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Unit 8: Thermohaline Circulation

David Bice, Department of Geosciences, Penn State
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Summary

In this module, students first review some background material on density-driven deep currents in the oceans, and then create a STELLA model of the thermohaline circulation in the North Atlantic Ocean. The model is based on a classic 1961 paper in oceanography by Henry Stommel in which he demonstrated that some fairly simple physics and math lead to a system that exhibits real complexity — with multiple steady states and great sensitivity to initial conditions. Although the model is surprisingly simple, it does appear to capture some essential characteristics of the real world system. Students perturb the system as a means of exploring what kinds of changes can trigger the system to flip from one steady state to another.

In developing their numerical model of thermohaline circulation, students learn about the causes and consequences of density changes in seawater. They also discover that this dynamic system, like many others, can have multiple stable states, which have important implications for regional and even global climate change. Students also gain some insight into what might have triggered the onset and end of the Younger Dryas abrupt climate change event.

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Learning Goals

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

  • Create a model of thermohaline circulation based on Stommel's (1961) classic model.
  • Experiment with different initial conditions to identify and characterize the multiple steady states of this system and the importance of initial conditions.
  • Experiment with a range of perturbations of the system in order to understand what is needed to flip the system from one state to another.
  • Use the model as a means of testing hypotheses for the onset and termination of the most recent abrupt climate change event — the Younger Dryas.

This exercise addresses several of the guiding principles of the InTeGrate program. In particular, it helps add some sophistication to their systems thinking toolbox, develops students' abilities to use numerical modeling to generate and test geoscientific hypotheses, uses ice core paleoclimate data as a motivation for model experimentation, and addresses a grand challenge facing society, the potential danger of thresholds or tipping points in the climate system.

Context for Use

We intend this module to be used in a three- to four-hour class period that meets once a week (or two shorter periods in the same week). It can be used as part of this modeling course or it can be adapted as a lab exercise for a course in oceanography or paleoclimatology. We assume that the students will have a basic understanding of differential equations, which essentially provide the recipe for making this model. 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 8 Student Reading.

For advanced courses, instructors may also wish to have students read and present the papers by Broecker and/or Rahmstorf cited below.

Students should take the following quiz prior to coming to class to ensure they have done the assigned reading:Pre-lab quiz (Microsoft Word 2007 (.docx) 53kB Dec3 16). The instructor's key to the quiz is here:

.

In class, students should be provided with the exercise found here: THC Lab Exercise (Microsoft Word 2007 (.docx) 329kB Dec3 16).

An answer key for the exercise can be found here:

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

Instructors can download a version of the STELLA THC model by clicking on this link: THC_STELLA_model (Stella Model (v10 .stmx) 11kB Aug11 16) . The model includes an optional interface that is really not necessary, but some users may find it useful. The model was created using STELLA Professional. 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 time trying to figure out where they left off, making this inefficient. 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, and the relationship between the differential equations and the system components.
  • 1+ to hour to build the model
  • 2+ 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 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 reference:

Stommel, H., 1961, "Thermohaline Convection with Two Stable Regimes of Flow," Tellus, v. 13, p. 224-230. DOI: 10.1111/j.2153-3490.1961.tb00079.x

Related Readings:

Broecker, W., 1997, "Thermohaline Circulation, the Achilles Heel of Our Climate System: Will Man-Made CO2 Upset the Current Balance?", Science, v. 278 , p. 1582–1588.

Rahmstorf, S., 2002, "Ocean circulation and climate during the past 120,000 years," Nature, v. 419, p. 207–214.

Rahmstorf, S., Box, J.E., Feulner, G., Mann, M.E., Robinson, A., Rutherford, S., and Schaffernicht, E.J., 2015, "Exceptional twentieth-century slowdown in Atlantic Ocean overturning circulation," Nature Climate Change, v. 5, p. 475–480.

Cessi, P., 1994, "A box model of stochastically forced thermohaline flow," Physical Oceanography, v. 24, p. 1911–1920.

Mooney, C., 2015, Global warming is now slowing down the circulation of the oceans — with potentially dire consequences, Washington Post.

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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 »