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Unit 4: Measuring Ice Mass Changes: Vertical Bedrock GPS

Bruce Douglas (Indiana University)
Susan Kaspari (Central Washington University)

Summary

This unit shows how GPS records of bedrock surface elevation may be used to monitor snow and ice loading/unloading on decadal and annual time scales. Students calculate secular trends in the GPS time series and then use the original and detrended records to identify sites that exhibit similar behavior. Students gain experience with the challenges and benefits of using bedrock geodetic data to study snow and ice mass changes. They also consider the magnitude and timing of the elastic component of vertical change compared to that associated with post-glacial rebound (viscoelastic response). There is a MATLAB option available if instructors are interested in giving students an introduction to visualizing data in MATLAB and modeling ground surface response to ice sheet retreat.

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Learning Goals

Unit 4 Learning Outcomes

Students will:

  • Calculate secular trends in GPS vertical-position data and compare these trends to variations at seasonal and interannual timescales.
  • Quantitatively compare records from GPS sites that may be dominated by the elastic response to ice mass loss versus those dominated by the viscoelastic response to post-glacial rebound.
  • Contrast the spatial variations in the magnitude of changes in Earth's surface elevation that can be observed.
  • Critique/evaluate the utility of GPS vertical-position data for monitoring changes in ice mass loss, compared to other geodetic data types.

Unit 4 Teaching Objectives

  • Cognitive: Facilitate the students' ability to calculate and compare secular trends versus seasonal-to-interannual fluctuations. Enable students to demonstrate the connection between changes in ice mass loss and the processes that result in changes in Earth's surface elevation.
  • Behavioral: Promote skills in making and interpreting graphs that isolate secular trends and higher-frequency fluctuations. Facilitate an understanding of how numerous processes must be considered when using geodetic data to study the response to climate change as seen in ice mass loss.
  • Affective: Facilitate the students' appreciation of the complex interactions between various hydrologic and geophysical processes, and how this complexity leads to uncertainty in our estimates of changes in ice mass loss and sea-level changes.

Context for Use

The content in Unit 4 is appropriate for advanced Climate, Cryosphere, Geology, Geoscience, or Environmental-related courses conducted at the junior and/or senior level in which geodesy data can be introduced. Unit 4 can be adapted to lecture or lab settings as a series of interactive lecture activities, a lengthier in-class activity, or as the basis of a laboratory investigation on the use of geodesy to understand the snow and ice mass components of the hydrologic cycle.

If the entire two-week module will not be used, we recommend pairing Unit 4 with Unit 2: Global Sea-Level Response to Temperature Changes and Unit 3: Global Sea-Level Response to Ice Mass Loss to give students an opportunity to attain a firm grasp of all of the components that contribute to sea-level change that is a result of climate change. It is possible to skip Unit 1: Climate Change and Sea Level: Who Are the Stakeholders? as long as students are familiar with how changes in sea level affect the lives and social infrastructures across the globe. However the process of having the students more directly consider the societal costs of sea-level rise is powerful and recommended if you have time.

Description and Teaching Materials

Introduction

This unit is centered around analysis of vertical-position data from six GPS stations installed on bedrock in Greenland. The student exercise takes ~2.5 hours and can be done in a lab period, stretched across several shorter class periods, or done partly/largely as a homework assignment. The teaching materials include a short presentation on how GPS vertical motion relates to local ice changes, the student exercise and data spreadsheets, several optional animations and readings, and other supporting resources. The student exercise has a page or so of background reading. If you are trying to save class time, you may wish to give students the exercise a day ahead and require they come to class with the background already read.

Student Exercise Elements

The Unit 4 student exercise requires that students have access to a computer and Excel (or other spreadsheet software). Students can complete the Unit 4 student exercise either during class or lab time or as a take-home activity. The exercise is designed to be completed in groups of three students. Each student works with data from two of the six GPS sites and shares answers with other members of the group. The primary goal of the exercise is for the students to identify how the GPS sites are affected by snow and ice mass changes. This is further affected by where the stations are located relative to the present ice front and the flow properties of the local glaciers.

The students do not know this ahead of time, but each student is given data from 1) a site where there is an actively changing ice (rapid ice flow and/or rapid thinning, etc.) and 2) a site that is has little nearby glacier flow/ice change. The student plots the data and calculates a trend for each site. Then, if the instructor would like to add additional computational components, the students may be asked remove the trend and construct a detrended time series for each site that highlights seasonal and inter-annual variations. The students in each group share data, then classify the six GPS sites into distinct sets based on what patterns emerge. Seasonal variations are evident as snow and ice mass change as part of the decadal patterns. In the final component of the lab, the students describe and sketch a conceptual model for how snow and ice mass changes affect ice proximal and distant sites and compare the magnitude spatial variability of uplift due to the elastic response to change in loads. The students are also asked to reflect on the strengths and limitations of monitoring snow and ice mass changes using variations in vertical position recorded by GPS instruments.

As currently written, the students are pointed toward the Nevada Geodetic Laboratory (NGL) interactive map, the GRACE (Gravity Recovery and Climate Experiment) Greenland Ice Mass Animation, the recently produced maps that show ice velocity, and ice mass loss maps based on various methods of reducing Synthetic Aperture Radar (SAR) images (also used in Unit 3) to help them test their hypotheses for how the station's proximity to ice affects GPS-measured bedrock movements. Instructors could opt to use just one of these methods, if they wish. By zooming in on the NGL interactive map map and using the satellite image option, students can judge the position of the station relative to the ice front and view the vertical position changes (also north–south and east–west for interest). The GRACE animation shows ice mass changes as well as ice flow lines, allowing students to further connect the GPS observations with ice sheet behavior.

A possible extension that is not currently written into the exercise would be a comparison with Antarctica. If an instructor is interested in fostering a larger comparison between Greenland and Antarctica, Nevada Geodetic Laboratory has data from many Antarctic GPS stations. There is another equivalent GRACE data animation for Antarctica that could be used as a comparison.

Teaching Materials

MATLAB Option

  • There is a MATLAB addendum available that builds on the original exercises performed in Excel. A set of MATLAB scripts have been created that can be used to plot the GRACE, GPS, and InSAR datasets and evaluate some of the mechanics associated with ice mass changes in Greenland.
    • MATLAB Ice Mass Loss Exercise (Microsoft Word 2007 (.docx) 8.6MB May19 21)
      • Provides an explanation of the three MATLAB scripts included for plotting the datasets and modeling ground surface motion due to the removal of ice, along with an introduction and tutorial to the MATLAB interface.
    • Greenland MATLAB Scripts and Tools (Zip Archive 34.9MB May19 21)
      • A zip file containing the three MATLAB scripts for plotting and modeling the data, examples of the GPS, GRACE, and InSAR data, and other tools used within the MATLAB scripts.

Teaching Notes and Tips

  • The unit requires use of computers. Ideally each student will have their own computer or laptop. At least there should be one computer per work group. If it is not feasible to use computers during the class/lab period, the instructor should take extra steps to make sure that students understand what is required to do the exercise outside of class.
  • It is important to stress that the lab is based on real GPS data, which makes the data analysis more challenging (but more interesting) than if an "idealized" data set were used. It is also fun to emphasize how this is the same technology they are so familiar with in their phones, but with higher precision and applied to understanding earth processes.
  • The provided data files are in Excel. Students may actually prefer to use another spreadsheet program such as Google Sheets if they are working on their own computers. Google Sheets, while less powerful than Excel, has the capability to do the analyses for this unit. The Excel files should open fine in Sheets, but you may want to double-check this process yourself if you are not familiar with it. If you have students working on their own computers and thus have different software and different versions, it is better to emphasize the processes and how to query Help rather than try to show exactly the on-screen steps for the different programs.
  • Students may need help with specific spreadsheet functions such as "slope" to calculate the trend (= slope(y-values,x-values)). They may also need help thinking through how to "detrend" the position data if you choose the exercise with that component.
  • Likely unit-conversion issues for students: When a trend is fit to data in a spreadsheet program, the slope of the best fit line has units of mm/day (because the data are daily). In the exercise, trends are considered in terms of mm/yr. Remind students they will need to do a unit conversion.
  • This unit may be turned in in two different options. One would be to ask for a paper report that includes all of the responses to the calculations, questions, and plots. Details for how this report should be compiled will need to be provided to the student and the student handout itself may need to be reformatted to provide space for students to enter their responses. Plots can be added as extra pages. If a digital report is to be submitted, then instructions for how the digital materials/files are to be arranged and the type of program used to create the report will need to be explicitly given to the students.
  • The Teaching with Spreadsheets across the Curriculum site provides support for teaching with programs such as Excel. If your students need supporting math practice, The Math You Need site provides an opportunity to brush up on skills such as graphing and unit conversion. Teaching with Google Earth provides a variety of resources for using this powerful program during teaching.
  • Misconceptions: Most undergraduate geology majors have heard of isostasy, so they might think the vertical displacement due to snow and ice mass changes is an isostatic adjustment. It needs to be clarified that what is being studied 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.
  • 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 responding to seasonal changes in air mass as well as ice mass. Only more astute students will notice this, but we wanted to mention the explanation in case it comes up. The GRACE data show the cycling timing that is not complicated by air mass changes.
  • Instructions for downloading data from the Nevada Geodetic Laboratory web page: Accessing GPS data on NGL website (PowerPoint 2007 (.pptx) 18.6MB Jul19 24). Note: the map opens centered and zoomed into Nevada, so users will need to zoom out and then navigate to Greenland or Antarctica.
  • Streamlining/simplification options: If you wish to greatly streamline the unit or do the unit with less advanced students, the instructor may supply the GPS graphs (available in the Instructor version of the spreadsheet) and just have the students interpret them for the exercise. It would be appropriate to use the version of the activity without detrended data. One could also choose to de-emphasize or not mention the difference between elastic and viscoelastic (isostatic) vertical adjustments.
  • If students will be completing the Stakeholder Report in Unit 5, it is useful for the instructor to remind the students that they can be incrementally working on Unit 5 by beginning to incorporate their findings from Units 1–4.

Assessment

Formative assessment of student learning may be done through conversations with individuals and groups during the exercise if it is done during class time. The student exercise is the summative assessment for the unit. The Unit 4 Student Exercise Rubric (Microsoft Word 2007 (.docx) 16kB Nov11 19) PDF (Acrobat (PDF) 54kB Dec8 19) provides an example of how the exercise may be evaluated. We suggest including the rubric with the student exercise so the students know the criteria ahead of time. The discussion provides a less formal form of summative assessment and is also helpful for encouraging student reflection.

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This module is part of a growing collection of classroom-tested materials developed by GETSI. The materials engage students in understanding the earth system as it intertwines with key societal issues. The collection is freely available and ready to be adapted by undergraduate educators across a range of courses including: general education or majors courses in Earth-focused disciplines such as geoscience or environmental science, social science, engineering, and other sciences, as well as courses for interdisciplinary programs.
Explore the Collection »