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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 1: Introduction to Modeling Dynamic Systems

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 get started using modeling software to design a simple computational "sink" model and compare it to a real sink.

Science and Engineering Practices

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

Systems and System Models: When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models. HS-C4.2:

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:

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 we introduce students to the reasons why Earth and environmental scientists use numerical modeling as a tool for understanding complex systems and then teach them how to use the STELLA software that we will employ for model construction throughout the semester. We note that many Earth systems involve spatial and/or temporal scales that make it difficult for us to study them directly, and that numerical modeling can help us further our knowledge of how these systems operate.

Using simple models of sinks, bank accounts, and cooling cups of coffee, we lead students to identify system components, such as reservoirs and flows, and to think about how these components are related to one another. We explain that the computer allows us to simulate system behavior over time without needing to solve differential equations. Toward that end, we address how to correctly choose a model time step in order to avoid spurious results and demonstrate different integration methods (Euler, Runge-Kutta 2, and Runge-Kutta 4).

Learning Goals

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

  • Explain why numerical modeling is a useful tool for studying Earth.
  • Describe the components of systems, such as reservoirs and flows.
  • Construct simple models of a bathtub, bank accounts, and cooling coffee using the STELLA software.
  • Experiment with simple models to learn about different system behaviors.
  • Explain the importance of the model time step and when to use different integration methods.
  • Discuss the limitations of models.

The exercise serves as the foundation for future exercises that address many of the guiding principles of the InTeGrate program. It introduces students to systems thinking and develops their abilities to use numerical modeling to generate and test scientific hypotheses.

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. 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).

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 1 Student Reading

Students should complete the Reading quiz (Microsoft Word 2007 (.docx) 70kB Oct21 16) before coming to class. The

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.

can be found here.

In class, students should be provided with the exercise found here: Student exercise for unit 1 (Microsoft Word 2007 (.docx) 461kB Nov12 16).

An answer key for the exercise can be found here:

Answer key for unit 1 exercise


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.

.

A copy of the final sink model (developed over questions 1–9) can be found here: Sink model (Stella Model (v10 .stmx) 8kB Aug11 16).

The models to be used to explore the importance of time step choice (questions 10–11) can be found here: Bank account models (Stella Model (v10 .stmx) 13kB Aug11 16).

The model to be used to explore different integration methods in questions 12–15 of the student exercise can be found here: Cooling coffee model (Stella Model (v10 .stmx) 9kB Aug11 16).

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 each STELLA model and then answer the questions by typing directly into the document. Students can then 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 then 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 four-hour class session might be broken up into the following sections:

  • 35–45 minutes for students to work their way through tutorials on the STELLA software (see the student exercise and answer key).
  • 1–1.5 hours to build and experiment with the sink model, during which time students and the faculty member should take a field trip to a sink in their building to study that system's behavior.
  • 1 hour to explore the importance of model time step.
  • 1 hour to explore how different integration methods work.
For those teaching at institutions that lack an extended once weekly course time slot, we recommend the following modifications:
  • Assign the STELLA tutorials as homework to be completed prior to coming to class.
  • Use a standard class lecture period to construct and experiment with the sink model.
  • Use a 2-hour lab period to carry out the model time step and integration methods exercises.

Assessment

Answers to exercise questions are located in the answer key for this unit (see Description and Teaching Materials section above). We generally do not grade this first exercise because we lead students through the model construction and experimentation process by having them follow along on their computers while we project what we are doing onto a screen in the classroom. Should instructors wish to grade this assignment, however, they 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 models, 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

Bierman, P.R., and Caffee, M., 2001, Slow rates of rock surface erosion and sediment production across the Namib Desert and escarpment, southern Africa, American Journal of Science, v. 301, p. 326–358.

Cross, M., and Moscardini, A.O., 1985, Learning the Art of Mathematical Modeling, New York: Halstead Press, 155 p.

Ghosh, A., and Holt, W.E., 2012, Plate Motions and Stresses from Global Dynamic Models, Science, v. 335, p. 838–843.

Glatzmaier, G.A., 2013, Introduction to Modeling Convection in Planets and Stars: Magnetic Field, Density Stratification, Rotation, Princeton University Press, 328 p.

Jolivet, R., Simons, M., Agram, P.S., Duputel, Z., and Shen, Z.-K., 2015, Aseismic slip and seismogenic coupling along the central San Andreas Fault, Geophysical Research Letters, v. 42, p. 297–306.

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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 »