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002: Dynamic Equilibrium

posted Apr 30, 2017, 12:07 PM by Jon Darkow   [ updated Sep 3, 2017, 9:44 AM ]

002: Dynamic Equilibrium


Carbon is accumulating in our atmosphere. NASA reported that the average global CO2 concentrations in the atmosphere during January 2017 were 405.34 ppm (ESRL web.) In 1958, when global CO2 concentrations in the atmosphere were first collected reliably and routinely, the concentration was 338.45 ppm (ESRL web.) Accumulations in a system with inflows and outflows often lead to misconceptions. Students tend to pattern match an accumulation in a stock with only the inflow.


Imagine the atmosphere. Beautiful right! Now carbon dioxide can be an inflow (emissions, respiration, volcanoes), and an outflow (photosynthesis, runoff, ocean absorption.) However, most people tend to pattern match how a stock changes, by the changes in either the inflow or the outflow (Stave, 2010.) For example, if emissions from fossil fuels or volcanoes increases, students assume the stock will accumulate carbon. In dynamic systems, outflows are not always constant. Rather, outflows can behave independently of inflows, or be regulated by changes in the stock or the inflows.


The explorable simulation below allows you to change the inflow rate and outflow rate over 30 years. By clicking on the graphical input by the inflow and outflow you can change the pattern of behavior. Also, in the graphical input below the stock predict how the stock will behave given your changes to the flows. This is fun. Predict the change in the stock’s behavior before you run the simulation to test your systems thinking skills.





Here is an assessment I give my students to test their systems thinking skills. Match flows A, B, and C with the stocks X, Y, and Z. The answer key is at the bottom of this post. While the system is simple, one input, one output, understanding their dynamics can be confusing. If we are to help people, appreciate the accumulations of carbon emissions, and the actions required to maintain sustainable levels of emissions, we need heuristics that can teach these systems. Having students experience systems by perturbing and creating computational models can help reduce the cognitive load necessary to become systems thinkers.


Figure 1: Assessment 1



Assessment 2:

Here is another assessment I have given to middle school students, high school students, and science teachers at a technology conference. In all cases, nearly 100% of the audience answers question 1 correctly, and around 15% of the audience answers question 2 correctly. This assessment is based on work from John Sterman and Krystyna Stave. Examine Figure 2 below. Answer the following questions to understand accumulations with dynamic sources and sinks.

  1. What year is the highest rate of carbon dioxide added to the atmosphere? (Flow question)

  2. What year is the amount of carbon in the atmosphere rising? (Stock question)


Figure 2: Stock and flows dynamic


Check the answer key yourself. Run the simulation. Play with others. Accumulations, slow and fast, our changing our world and their trajectory is extremely challenging to reverse. Understanding accumulations in the context of inflows and outflows is an important aspect of our changing world.















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Assessment 1 Answer Key:

Flows A = Stock Z, Flows B = Stock Y, Flows C = Stock X

Assessment 2 Answer Key:

Answer Key:

1 = Year 26, 2 = Year 19



Here are the major stocks and flows of the carbon cycle reported by the IPCC that I used for the simulation.

                                                                                            7.3 The Carbon Cycle and the Climate System - AR4 WGI, 2007




Works Cited

"7.3 The Carbon Cycle and the Climate System." 7.3 The Carbon Cycle and the Climate System - AR4 WGI Chapter 7: Couplings Between Changes in the Climate System and Biogeochemistry. Web. 19 Apr. 2017.

Stave, Krystyna. "Participatory System Dynamics Modeling for Sustainable Environmental Management: Observations from Four Cases." Sustainability 2.9 (2010): 2762-784. Print.

Sterman, John D. "Does Formal System Dynamics Training Improve People's Understanding of Accumulation?" System Dynamics Review 26.4 (2010): 316-34. Print.

Team, ESRL Web. "ESRL Global Monitoring Division - Global Greenhouse Gas Reference Network." ESRL Co2 Trends RSS. 01 Oct. 2005. Web. 30 Apr. 2017.


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