Unit 4: An Uplifting Story of Sea Level Change

Unit 4 Learning Outcomes

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GPS vertical motion shows glacial melting in Greenland. (https://www.youtube.com/watch?v=FVm3rZZs49s&list=PLzmugeDoplFOot41MIBBZiLYBCB0M-p1P)

Provenance: UNAVCO
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• Students will identify the relationship between ice mass loss and uplift using geodetic data from Helheim Glacier.
• Students will evaluate the relative importance of freshwater input vs. elastic rebound on modern regional sea level changes in Greenland.
• Students will recognize how modern landforms reflect past changes in sea level.
  
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  Supports Module Goals 1 and 2; Earth Science Big Ideas ESBI-1: Earth scientists use repeatable observations and testable ideas to understand and explain our planet, ESBI-3: Earth is a complex system of interacting rock, water, air, and life, ESBI-4: Earth is continuously changing, ESBI-9: Humans significantly alter Earth; and Climate Literacy Principles CLP-2: Climate is regulated by complex interactions among components of the Earth system, CLP-4: Climate varies over space and time through both natural and man-made processes, CLP-5: Our understanding of the climate system is improved through observations, theoretical studies, and modeling, CLP-8: Human activities are impacting the climate system. (links open in new windows)

Unit 4 Teaching Objectives

• Cognitive:
• Provide a framework, using bedrock GPS and ice elevation data from Helheim Glacier, with which to characterize the relationship between changes in ice mass and crustal deformation over short timescales.
• Promote an understanding of the relative contributions of freshwater input vs. elastic rebound on modern regional sea level changes in Greenland.
• Investigate geologic and archaeological evidence that supports past sea level changes of different spatial and temporal magnitudes than those observed in Greenland during the 21st century.
• Behavioral:
• Promote skills development in reading and interpreting decadal bedrock GPS time series data and understanding its relationship to changes in ice mass.
• Facilitate the quantification of contributions of isostatic rebound vs. ice discharge to regional sea level changes in southeast Greenland.
• Affective:
• Encourage reflection about the magnitude of past sea level changes and the influence of these sea level changes on landscape and archaeological features.
• Encourage reflection about the role of uncertainty in scientists' understanding of a complex system.

The content in Unit 4 is appropriate for introductory geology, oceanography, meteorology, and other geoscience courses; sophomore-level courses in which geodesy and/or climate studies are being introduced; or non-geoscience courses where climate studies and/or the nature and methods of science are being investigated. Unit 4 activities can easily be adapted to serve small- or large-enrollment classes and can be executed in lecture and lab settings as a series of interactive lecture activities, a lengthier in-class activity, a collaborative lab exercise, or as part of a two-week investigation of the use of geodesy to understand cryosphere and sea level changes using the entire Ice Mass and Sea Level Change module. In the Ice Mass and Sea Level Change module, this unit follows Unit 3: Warm with a chance of melting on spatial and temporal changes in Greenland ice mass using snowmelt, ice velocity, ice elevation, air temperature, and GRACE data and precedes Unit 5: Regional sea level changes—a tale of two cities on the potential societal impacts of sea level change. If the entire two-week module will not be utilized, we recommend pairing Unit 4 with Unit 3: Warm with a chance of melting to give students an opportunity to consider ice sheet behavior's influence on sea level and gain experience reading and interpreting GRACE time series.

Part 1:

Animation:
YouTube: Glaciers Are Retreating-How Can We Measure the Full Ice Loss? - English and Spanish closed captions are available in YouTube; click "Settings" icon and select the subtitle version of your choice
File: Measuring Changing Glaciers with GPS (MP4 Video 14.6MB Feb13 19)

Prior to the class meeting, students will complete a preparation exercise in which they watch the animation to get a conceptual understanding of:
(a) the relationship between uplift and ice mass change;
(b) how bedrock GPS is used to measure modern, elastic post-glacial rebound;
(c) the manifestation of seasonal and decadal changes in snow and ice mass in a bedrock GPS time series.

• Student version: Unit 4: Animation questions (student) (Microsoft Word 2007 (.docx) 307kB Feb25 19)
  Unit 4: Animation questions (student) PDF (Acrobat (PDF) 343kB Feb25 19)
• Instructor version:
  Unit 4: Animation questions (instructor) -- private instructor-only file
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  Unit 4: Animation questions (instructor)

  
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Part 2:

During class, students will complete an in-class exercise (depending on class size and format, this could be implemented as a small-group activity with periodic breaks for group report-outs or as a lab exercise) where they use bedrock GPS data (near Helheim Glacier) and repeat satellite and airborne altimetry from Helheim to calculate uplift and ice elevation changes from 2000 to 2007. They should conclude that when Helheim's ice elevation began to decrease dramatically in 2003, the bedrock GPS data began showing a positive displacement.

• Student version: Unit 4: Student activity (Microsoft Word 2007 (.docx) 750kB Dec8 17)
  Unit 4: Student activity PDF (Acrobat (PDF) 829kB Dec8 17)
• Instructor version:
  Unit 4: Student activity (instructor answer key) -- private instructor-only file
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  Unit 4: Student activity (instructor answer key)

  
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• Figures: Unit 4: Figures (PowerPoint 2007 (.pptx) 7.8MB Dec8 17)
  
  
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• Anatomy of a glacier (in case glacial background is needed): Unit 4: glacier anatomy (PowerPoint 2007 (.pptx) 3.6MB Oct13 15)
  
  
  Click to view
  
  

Next, students will use the schematic diagram shown on the right to sketch the bedrock uplift that they calculated (should be 75 mm of positive displacement between 2004 and 2011) and 21 mm of global sea level rise (3 mm/year for 7 years) to visualize that for this area, modern, rebound-induced uplift dominates over sea level rise. [Helheim Glacier's individual contribution to sea level rise is on the order of 0.01 mm/yr]. However, this is the result for a single (glaciated) area over a time period of less than 10 years.

The activity can be supplemented by a short quantitative exercise in which students calculate Helheim's contribution to global sea level, rather than being provided with Helheim's contribution as they are in the activity.

• Student version: Unit 4: Additional calculations (student) (Microsoft Word 2007 (.docx) 14.4MB Dec8 17)
  Unit 4: Additional calculations (student) PDF (Acrobat (PDF) 27.1MB Dec8 17)
• Instructor version:
  Unit 4: Additional calculations (instructor answer key) -- private instructor-only file
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  Unit 4: Additional calculations (instructor answer key)

  
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In reality there are even more factors that influence local sea level than presented here for the students. For instance, Greenland local sea level is also affected by the loss of gravitational pull from the ice sheet. As ice mass is lost, the horizontal gravitational pull of ocean water towards the ice is reduced. As the ocean water moves away, Greenland will experience local sea level drop from this factor as well. This rate has been measured at 1.5 mm/yr for many parts of Greenland (Riva et al. 2010). This is most likely not something you will introduce to your students, but as an instructor, it may be interested to know it. You can learn more about this from a seminar available through UNAVCO by Steve Nerem (search page for "nerem").

Part 3:

Students will reconvene for an interactive lecture/discussion or a gallery walk (choice of format depends on class time available, class size, and configuration of classroom) to compare the decadal-scale sea level changes in Greenland investigated in Parts 1–2 of Unit 3 to larger-magnitude sea level changes over geologic timescales.
Unit 4: Gallery walk (Microsoft Word 2007 (.docx) 330kB Dec8 17)
Unit 4: Gallery walk slides (PowerPoint 2007 (.pptx) 9MB Dec8 17)

General suggestions

Depending on the components of Unit 4 that are implemented in class (ex. calculation exercise on Helheim's contribution to sea level rise) and the teaching techniques employed (i.e., gallery walk vs. small group work vs. lecture vs. discussion), Unit 4 should take 1.5–2 hours of class time. The class meeting prior to implementation, each student should be given a copy of the preparation exercise. Prior to classroom implementation, copies of the activity should be made for each student. We also recommend making a separate copy of the schematic diagram (with the GPS unit) for each student. If Part 3 will be implemented as a gallery walk, large pieces of paper with the questions should be created and affixed to the wall prior to the beginning of the class meeting. For additional teaching tips and descriptions of classroom implementation strategies, refer to the Instructor Stories page.

Student understanding of sea level change

A challenging conceptual aspect of Unit 4 involves students identifying the relationship between bedrock elevation and ice mass change (in the case of the Helheim study area, crustal rebound as a result of decreasing ice mass).

Here are some suggested teaching strategies for addressing this conceptual challenge:
At the beginning of the class meeting, replay the animation on using GPS to measure ice mass loss that students have watched in preparation for the class meeting. Upon the conclusion of the animation, evaluate student understanding of the bedrock elevation/ice mass change relationship by administering a think-pair-share, multiple-choice, or concept sketch question to the class. Suggested questions:

Think-pair-share:
How does bedrock elevation change as mass is added via the growth of an ice sheet? How does bedrock elevation change as mass is removed via the melting of an ice sheet?

Multiple choice:
Which TWO statements accurately describe the relationship between bedrock elevation and ice mass changes in areas covered by snow and ice?
(a) As ice mass increases, uplift (elevation increase) of the crust occurs
(b) As ice mass increases, subsidence (elevation decrease) of the crust occurs
(c) As ice mass decreases, subsidence (elevation decrease) of the crust occurs
(d) As ice mass decreases, uplift (elevation increase) of the crust occurs

Concept sketch: (concept sketches could be shared with classmates or with the entire group after they are completed)
Make two labeled drawings: one illustrating how bedrock elevation changes when an ice sheet grows, and a second drawing illustrating how bedrock elevation changes when an ice sheet shrinks.

Instructor understanding of sea level change

We want to impress upon instructors that sea level change experienced at any given location may include more factors than just the two given here as an example. At the end of the Unit 4 exercise, students are asked to estimate the local sea level change near Helheim glacier that might result from the interplay between global sea level change (using an estimate of ~3 mm/yr) and bedrock movements from crustal unloading because of ice melt (as determined from GPS stations on bedrock sites). The main purpose of this introductory exercise is simply to have students understand that local sea levels depend on both global and local factors. In reality, sea levels along Greenland may be different than this simple estimate. Other factors that can affect local sea level include: vertical land motions due to tectonics or regional subsidence, prolonged changes in ocean currents or weather patterns, changes in regional mass that will lead to more or less gravitational attraction of ocean water (ex. Greenland may well also experience local sea level drop due to reduced gravitational attraction as ice melts and no longer draws ocean water towards the continent), and temperature-related thermal expansion of water.

If an instructor wishes to incorporate more nuanced data on local sea level changes, resources can be found at:

• AVISO Sea Level Altimetry site provides global maps that show how regional sea levels differ across the globe and offer an alternative to the simple ~3 mm/yr of sea level rise used in the Unit 4 exercise.
• University of Colorado Sea Level Explorer includes data from both global altimetry data and selected local tidal gauges.
• NOAA Sea Level Trends has tidal gauge data from around the world.

Background information on GPS and vertical movements

• The annual vertical cycle is very evident in Greenland, but at first glance the timing might seem surprising because the bedrock uplift cycle peaks several months after the ice mass cycle reaches its minimum in late summer. Bevis et al 2012 demonstrate that this is because the GPS vertical cycle is also responding to seasonal changes in air mass as well as ice mass. Only a very astute introductory student would notice this, but we wanted to mention the explanation in case it comes up.
• Many times geoscientists jump to concluding that vertical changes are a results of isostasy. It needs to be clarified that what is being studied in this unit is an elastic response of the rocks themselves, not an isostatic adjustment that involves viscoelastic processes. Elastic response is instantaneous and ~20 times smaller; whereas isostatic viscoelastic adjustment associated with post-glacial rebound has time scales of hundreds to thousands of years, but ultimately the adjustment will be much greater. Most likely there is some component of the long-term trend in the GPS measurements that is related to isostatic adjustment, but it is not what causes the seasonal and year-to-year variations. Depending on the length of the time series and the distance between the ice front and GPS station, there may also be a flexural response that will depend on the effective elastic thickness that is a function of the crust and mantle rheological properties. More about the differences between elastic, isostatic, and flexural responses are covered in the majors-level climate change module Understanding Our Changing Climate: Data Behind Melting Ice and Changing Sea Level.
• Although "How GPS works" should not be the emphasis of Unit 4, some faculty may choose to present some general material on how GPS is used to measure crustal deformation. This presentation "Introduction to GPS Basics" may be used to briefly address the how GPS works.
  Unit 4: GPS introduction (PowerPoint 2007 (.pptx) 19.7MB May29 19)
  
  
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Formative assessment:

Example #1: After students complete Part 2, a written think-pair-share can be conducted such that: (a) each student takes 2–3 minutes to record an answer to the question, "What is the relationship between ice mass change and ground displacement? Use data from Helheim Glacier and the surrounding area to support your answer"; (b) students meet in pairs and compare their responses; (c) instructor asks selected pairs to share their answers.

Example #2: Instructors can collect the schematic that students created in Part 3 to assess the accuracy of their uplift vs. discharge contributions. In smaller classes, instructors can circulate while students are completing Part 3 and quickly assess student work.

Example #3: If instructors choose to implement Part 4 (ancient sea level changes) as a gallery walk, there are several informal and formal methods that may be used to assess gallery walks available on the SERC website. Ultimately, students should be able to compare and contrast the spatial and temporal magnitudes of modern sea level changes in Greenland vs. ancient sea level changes. They should also be able to identify landscape features that reflect past sea level changes, whether these features indicate sea level increases or decreases, and the cause of these large sea level changes.

Summative assessment questions:

Level-1 example:
(1) During the last decade, southeast Greenland has experienced a:
(a) sea level rise because ice discharge into the ocean has been greater than bedrock uplift
(b) sea level drop because ice discharge into the ocean has been greater than bedrock uplift
(c) sea level rise because bedrock uplift has been greater than ice discharge into the ocean
(d) sea level drop because bedrock uplift has been greater than ice discharge into the ocean

Level-2 example #1:

You have been provided with a 2015 melt day anomaly map for Greenland from the National Snow and Ice Data Center (right). The 2015 melt anomaly illustrates how many days of melting occurred in 2015 compared to the average number of melting days from 1981 to 2010. Answer the following questions using the data provided and your knowledge of glacial and bedrock processes:

(A) Describe how the 2015 melt day anomaly differs between the two study areas circled on the map.

Scoring: scoring rubric below assuming that this is a 4-point question.
Example Unit 4 Rubric #1A (Microsoft Word 2007 (.docx) 82kB Nov12 15)

(B) Propose a hypothesis for how the bedrock elevation data might differ between the two study areas circled on the map. How did you develop your hypothesis?

Scoring: scoring rubric below assuming that this is a 4-point question.
Example Unit 4 Rubric #1B (Microsoft Word 2007 (.docx) 68kB Nov12 15)

(C) Which of the two study areas would you expect to exhibit the greatest amount of bedrock elevation change? Explain your answer.

Scoring: scoring rubric below assuming that this is an 3-point question.
Example Unit 4 #1C (Microsoft Word 2007 (.docx) 62kB Nov12 15)

Level-2 example #2:

The figure below illustrates the vertical profile of a wave-cut terrace on Santa Cruz Island in California. The isotopes in corals and shells on individual terraces are used to determine the age that the terrace was submerged. (The notation "ka" stands for "kiloannus" or thousand years; 400 ka is 400,000 years).

(A) Based on the geometry of the wave-cut terrace, sea level:

A. has risen consistently since 400,000 years ago
B. has risen intermittently since 400,000 years ago
C. has fallen consistently since 400,000 years ago
D. has fallen intermittently since 400,000 years ago

• Data: Record Melting in Greenland During 2010. Passive microwave data from NASA Earth Observatory.
• Data & Information University of Colorado Sea Level Research Group
• Science highlight: Observing Abrupt Melting in the Greenland Ice Sheet and Relating Air Mass Changes to Bedrock Changes.
• Calculation tool: Climate Sanity's conversion factors for ice and water mass and volume.
• Nerem, S., 2013, Using Geodesy to Study Sea Level Change - UNAVCO Science Seminar (search seminar page for "Nerem")
• Riva et al., 2010, Sea-level fingerprint of continental water and ice mass change from GRACE

• Reading: NASA Understanding Sea Level
• Bevis et al., 2012 Bedrock displacements in Greenland manifest ice mass variations, climate cycles and climate change