Unit 1: Introduction to Modeling Dynamic Systems
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).
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
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:
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.
- 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.
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.