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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. The materials engage students in understanding the earth system as it intertwines with key societal issues. The materials are free 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.
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Unit 7: Heat Flow in Permafrost

Kirsten Menking (Vassar College)
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These materials have been reviewed for their alignment with the Next Generation Science Standards as detailed below. Visit InTeGrate and the NGSS to learn more.

Overview

In this unit, students develop a model to simulate heat flow in permafrost. They conduct experiments to determine how changing surface temperatures affect the near-surface geothermal gradient.

Science and Engineering Practices

Using Mathematics and Computational Thinking: Use simple limit cases to test mathematical expressions, computer programs, algorithms, or simulations of a process or system to see if a model “makes sense” by comparing the outcomes with what is known about the real world. HS-P5.4:

Using Mathematics and Computational Thinking: Create and/or revise a computational model or simulation of a phenomenon, designed device, process, or system. HS-P5.1:

Obtaining, Evaluating, and Communicating Information: Critically read scientific literature adapted for classroom use to determine the central ideas or conclusions and/or to obtain scientific and/or technical information to summarize complex evidence, concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. HS-P8.1:

Developing and Using Models: Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system HS-P2.3:

Developing and Using Models: Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. HS-P2.6:

Constructing Explanations and Designing Solutions: Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. HS-P6.4:

Cross Cutting Concepts

Systems and System Models: Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. HS-C4.4:

Systems and System Models: Models (e.g., physical, mathematical, computer models) can be used to simulate systems and interactions—including energy, matter, and information flows—within and between systems at different scales. HS-C4.3:

Structure and Function: Investigating or designing new systems or structures requires a detailed examination of the properties of different materials, the structures of different components, and connections of components to reveal its function and/or solve a problem. HS-C6.1:

Stability and Change: Change and rates of change can be quantified and modeled over very short or very long periods of time. Some system changes are irreversible. HS-C7.2:

Energy and Matter: Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of, and within that system. HS-C5.2:

Disciplinary Core Ideas

Definitions of Energy: The term “heat” as used in everyday language refers both to thermal energy (the motion of atoms or molecules within a substance) and the transfer of that thermal energy from one object to another. In science, heat is used only for this second meaning; it refers to the energy transferred due to the temperature difference between two objects. MS-PS3.A4:

Definitions of Energy: The temperature of a system is proportional to the average internal kinetic energy and potential energy per atom or molecule (whichever is the appropriate building block for the system’s material). The details of that relationship depend on the type of atom or molecule and the interactions among the atoms in the material. Temperature is not a direct measure of a system's total thermal energy. The total thermal energy (sometimes called the total internal energy) of a system depends jointly on the temperature, the total number of atoms in the system, and the state of the material. MS-PS3.A5:

Weather and Climate: The foundation for Earth’s global climate systems is the electromagnetic radiation from the sun, as well as its reflection, absorption, storage, and redistribution among the atmosphere, ocean, and land systems, and this energy’s re-radiation into space. HS-ESS2.D1:

Earth Materials and Systems: The geological record shows that changes to global and regional climate can be caused by interactions among changes in the sun’s energy output or Earth’s orbit, tectonic events, ocean circulation, volcanic activity, glaciers, vegetation, and human activities. These changes can occur on a variety of time scales from sudden (e.g., volcanic ash clouds) to intermediate (ice ages) to very long-term tectonic cycles. HS-ESS2.A3:

Performance Expectations

Energy: Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. HS-PS3-1:

This material was developed and reviewed through the InTeGrate curricular materials development process. This rigorous, structured process includes:

  • team-based development to ensure materials are appropriate across multiple educational settings.
  • multiple iterative reviews and feedback cycles through the course of material development with input to the authoring team from both project editors and an external assessment team.
  • real in-class testing of materials in at least 3 institutions with external review of student assessment data.
  • multiple reviews to ensure the materials meet the InTeGrate materials rubric which codifies best practices in curricular development, student assessment and pedagogic techniques.
  • review by external experts for accuracy of the science content.


This page first made public: Sep 15, 2017

Summary

In this unit, students create a STELLA model of heat flow in the top 1 km of Earth's crust to explore the use of Arctic borehole temperature profiles as recorders of anthropogenic warming. The exercise draws on a 1986 Science paper by Arthur Lachenbruch and Vaughn Marshall in which they identified a pronounced kink in the geothermal gradient in several boreholes drilled for oil exploration in northern Alaska. After considering a variety of potential sources for the kink (for example, changes in thermal conductivity of crustal materials or thermal disturbances brought about by the drilling process), Lachenbruch and Marshall called on surface warming associated with anthropogenic climate change as the most likely cause.

In developing their numerical model of heat flow in permafrost, students learn about the physics of heat conduction and the factors that influence the geothermal gradient. They use trigonometry to impose a thermal oscillation at Earth's surface and explore the effects of different periods of oscillation on the depth of penetration of the temperature disturbance.

Learning Goals

On completing this module, students are expected to be able to:

  • Create a model of heat flow through the outer kilometer of Earth's crust using Fourier's law of heat conduction.
  • Experiment with different thermal conductivities and heat capacities to see the impacts of changes on the crust's geothermal gradient.
  • Experiment with a step increase in surface temperature to explore the impact of anthropogenic warming on the geothermal gradient.
  • Explain how borehole temperature data in permafrost can be used to show that the Arctic has experienced recent warming.
  • Evaluate the impact of different frequencies of surface temperature oscillation on the geothermal gradient over time.
  • Compare model results to published borehole temperature data.

This exercise addresses several of the guiding principles of the InTeGrate program. In particular, it requires the use of systems thinking, develops students' abilities to use numerical modeling to generate and test geoscientific hypotheses, makes use of authentic borehole temperature data, and addresses a grand challenge facing society, anthropogenic warming.

Context for Use

This unit is intended to be used in a three- to four-hour class period that meets once a week. It can be used as part of this modeling course or it can be adapted as a lab exercise for a course in geophysics. For this module, students should come to class prepared to take a short quiz on the assigned reading. Thereafter they will be led through a series of prompts designed to help them create and experiment with a number of simple models using the iconographic box modeling software STELLA (see https://www.iseesystems.com/store/products/ for different options for purchasing student or computer lab licenses of STELLA or for downloading a trial version). Students should have access to Microsoft Excel or similar spreadsheet software to allow them to graph temperature profiles as a function of depth as STELLA will only display time series of temperature change for an individual level in the crust.

For those learning to use STELLA, we suggest the online "play-along" tutorials from isee systems. You can find them here: isee Systems Tutorials.

Description and Teaching Materials

In preparation for the exercise, students should read the following: Unit 7 Student Reading.

For advanced courses, instructors may also wish to have students read and present Lachenbruch, A.H., and Marshall, B.V., 1986, "Changing Climate: Geothermal Evidence from Permafrost in the Alaskan Arctic," Science, v. 234, p. 689–696, and Davis, M.G., Harris, R.N., and Chapman, D.S., 2010, "Repeat temperature measurements in boreholes from northwestern Utah link ground and air temperatures at the decadal time scale," Journal of Geophysical Research, v. 115, B05203, doi: 10.1029/2009JB006875.

Students should take the following quiz prior to coming to class to ensure they have done the assigned reading: Heat flow in permafrost reading quiz (Microsoft Word 2007 (.docx) 137kB Dec3 16). An answer key for the quiz can be found here:

Heat flow in permafrost reading quiz - answer key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

.

In class, students should be provided with the exercise found here: Permafrost exercise for students (Microsoft Word 2007 (.docx) 310kB Dec3 16).

An answer key for the exercise can be found here:

Permafrost exercise answer key


This file is only accessible to verified educators. If you are a teacher or faculty member and would like access to this file please enter your email address to be verified as belonging to an educator.

. It contains answers to the different questions and strategies instructors can use to guide students through the exercise and information on typical stumbling blocks.

Instructors can download a version of the STELLA heat flow in permafrost model by clicking on this link: Heat flow in permafrost STELLA model (Stella Model (v10 .stmx) 45kB Aug11 16). The model is "spun up," containing values in the reservoirs that are non-zero. See the answer key for explanation. The model was created using STELLA Professional and should open on any subsequent version of STELLA. If you are using an earlier version of STELLA, the complete model graphic and equations can be found in the answer key so that you can reconstruct the model yourself.

Teaching Notes and Tips

We generally post the readings and assignments for students to an LMS site (e.g. Moodle, Blackboard, Canvas). Students can open the assignment in Microsoft Word on the same computer they are using to construct the STELLA model and then answer the questions by typing directly into the document. Students can either print a paper copy to hand in to the instructor or email their modified file to the instructor. It is straightforward to copy graphs and model graphics out of STELLA and to paste them into Word. Simply select the items to be copied, hit copy in STELLA, and paste into Word. There is no need to export graphics to jpg.

We teach the course in a three- to four-hour block once a week because we have found that models require a lot of uninterrupted time to construct. If students have a 50- or 75-minute class period several times a week, they spend at least 20 minutes of subsequent class periods trying to figure out where they were in the exercise at the beginning of the week. This is not a good use of time, hence the recommended three- to four-hour class session once per week. However, we also know that sustaining attention for this length of time can be difficult. We therefore recommend allowing students the freedom to take breaks throughout the modeling session to get snacks or coffee.

A typical 4-hour class session might be broken up into the following sections:

  • 20-minute discussion of the reading to ensure all the students are familiar with the mathematics behind the model, specifically Fourier's law of heat conduction.
  • 1.5 to 2 hours to build the model
  • 1.5 hours to conduct experiments

For instructors who have more limited contact hours with their students, we suggest that the model construction parts of this exercise be assigned as a pre-lab to be handed in a day or two before class along with the completed STELLA model itself. This would allow the instructor to determine whether students' models are working correctly and to provide feedback to address errors in construction, omissions in documentation, problems with unit conversions, and inappropriately sized time steps that might lead to spurious model behavior. Class time could then be devoted to running experiments and analyzing the results. If access to STELLA outside of class time is impossible due to computer lab scheduling or to financial constraints that prevent students from purchasing their own STELLA licenses, students could be asked to create a pencil and paper sketch of what their model should look like, annotated with equations and then sent to the instructor in advance of class for feedback. This should facilitate a faster model construction time during the limited class hours.

Assessment

Answers to exercise questions are located in the answer key for this unit (see Description and Teaching Materials section above). Instructors may download an assessment rubric for the modeling exercise here: Assessment rubric (Microsoft Word 2007 (.docx) 121kB Jan8 15). Rather than assign a point value to every question in the exercise, we employ a holistic approach that determines the extent to which a student has correctly built the model, supplied appropriate documentation of equations and units, thoroughly answered questions throughout the assignment, and provided appropriately labeled graphs and figures in answering questions.

References and Resources

This exercise is based on the following references:

Lachenbruch, A.H., and Marshall, B.V., 1986, "Changing Climate: Geothermal Evidence from Permafrost in the Alaskan Arctic," Science, v. 234, p. 689–696.

Turcotte, D.L., and Schubert, G., 2000, Geodynamics, 2nd ed., Cambridge, U.K.: Cambridge University Press, pp. 132–143, 150–152.

Another reading that can be given to advanced students is:

Davis, M.G., Harris, R.N. Chapman, D.S., 2010, "Repeat temperature measurements in boreholes from northwestern Utah link ground and air temperatures at the decadal time scale," Journal of Geophysical Research, v. 115, B05203, doi: 10.1029/2009JB006875.

Additional web resources include:

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These materials are part of a collection of classroom-tested modules and courses developed by InTeGrate. 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 »