accumulation area compared to the ablation area. (c) [2] Make sketches showing vertical cross-sections across the glacier in the accumulation area and in the ablation area, paying particular attention to how the shapes of the glacier surface differ in the 2 regions. Add flow vectors showing the directions and relative magnitudes of ice flow in the plane of your cross sections. (d) [2] Make a sketch showing a vertical cross-section along the center line of the glacier from the headwall to the terminus. Use vectors to show how ice-flow velocity varies with distance and depth in this section where the speed is maximim. (e) [2] Explain these patterns in terms of accumulation, ablation, ice flux and/or frictional drag. 12. Glacier sliding We identified two mechanisms that allow a glacier to slide over its bed. (a) [4] What are these two mechanisms and what physical process allows sliding in each case? (b) [2] Which sliding mechanism is more efficient for small bed obstacles? Why? (c) [2] Which sliding mechanism is more efficient for large bed obstacles? Why? (d) [2] What assumptions are built into this sliding theory? 5