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Unit 3: Simple Climate Models

Louisa Bradtmiller (Macalester College)

Based on materials from Kirsten Menking (Vassar College) and David Bice (Penn State)

Author Profile

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 simple computational climate model to test the relative influence of several forcing mechanisms, including sunspots and albedo, on Earth's temperature.

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:

Using Mathematics and Computational Thinking: Apply ratios, rates, percentages, and unit conversions in the context of complicated measurement problems involving quantities with derived or compound units (such as mg/mL, kg/m3, acre-feet, etc.). HS-P5.5:

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:

Cross Cutting Concepts

Scale, Proportion and Quantity: Time, space, and energy phenomena can be observed at various scales using models to study systems that are too large or too small. MS-C3.1:

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:

Stability and Change: Feedback (negative or positive) can stabilize or destabilize a system. HS-C7.3:

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:

Cause and effect: Changes in systems may have various causes that may not have equal effects. HS-C2.4:

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

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:

Electromagnetic Radiation: When light or longer wavelength electromagnetic radiation is absorbed in matter, it is generally converted into thermal energy (heat). Shorter wavelength electromagnetic radiation (ultraviolet, X-rays, gamma rays) can ionize atoms and cause damage to living cells HS-PS4.B2:

Performance Expectations

Earth's Systems: Use a model to describe how variations in the flow of energy into and out of Earth’s systems result in changes in climate. HS-ESS2-4:

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

Students will explore Earth's radiation budget using several versions of a simple climate model often referred to as a "layer model." Earth receives energy from the sun, some of which is reflected and most of which is absorbed near the surface. Energy is then re-radiated upward from the surface; some is absorbed and re-radiated by the atmosphere, and some goes nearly directly to space. An imbalance between incoming and outgoing energy results in a change in average global temperature until equilibrium is restored.

Over the course of this exercise, students will compare the effects on average global temperature of differing strengths of the greenhouse effect. Using this same simple model, students will examine the effects on temperature of changes in incoming solar radiation approximating sunspot cycles. Finally, students will drive the model using observed forcings from the last 1000 years, including volcanic eruptions, aerosols, sunspots, and greenhouse gas emissions, and compare the results to observed and reconstructed temperature records over this same period.


Learning Goals

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

  • Construct an energy balance model of Earth's climate using first-order laws describing radiation transfer.
  • Identify and analyze positive and negative feedback behaviors.
  • Utilize forcing data for the past 1000 years to drive the model.
  • Compare the model results derived from real-world forcing data with observed and reconstructed temperature data, and analyze the reason(s) for any discrepancies.
  • Evaluate the magnitude of the greenhouse effect on Earth, and the effects of changes in the greenhouse effect on surface temperature.

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 Earth surface 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 courses in environmental science or climate science. 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 also have access to Microsoft Excel or similar spreadsheet software.

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 addition to the Kump et al. reading (see References and Resources below), students should complete the Unit 3 Student Reading, which contains extra background information as well as explanation of some of the mathematics involved.

Students should complete the simple climate model reading quiz (Microsoft Word 2007 (.docx) 59kB Nov30 16) before coming to class. The

simple climate model reading quiz 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.

can be found here.

In class, students should be provided with a copy of the simple climate model exercise (Microsoft Word 2007 (.docx) 349kB Sep14 17) and the forcing data spreadsheet (Excel 2007 (.xlsx) 96kB Mar10 15).

The

simple climate model exercise 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.

contains answers as well as tips and strategies instructors can use to guide students through the exercise and information on typical stumbling blocks.

Instructors can download versions of the STELLA simple climate models below:

  1. no albedo Model 1 (Stella Model (v10 .stmx) 17kB Aug11 16)
    (or see alternative version (Stella Model (v9 .stm) 83kB Oct19 17) for earlier versions of STELLA)
  2. albedo Model 2 (Stella Model (v10 .stmx) 18kB Aug11 16)
    (or see alternative version (Stella Model (v9 .stm) 84kB Oct19 17) for earlier versions of STELLA)
  3. 1-layer atmosphere Model 3 (Stella Model (v10 .stmx) 25kB Aug11 16)
    (or see alternative version (Stella Model (v9 .stm) 145kB Oct19 17) for earlier versions of STELLA)
  4. 1-layer atmosphere with emissivity Model 4 (Stella Model (v10 .stmx) 27kB Aug11 16)
    (or see alternative version (Stella Model (v10 .stmx) 27kB Oct19 17) for earlier versions of STELLA)
  5. as in 4, with sinewave sunspot cycle Model 5 (Stella Model (v10 .stmx) 27kB Aug11 16)
    (or see alternative version (Stella Model (v10 .stmx) 27kB Oct19 17) for earlier versions of STELLA)
  6. as in 4, including observed/reconstructed forcings Model 6 (Stella Model (v10 .stmx) 51kB Aug11 16)
    (or see alternative version (Stella Model (v10 .stmx) 105kB Oct19 17) for earlier versions of STELLA)

Teaching Notes and Tips

All models were 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 graphics and equations can be found in the answer key so that you can reconstruct the models yourself.

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 very 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. Alternatively, you can have students use screenshots. 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 four-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
  • 1.5 to 2 hours to build the model
  • 1.5 hours to conduct experiments

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

Kump, L. R., J. F. Kasting and R. G. Crane, 2010, The Earth System, 3rd Edition. San Francisco: Prentice Hall, p. 36–52.

M. I. Budyko, 1969, The effect of solar radiation variation on the climate of the Earth. Tellus, v. 21, p. 611–619.

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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 »