Modeling the Melt in the Arctic Tundra

Subject: Math
Grade Level: 9-12

Summary

This lesson covers linear regressions for high school mathematics students. Students will explore different linear regressions to discover relationships between salinity, elevation, and thaw depth in Prudhoe Bay, Alaska. Students will determine how these different variables are related and what it means for the arctic ecosystems. Students will explain their models in the context of the problem and create a one page public service announcement about the dangers of saltwater intrusion.

Materials and Preparation

At this point, students should know how to create a linear regression using technology and have a basic understanding of the format of the equation.

Teachers and students will need the Saltwater Data Set to use for the linear regression. They will also need to have access to the videos below as well as the worksheet printed for students. Students will need to have access to graphing software (e.g. Desmos).


Learning Objectives

Objective #1
Create and compare linear regression equations based on real world data.
Objective #2
Explain linear regression features in the context of saltwater intrusion.
Objective #3
Make predictions about how the Arctic is changing based on elevation, salinity, and thaw depth.
Objective #4
Identify the implications on saltwater intrusion in the Arctic.

Opening Activity

Part 1: Understanding the Problem (10 minutes)

Use the images for Part 1 in the Modeling the Melt in the Arctic Tundra Images PDF linked above. Allow observation time. These images are also on the student sheet. Ask students where they think both of these pictures are taken and why they think that? Give students 2 minutes to discuss and come up with where they think the pictures are located and why.

Explain to students that both of these pictures were taken in Prudhoe Bay, Alaska which is in the Arctic Circle. It may be helpful to show students where this place is on Google Maps or something similar.

Ask students to discuss in groups why these pictures from the same location are so drastically different. What could have caused this? 

Show students the video “What is Saltwater Intrusion” to explain what saltwater intrusion is. 

Discuss with students that saltwater intrusion is happening all over the world, including the Arctic and it is changing how the Arctic ecosystem operates. Connect this to the pictures shown before. The picture on the left shows a healthy tundra and the picture on the left shows tundra that has been saturated with saltwater from the ocean.

Have students hypothesize why this is an issue and what could happen if the tundra continues to be inundated with saltwater.


Activity Overview

Part 2: The Math

Explain to students what thaw depth is and how it is measured. This is particularly important if students are from a warmer climate where the ground does not freeze. This “Taking Thaw Depth Measurements” video (2:38 minutes) helps explain thaw depth and how it is measured. Researchers also measure salinity by pulling up the groundwater from different sections to see how much salt is in the soil. Using Part 2 in the images document, show the pictures of the sipper and the location of data collection. The sipper pulls up the groundwater and then it can be sucked into the syringe (The sipper is the skinny T rod with the syringe coming out the top). It is important to explain this so students have an understanding of where the data is coming from.

Students will then use Desmos and/or Google Sheets to create a scatter plot and linear regression of the data here. They will measure the below relationships and look for trends in the data. 

  1. Salinity vs. Elevation
  2. Salinity vs. Thaw Depth
  3. Thaw Depth vs. Elevation

Students will also interpret the slope, y intercept, and correlation coefficient in the context of the data.

Students will then research correlation and causation and decide how these apply to the given data. Students will also explain how the different variables affect each other and what that could mean for different parts of the tundra. Given different tundra scenarios, students will make predictions about the salinity and thaw depth and draw a picture of what the tundra might look like given its statistics. 

Part 3: The Outreach

Lastly, students will take on the role of being a climate scientist and predicting what areas will be most at risk for saltwater intrusion and what that will mean for the ecosystem. This will include different scenario cards for students to work with and draw conclusions based on their model. This will include students completing their own research on what is happening in the tundra and who/what is being affected. After completing this, students will create a one page public service announcement to hang in the hallways informing others on saltwater intrusion. 

Alternatively, teachers can consider using art integration strategies in the final product such as creating an infographic, presenting a skit, or creating artistic work to convey their information and insights.


Reflection

Students will reflect on their learning by answering the following questions:

  1. How does modeling saltwater intrusion help us create interventions?
  2. Why is saltwater intrusion a problem for Arctic communities?
  3. We know that saltwater intrusion affects the permafrost and melts it. Why does this matter for the rest of the world?

Supporting Documents

Math standards:

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (CCSS: S-ID.6)

  1. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (CCSS: S-ID.6a) 
  2. Informally assess the fit of a function by plotting and analyzing residuals. (CCSS: SID.6b) 
  3. Fit a linear function for a scatter plot that suggests a linear association. (CCSS: SID.6c)

Interpret linear models. (CCSS: S-ID)

  1. Interpret the slope and the intercept of a linear model in the context of the data. (CCSS: S-ID.7)
  2. Using technology, compute and interpret the correlation coefficient of a linear fit. (CCSS: S-ID.8) 
  3. Distinguish between correlation and causation. (CCSS: S-ID.9)

Credit: Dr. Julia Guimond and Saltwater intrusion and fluxes in the tundra team


Standards:

Science Practice 2
Developing and using models
Science Practice 4
Analyzing and interpreting data
Science Practice 8
Obtaining, evaluating, and communicating information
Crosscutting Concept 1
Patterns
Crosscutting Concept 2
Cause and effect: mechanism and explanation
LS 2
Ecosystems: interactions, energy, and dynamics

Polar Literacy Principles:

2B-1
Tundra is a treeless area with permanently frozen soil (permafrost) and low growing vegetation.
6C-3
Thawing permafrost is damaging homes, roads, pipelines, buildings and ecosystems.
6E
The Arctic region of the United States holds sizable proved and potential conventional energy (oil and natural gas resources) and renewable energy (geothermal, tidal, wind, etc.). The impacts of extraction of the resources is questionable.

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