Metuchen High School: STEM Project

Analysis of Sea Ice and Sea Level

Introduction

Human activity is warming the planet, causing the extent of sea ice in the Arctic to shrink and sea levels to rise. In this project we graph and analyze data on sea ice extent and sea level rise.

To get started, watch this brief video on global temperatures over time:
Video of global temperatures, 1880-2021

 

The Data

Download the Excel file that holds data on sea ice, sea level and global temperatures.

- The sea ice data give the extent (in millions of square kilometers) of sea ice in the Arctic in September of each year from 1979 to 2022. The sea ice changes in extent over the course of a year, but it reaches a minimum each year in September. So these values represent the minimum extent of sea ice each year.

- The sea level data represent how a given time's sea level differed from the global mean (average) sea level in the period 1996 - 2016. For example, the value -38.61 for time 1993.011526 indicates that the sea level at the beginning of 1993 was 38.61 mm below the global mean sea level in the period 1996 - 2016.

- The temperature data represent how a given year's global mean (average) temperature differed from the global mean temperature in the period 1961 - 1990. For example, the value -0.417 for 1850 indicates that the global mean temperature in 1850 was 0.471 °C below the global mean temperature in the period 1961 - 1990.

 

Making a Graph in Desmos

Making a graph in Desmos (desmos.com) is straightforward. Copy the 2 columns of data from Excel and paste them into Desmos. Desmos will adjust the window to accommodate the data. To add labels on the x-axis and y-axis, click on in the upper-right. Here you can also adjust the minimum and maximum values on the X or Y axis.

To make a copy of the graph, screenshot it and edit it in Paint. Or, on a Windows device, the keyboard shortcut Windows Key-SHIFT-S allows you to take a screenshot. You can include the regression statistics that appear in Desmos in your screenshot (more on regression below).

Another way to get a copy of your Desmos graph: click on in the upper-right. Then choose Export Image and Download PNG.

 

Regression

Regression involves fitting a straight line or a curve to data points.

Below is an example of a "best fit" regression line that has been fit to data points. The "best fit" line results from a mathematical process that minimizes the distances between the data points and the line.

Data points and a best-fit line

 

Another type of regression involves fitting a curve to data points. Here is a curve fitted to the same data points:

Data points and a curve fit to the data.

( Source of the 2 plots: https://statisticsbyjim.com/regression/curve-fitting-linear-nonlinear-regression/ )

 

Regression in Desmos

Desmos makes it straightforward to do a regression.
Click on in the upper left. Choose f(x) expression and then:
- To fit a straight line to data points (known as linear regression) enter y1 ~ mx1 + b into Desmos.
- To fit a quadratic curve to data points (known as quadratic regression) enter y1 ~ ax12 + bx1 + c into Desmos.

For more information on doing a regression in Desmos, view the video on the topic here: Regressions in Desmos

Also, I can help you with this.

 

 

Graphs and Regressions

Graph 1: Sea Ice vs. Time

  1. Make a graph of sea ice vs. time in Desmos.
  2. Do a linear regression in Desmos.

Zoom out so that the years 1988 and 2029 are shown. In the "Export Your Graph" window, you may need to choose a Size from the dropdown, for example "Medium Rectangle." The x-axis should have the label "Year" and the y-axis should have the label "Sea Ice (million sq. km.)". In your report, include the Desmos graph (showing the data points and the regression line) and the equation of the regression line.

Also in your report, answer these questions:

  1. Using your regression line, estimate the amount of sea ice in the Arctic in 1988.
  2. Using your regression line, estimate the amount of sea ice in the Arctic in 2029.
  3. What is happening to sea ice in the Arctic over time?
  4. What do you think is the effect of the melting of sea ice in the Arctic?

 

 

Graph 2: Sea Level vs. Time

  1. Make a graph of sea level vs. time.
  2. Do a linear regression.
  3. Do a quadratic regression.

The x-axis should have the label "Year" and the y-axis should have the label "Sea Level (mm)". In your report, include the Desmos graph and the equations of the 2 regression curves.

Also in your report, answer these questions:

  1. What is happening to sea level over time?
  2. Using your quadratic regression curve, estimate the sea level in 1988.
  3. Using your quadratic regression curve, estimate the sea level in 2029.
  4. Which regression (line or quadratic) do you think does a better job of matching the data? Explain.
  5. Why do you think the level of the sea is rising?

 

 

Graph 3: Global Temperature vs. Time

Make a graph of global temperature vs. time.

The x-axis should have the label "Year" and the y-axis should have the label "Degrees Celsius". In your report, include the Desmos graph.

Also in your report, answer these questions:

  1. What is happening to global temperatures over time?
  2. Have global temperatures always been rising at the same rate, or have they been rising more rapidly in recent decades?

 

 

Graph 4: Sea Level vs. Sea Ice

  1. Make a graph of sea level vs. sea ice.
  2. Do a linear regression.

The x-axis should have the label "Sea Ice" and the y-axis should have the label "Sea Level". In your report, include the Desmos graph and the equation of the regression line.

Also in your report, answer these questions:

  1. What does the graph say about the relationship between the level of the sea and the extent of sea ice in the Arctic?
  2. Using your regression line, estimate what the sea level would be if the extent of sea ice fell to 3 million km2.

 

Grading

Here is a rubric that will be used to grade each project.