Volume of oceans, and sea-level variations

Charly Bank
University of Toronto,
Author Profile


The activity combines aspects of Earth science (volume of oceans and ice sheets) with calculus (area of a 1x1 degree tile) and Matlab programming. Students calculate the volume of oceans and of ice sheets given the 1x1-degree digital elevation file. They then determine how much ocean levels would rise if all is on Antarctica and Greenland were to melt. To solve this problem in Matlab entry-wise matrix multiplication, loops, selection of cells using the "ginput" command, and different visualizations (grid and contours) are useful. Conceptually students need to think about inundation of coastal areas and shifting of coastlines.

Learning Goals

Students tackle the question of ocean-level rise by working with real data. In addition to advancing their computing skills, they also need to consider the limitations of their model and are asked to compose a scientific paper. Matlab is at the center of the activity, because it provides both the data and the vehicle to analyze it. Students need to assess their result, analyze the data, and synthesize their ideas. In addition the activity provides an avenue for engaging in meaningful group work, as 3 students start off with individual tasks and then combine their findings to continue together.

Context for Use

This 3-rd year course is taken by ~35 students enrolled in a large public research institution, centers on problems, and takes a holistic approach to teaching computing skills to geoscience students. Each problem asks students to create a model in Matlab, use that to make predictions and/or fit existing data, and deliberate on their model and findings by writing a paper. For most students this is the first time they encounter Matlab, and without much lecturing students have to solve quantitive geologic problems by programming in Matlab. They have to synthesize their findings into a paper format.

Description and Teaching Materials

Students are randomly assigned into groups of three (using slips of paper, or by shuffling student names in Matlab). Each team member is responsible for one aspect of the assignment; however the activity is set up that an individual will not be penalized if another group member does not follow through or is late. By giving clear responsibilities I hope to set them up for effective team work later on.

We briefly discuss what contributes to sea-level rise (melting of glaciers/icesheets versus that of sea ice, warming of ocean water) before turning to the "problem sheet" -- see attached file. Students are also given the "report checklist"; this is used for each of their 6 assignments in this course.

A sample script is attached, and the course outline provides more information about the course overall.

This activity could be done by using for example NOAAs etopo digital data and another programming language. However, I was excited to find the world topography in Matlab and the calculated results (e.g., volume of oceans 1.337e9 km^3) are close to NOAAs value (1.335e9 km^3, see https://www.ngdc.noaa.gov/mgg/global/etopo1_ocean_volumes.html ).

problem sheet (Acrobat (PDF) 85kB Sep23 15)

marking guide (Acrobat (PDF) 32kB Oct12 15)

Report checklist (Acrobat (PDF) 99kB Sep23 15)

possible solution ( 3kB Sep23 15)

course outline (Acrobat (PDF) 88kB Sep23 15)

Teaching Notes and Tips

I have found that students need help with the following challenges:
- distribution meltwater over coastal areas (as opposed to simply dividing the melt volume by the current ocean area),

- using entry-wise multiplication in lieu of loops,

- adding helpful annotations to their code (date, author, brief description that would come up with the "help" command, and highlighting key steps of the script),

- how to equitably contribute to a group.


Students are graded on

1. code (that it runs, includes header info and comments, and matches what they describe in their paper),

2. paper (title, abstract, introduction, method, data, results, discussion/conclusion, references, figures, writing), and

3. submission (all required parts in one email).

See attached marking guide and report checklist for details.

References and Resources