problem solving activity climate change and feedback loops answer key

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AP®︎/College Environmental science

Course: ap®︎/college environmental science   >   unit 8.

• Ocean acidification
• Climate emergency: feedback loops - albedo

Climate emergency: feedback loops - permafrost

• Climate change

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Video transcript

• JOIN A TRAINING

Climate Change Feedback Loops and Tipping Points

Our climate has been pushed to its limit. Yet, because of our continued reliance on fossil fuels, the planet continues to warm – and the impacts are getting worse.

Many facets of our climate-regulating system are already acting as part of dangerous positive feedback loops – creating compounding climate conditions and worsening impacts for people all over the world.

It’s a vicious cycle – climate change causing a cascade of effects that result in even more climate change. Irreversible tipping points are just around the corner.

What does all that mean? Discover more in our latest  free  fact sheet, “Climate 101: Feedback Loops and Tipping Points.”

In this downloadable PDF, we explain what climate feedback loops are and how they can spiral out of control, escalating to truly dangerous tipping points beyond which, well, we don’t really have all of the answers.

Get yours now.

2 f Equilibrium and feedback loops in climate system

f. The interconnectedness of Earth's systems means that a significant change in any one component of the climate system can influence the equilibrium of the entire Earth system. Positive feedback loops can amplify these effects and trigger abrupt changes in the climate system. These complex interactions may result in climate change that is more rapid and on a larger scale than projected by current climate models.

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This Overlooked Feedback Loop Is Accelerating Climate Change

By Tufts University March 16, 2024

Climate models must account for numerous factors, including overlooked natural processes like soil degradation. Soil, holding 80% of the Earth’s carbon, releases greenhouse gases under drought conditions, potentially exacerbating climate change. New research highlights the importance of incorporating soil health into climate predictions and advocates for sustainable land use to mitigate these effects. Credit: USDA

Scientists at Tufts University state that soil, which contains 80 percent of the Earth’s carbon, emits more greenhouse gases as droughts cause soils to crack due to drying.

The precision of climate models is influenced by numerous elements, including greenhouse gas emissions stemming from industrial operations and transportation, emissions from farm animals, the expansion of urban areas and the reduction of forests, as well as the reflection of solar rays off snow and other ground surfaces. Additionally, natural occurrences such as volcanic eruptions play a role and are factored into these models.

However, some other natural processes have been overlooked. Farshid Vahedifard, professor and Louis Berger Chair in civil and environmental engineering, points to an important one that lies directly beneath our feet and covers most of our planet above water.

In a study published in Environmental Research Letters , Vahedifard notes that soil stores 80 percent of carbon on Earth, and with increasing cycles and severity of droughts in several regions, that crucial reservoir is cracking and breaking down, releasing even more carbon dioxide and other greenhouse gases into the atmosphere. In fact, it may be creating an amplified feedback loop that could accelerate climate change well beyond current predictions.

“This process has not been sufficiently evaluated in the existing literature or incorporated into models,” said Vahedifard. “If we don’t consider the interplay of drought, soil desiccation cracking, and CO 2 emissions, that could result in significant inaccuracies when modeling and predicting climate change. There are other repercussions as well. Poorer soil health can lead to reduced photosynthesis and lower carbon dioxide uptake, and it can compromise the structural integrity of earthen dams that protect against floods.”

Additional Feedback Loops and Climate Change

There are also other amplifying feedback loops that may not have been fully accounted for in climate change models, he said. These include melting of sea ice and exposure of darker ocean surfaces that absorb more heat from the sun. The increase of wildfires due to warm, dry conditions releases a lot of carbon dioxide into the atmosphere, which in turn creates hotter, drier weather more conducive to fires.

Another amplified feedback loop is the thawing of Arctic and sub-Arctic permafrost, which also releases carbon dioxide into the atmosphere and raises climate temperature, leading to more melted permafrost.

Cycle of drought, drying and cracking soil, and ground carbon release creates and amplified feedback loop that has not been accounted for in most models of climate change. Credit: Farshid Vahedifard, Tufts University

But soil changes caused by drought could be as significant, if not more significant, than any of those factors. Drought, manifested by long periods of low soil moisture content and high temperature, leads to cracking in fine-grained soils, sometimes extending meters below the surface. The cracks result in more exposure to the air, increased microbial activity and breakdown of organic matter, released carbon dioxide, and loss of nutrients and ability to support plant growth, reducing carbon dioxide sequestering.

The deep cracks expose much older reserves of carbon that had previously been stable and protected. The permeation of air into the soil accelerates the release of not only carbon dioxide from organic matter but also other greenhouse gases like nitrous oxide .

Small animals like earthworms and millipedes that help turn the soil over are also affected by the reduced moisture and increased air exposure, being less able to play active roles in nutrient cycling and soil structure maintenance. That, in turn, increases the likelihood of soil cracking and aeration.

“The amplifying effect of soil carbon feedback loops and its interactions with other loops could carry us across tipping points and lead to even more severe and permanent shifts in climate,” said Vahedifard.

He noted that government agencies and policymakers need to promote sustainable land use, “which can include adoption of precision irrigation techniques and water conservation practices, and use of drought tolerant crops,” he said. “Organic fertilizers and compost can enhance soil organic matter content and improve soil water-holding capacity. Of course, this can only help if it’s part of a comprehensive effort to reduce greenhouse gas emissions from all human activity.”

Reference: “Amplifying feedback loop between drought, soil desiccation cracking, and greenhouse gas emissions” by Farshid Vahedifard, C Clay Goodman, Varun Paul and Amir AghaKouchak, 5 March 2024, Environmental Research Letters . DOI: 10.1088/1748-9326/ad2c23

The study was funded by the U.S. National Science Foundation.

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1 comment on "this overlooked feedback loop is accelerating climate change".

“Small animals like earthworms and millipedes that help turn the soil over are also affected by the reduced moisture and increased air exposure, …”

What role does moisture play in the bacterial decomposition of organic material in soil? I suspect it is significant with every day experience of how moisture accelerates rot in most things. Also, increased exposure to air will reduce methane production, which is touted as having a higher potential global warming impact than CO2.

Yes, Carbon Cycle models leave a lot to be desired. They leave out a lot of anthropogenic emissions [ http://wattsupwiththat.com/2015/05/05/anthropogenic-global-warming-and-its-causes/ ] and they appear to do a poor job of estimating respiration from the roots of seasonally-dormant trees, particularly Boreal trees south of the tundra. The recent Carbon Cycle models show plant respiration at about half of photosynthesis, and only include CO2 from terrestrial volcanoes.

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Solving the Carbon Dioxide Problem

Students use information from Project Drawdown to learn about the sectors where climate solutions are being implemented to help slow down climate warming. Students construct a plan for using specific solutions to reduce and remove the amount of carbon dioxide in the atmosphere, and make a claim describing how their plan could work to keep global temperature change below 1.5 °C .

Learning Goals

• Students will analyze the sources and sinks of carbon dioxide in the atmosphere to determine the complexity and uncover questions.
• Students will investigate and evaluate current solutions for reducing the amount of carbon dioxide in the atmosphere
• Students will propose a plan to use viable mitigation strategies for meeting the demand of reducing atmospheric carbon dioxide and consider the challenges associated with each strategy
• Students will make a claim, supported by evidence and reasoning, as to how their plan will remove enough carbon dioxide from the atmosphere to limit global warming to 1.5 °C.
• Laptops or tablets with access to the Project Drawdown website for each group
• Sector Analysis Planning Sheet
• Carbon Dioxide Solutions: Plan Guide
• Emissions Sources and Natural Sinks diagram (as PDF  or Google Slides )
• Staying Below 1.5 Degrees of Global Warming diagram (as PDF  or Google Slides )
• Chart paper, markers, or digital format for students to make their visual presentations
• Sticky notes

Preparation

• Students will benefit from having some knowledge of the carbon cycle and the role of carbon dioxide emissions in climate change. Plan to have a discussion or lesson to introduce these ideas before beginning this activity.
• Plan for student grouping arrangements in advance. In Part 1, six groups of students are needed; each group will focus on analyzing a different sector. In Part 2, it might be best to create new groups that contain one student from each of the sector groups from Part 1.

Part I: Uncovering the Parts, Purposes, and Complexities of Reducing Carbon Dioxide in the Atmosphere (70 minutes)

• Ask students to think about the challenge of slowing climate warming by reducing the amount of carbon dioxide in the atmosphere. How would we get started? What actions would we need to take as a society?
• Ask students to share observations from this diagram. What do you notice? What do you wonder about? (They might notice that there are more sources than sinks, that more than half of the carbon dioxide that enters the atmosphere is staying there, that some sources are adding more carbon dioxide than others, etc.)
• Make connections between student wonderings and previous experiences your class has had about the carbon cycle and carbon dioxide sources/sinks.

• reducing greenhouse gases and sources of carbon dioxide entering the atmosphere
• increasing sinks to remove carbon dioxide from the atmosphere
• improving society through education and health (not shown as part of the diagram, but an important cross-cutting component).
• Tell students that coming up with solutions to reduce and remove carbon dioxide within each sector is complex, but not impossible. Share the quote from Project Drawdown: “Almost daily, there is promising evolution and acceleration of climate solutions.”
• Electricity Production
• Food, Agriculture, and Land Use
• Transportation
• Sinks: Land, Coastal & Ocean, Engineered

Note: you could split Sinks into two groups if needed, making land sinks its own group and coastal, ocean and engineered sinks another group.

• Parts : Define the components of this sector. How does the sector contribute to the problem of climate change? In what different areas are solutions needed? Provide information to help us really understand this sector and how to address it. Include data where possible.
• Purposes : Explain how addressing different parts of this sector will help reduce atmospheric carbon dioxide. What is their role? Provide 1-2 examples of the type of solutions that are currently being implemented in this sector, and explain how they will help. 
• Complexities : What are the challenges with implementing solutions to this sector? What further developments are needed to make reducing atmospheric carbon dioxide in this sector successful? What questions do you have?

Sector Analysis Example (for teacher reference)

Sector - Electricity * Note: most all of this information can be found on the Project Drawdown website.

PARTS : Many parts of our everyday lives (if you live in a developed or developing nation) require electricity, from our homes to transportation, work, and manufacturing of goods and services. Most electricity today is created by burning fossil fuels, which releases lots of carbon dioxide in the atmosphere. About 25% of greenhouse gas emissions comes from generating electricity. Climate solutions are needed in the following areas: we need to enhance the efficiency of things that use electricity, we need to shift the production of electricity from fossil fuels to renewable energy, and we need to improve technologies for transmitting and storing electricity so that renewable energy supply can meet demand.

PURPOSES : Enhancing energy efficiency in buildings and industry will decrease the amount of electricity that needs to be generated. Buildings and industry are the largest users of electricity, so decreasing their energy draw will decrease the amount of fossil fuels that are burned at the power plants. Using alternative energy sources like wind, solar, water, or even nuclear will allow us to move away from burning fossil fuels for electricity, which will drastically decrease the amount of carbon dioxide that is entering the atmosphere. Upgrading our entire electricity system will allow us to use electricity generated from alternative sources better. Advancements in storing energy from the Sun and wind will make these energy sources available even when Sun and wind are not present. Examples of ways to improve efficiency are adding insulation and using LED lighting. And installing micro wind turbines provides a clean source of electricity to rural areas without access to a centralized grid.

COMPLEXITIES : Efforts to transfer electricity production away from fossil fuels need to increase so that this can happen on a much shorter timeline. And it is challenging to provide equal access to electricity solutions to everyone. The technology to improve energy storage is underway, but it is not yet usable on a global scale. It seems uncertain if every community will be able to afford the new technologies that are needed to shift away from fossil fuels. Possible questions: How much of an impact does improving energy efficiency in my home make? How can we speed up the transition away from fossil fuels? What is a bigger obstacle-- cost or innovation (ie, do we have the technology but lack the funds, or do we still have a long way to go to invent the technology)?

• Students will be successful finding most all of the information to complete this part of the assignment from the Project Drawdown- Sectors webpages, but encourage them to research further (from reliable sources!) as needed and to spend time learning about any terms or concepts they encounter along the way that are unfamiliar to them.
• At the beginning of the next class period, have students present their sector analyses as a gallery walk, or as group presentations. Spend about 20 minutes before moving on to Part 2.

Part II: Exploring Solutions (80 minutes)

• Even if we could reduce carbon dioxide emissions to zero immediately, the climate has already warmed about 1 °C above what it was in pre-industrial times, and will continue to warm for many years.
• Thus, to prevent environmental changes that will be extremely difficult to adapt to, scientists have determined that we must limit global temperature increase to 1.5°C (which means only 0.5°C more in warming).
• Present the challenge: Even with rapid emissions reductions, the world will need to remove about 10 gigatons of CO2 from the atmosphere every year by mid-century and 20 gigatons of CO2 per year by 2100. (Source: National Academies of Sciences, Engineering, and Medicine)
• Use 2050 as "mid-century" and assume that carbon removal ramps up steadily from 10GtC/year in 2050 to 20 GtC/year in 2100.
• Example: Starting from the year 2020, we need to remove 300 GtC by 2050 (at a rate 10 GtC/year). From 2050-2100, we need to remove an additional 751.2 GtC, which means an extra 0.2 GtC each year to ramp up to 20 GtC/year by 2100. This means we need to remove a total of 1051.2 GtC between 2020-2100.
• For the purposes of this activity, we will use removal of 1000 GtC by 2100 as our target goal . You may choose to use the exact value calculated, adjust the directions accordingly if so.
• GtC = gigatons of carbon; 1 gigaton = 1 billion metric tons; a metric ton = 1000 kilograms or 2204.6 pounds (an English system ton is 2000 pounds).
• Have students calculate how many kilograms or pounds are equal to 1000 GtC.
• About how much carbon dioxide are we currently adding to the atmosphere each year? (about 40 Gt/yr)
• What is significant about 2050, according to the diagram? Explain. (2050 is the target to reach net-zero carbon dioxide emissions, which means human activities are no longer increasing the amount of carbon dioxide that is in the atmosphere. Mitigation and carbon removal actions are needed to make this happen.)
• Why are negative emissions needed in the future? (Because we are already experiencing climate warming due to increasing the amount of carbon dioxide in the atmosphere, it is not enough to stop adding carbon. We must also remove the excess carbon dioxide from the atmosphere to slow down climate warming.)
• Why is the conventional mitigation techniques (blue) part of the plan so much larger than the carbon removal approaches (green) part? (Mitigation, or reducing the amount of carbon dioxide that we are adding to the atmosphere, is the biggest priority right now. Carbon dioxide removal is important too, but large-scale carbon removal requires technologies that are not widely available at this time. To get to net-zero, wide-scale mitigation solutions are needed.)
• Discuss terms used in the diagram, such as "net-zero" and "negative emissions" to ensure common understanding.
• Point out that in 2018, global carbon dioxide emissions totaled 37 billion tons, which is a value that might be helpful in the next steps as students begin to construct their plan.

• Rather than having students return to their group from the day before, it might be best to create new groups that contain one student from each of the sectors (E.g. one student who was in the electricity group; one from the Food, Agriculture, & Land Use group; one from the Industry group; one from the Transportation group; one from the Buildings group; and one from the Sinks group).
• Orient students to the website, showing them that each solution can be accessed from the Solutions page , and also in the Table of Solutions . From the table, solutions can be sorted by sector, which might be helpful. Students should focus on carbon dioxide removal values from the Scenario 2 column, which aligns with the 1.5 °C goal. Scenario 1 values align with the 2 °C goal. Note: The Paris Agreement of 2015 set the goal of keeping global temperature increase below 2 °C, while also striving to meet the 1.5 °C goal, which is why both scenarios are presented.
• Point out that the solutions are based on a "reasonable yet optimistic" forecast for how the solution will be enacted in the future. Thus, it is important to consider a range of potential impacts from each solution.
• Choose one solution to look at together as an example, pointing out the various information that can be found (carbon dioxide reduction value, cost, description, etc.) and also the Technical Summary link, which often contains more information than is needed for the assignment, but could be helpful when thinking about limitations and other details.
• Students should consider the Staying Below 1.5 Degrees of Global Warming diagram as well, to help them approximate the proportion of carbon dioxide emissions reduction to carbon dioxide removal approaches that might work best.
• There are more potential solutions than are provided on the Project Drawdown website. In fact, more innovations come about all the time. Encourage students to research additional ideas about solutions if they desire, but remind them that they will need to make sure there is a way to include how much carbon dioxide will be saved from any solution they include. Have students brainstorm how they could include solutions that they cannot quantify in their plan (perhaps as a section about possibilities for the future, for example).
• A Claim that explains their plan for reducing atmospheric carbon dioxide by 1000 Gigatons by 2100. A diagram that walks us through their plan may be helpful here.
• Name and briefly describe how it reduces the amount of carbon dioxide in the atmosphere.
• What sector does it address?
• How much carbon dioxide can it remove by 2050?
• How much does it cost to implement and/or maintain?
• What, if any, limitations are there to this solution?
• Are there places that the solution might work better than others, or will it likely work well anywhere on Earth? Why? (E.g., consider how ecological, economic, political, or social conditions might affect how well the solution works in a particular area.)
• Reasoning that justifies their climate solution choices. In the reasoning, they should also mention any questions that remain unanswered or limitations to their plan.
• Provide students access to Internet-enabled devices and the link to the Project Drawdown Solutions website.
• Students might find it helpful to use sticky notes and/or chart paper as they design their plans.
• Discuss additional supplies needed for group presentations, such as poster board, or presentation tools (like Google Slides or PowerPoint).
• Consider what scaffolds or supports your students might need to be successful during extended group work, such as assigning group roles.

Part III: Sharing Our Plans (50 minutes)

• If students have made posters to communicate their plans, consider holding a gallery walk, and encouraging 1-2 group members to remain at their group’s poster to answer any questions their classmates might have about their plan. Group members could take turns staying to answer questions and visiting other group’s posters throughout the classroom.
• Alternatively, each group could present their plan to the entire class one at a time with presentation slides that share their visuals. Encourage questions and answers following each presentation.
• Consider having students rank solutions and discuss why they chose to rank them as they did. You could rank according to: solutions with the greatest impact on carbon dioxide reduction, solutions with the greatest implementation range, or solutions with the greatest likelihood of success.
• Steer students towards a final concluding idea: there is no one solution to climate change. All of the solutions are needed, including more that we haven’t discovered yet. Climate change solutions will vary from one community to the next, depending on their unique needs and capabilities, but our ability to reach the 1.5 °C goal is greatest when the entire global community participates in finding solutions.

The Carbon Cycle and Climate Change

Most of the carbon on Earth is sequestered in rocks, but it is also stored in the ocean, the atmosphere, soils, and plants. Carbon cycles between the Earth's spheres (geosphere, hydrosphere, biosphere, and atmosphere), sometimes quickly, like when fossil fuels are burned, and sometimes slowly, like when layers of sediment and shells form rock on the ocean floor. The movement of carbon between Earth's spheres is naturally balanced, but human activities since the Industrial Revolution are adding carbon to the atmosphere in a way that is out of balance. Rapid increases in the amount of carbon dioxide entering the atmosphere is causing the climate to warm. The extra carbon dioxide that is added to the atmosphere can remain there for centuries. To put the system back into balance, we must drastically reduce the amount of carbon entering the atmosphere and also remove carbon dioxide from the atmosphere to the other spheres.

Learn more about the carbon cycle:

• https://scied.ucar.edu/learning-zone/earth-system/biogeochemical-cycles
• https://earthobservatory.nasa.gov/features/CarbonCycle

The Role of Carbon Dioxide in Climate Warming

Carbon enters the atmosphere both through natural processes, such as decomposition or volcanic eruptions and also as a result of human activity, such as burning fossil fuels. Carbon dioxide and methane (CH4) are two types of greenhouse gases that trap energy from the Sun in the atmosphere, which causes the planet to warm. Without any greenhouse gases, the Earth would be too cold to sustain life at current levels, but with the current rapid increase of greenhouse gases, the climate is warming too much. Human-caused carbon emissions have been rising since the 1850s when the Industrial Revolution brought about wide-scale use of combustion engines and the burning of coal for electricity. The concentration of CO2 in the atmosphere is increasing along with the increase in human-caused carbon dioxide emissions, as seen in the graph below.

The warming climate is causing many changes on Earth, such as melting ice sheets, sea level rise due to thermal expansion of ocean waters, and changing weather patterns which lead to drought in some areas and intensified storms in others. As more carbon dioxide enters the water, the oceans are becoming more acidic, which is harmful to marine ecosystems. The effects of increased carbon dioxide in the atmosphere are compounded by feedback loops, in which warming leads to more warming. For example, when warming surface temperatures cause ice sheets to melt, less energy from the Sun is reflected from the darker, ice-free surface, and instead is absorbed, which leads to more warming. Because of these and other types of feedback loops, the effects of adding carbon dioxide to the atmosphere are often compounded.

Learn more about the role of carbon dioxide in climate warming:

• NOAA Climate Change: Atmospheric Carbon Dioxide

Reducing and Removing Greenhouse Gases to Slow Climate Warming

To stop climate change, we need to reduce the amount of greenhouse gases, like carbon dioxide, in the atmosphere. There are two main ways that we can stop the amount of greenhouse gases from increasing: we can stop adding them to the air and we can increase the Earth's ability to pull them out of the air.

This is called climate mitigation . There is not one single way to mitigate climate change. Instead, we will have to piece together many different solutions to stop the climate from warming. Many of these solutions are already being implemented in places around the world. Some can be tackled by individuals, such as reducing energy use, riding a bike instead of driving, driving an electric car, and switching to solar power. Other actions to mitigate climate change involve communities, regions, or nations working together to make changes, such as: switching power plants from burning coal or gas to renewable energy sources, and growing public transit.

Learn more about removing carbon dioxide from the air:

• Negative Emissions Technologies and Reliable Sequestration: A Research Agenda

Project Drawdown

Project Drawdown is a non profit research organization that exists as a resource to educate about climate solutions. They help to advance climate actions by reviewing and assessing climate solutions to ensure that communities, businesses, and even governments, are armed with the information they need to implement effective actions. "Drawdown" refers to the time in Earth's future when levels of greenhouse gases in the atmosphere are steadily declining. Many resources, including a download of The Drawdown Review publication, are available from their website at no cost.

Parts, Purposes, and Complexities Routine

The Parts, Purposes, and Complexities routine is one of Harvard’s Project Zero Thinking Routines which provide structure to help make student thinking visible. The Parts, Purposes, and Complexities routine can be used when introducing and exploring ideas to help students think about the complexity of a system or object and is used in this activity as a way to help students analyze the complexity of the different sectors where climate solutions are needed. As with any new classroom practice, the first time students engage with it they may need extra support. There are tips for launching the Parts, Purposes, and Complexities routine with your students provided along with the description of the routine at the link above.

• Ask students to consider the following: Project Drawdown is ranking solutions based on their carbon dioxide reduction potential, but what other factors did you consider when making your plan?
• Have students make a list of the pros and cons of considering other factors (such as cost, unique needs of certain communities, social implications) and not just carbon dioxide reduction.
• Hold a discussion, using the students' list of pros and cons.

Related Resources

• Biogeochemical Cycles
• A Degree of Concern: Why Global Temperatures Matter
• Investing in Carbon Removal: Demystifying Existing Approaches
• Impacts of 1.5 degrees of Global Warming on Natural and Human Systems
• Global Warming: Not Reversible, But Stoppable
• To truly grasp what we're doing to the planet, you need to understand this gigantic measurement

Related Activities

• Mitigation or Adaptation?
• Carbon Dioxide Sources and Sinks Activity
• Climate & Water Teaching Box
• The Very Simple Climate Model Activity
• Modeling Carbon Dioxide with a Bathtub

This activity was developed by Melissa Rummel at the UCAR Center for Science Education .

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Developing Student Understanding of Complex Systems in the Geosciences Topical Resources

• ⋮⋮⋮ ×

What Constitutes a Complex System?

This summary was written by Carol Ormand , SERC.

• Feedback loops , where change in a variable results in either an amplification (positive feedback) or a dampening (negative feedback) of that change
• Many strongly interdependent variables , with multiple inputs contributing to observed outputs
• Chaotic behavior : extreme sensitivity to initial conditions, fractal geometry, and self-organized criticality
• Multiple (meta)stable states , where a small change in conditions may precipitate a major change in the system
• A non-Gaussian distribution of outputs, often where outcomes that are far away from the average are more likely than you might think

Systems Consist of Components and Their Relationships

Examples are as diverse as the global economy, the human nervous system, ecosystems, the climate system, and the Earth system. The Earth system consists of the atmosphere, hydrosphere, biosphere, and lithosphere (solid Earth, including the soil) and the interactions among those spheres.

Cycles Within Systems

One way to examine a system is to study the movement of material within it. For example, the hydrologic cycle tracks the movement of H 2 O through the Earth system. Water may be temporarily stored in the atmosphere (in clouds), in the hydrosphere (in the oceans, rivers, lakes, or other surface waters, or in snow or glacial ice), in the biosphere (in plants, animals, or other living organisms), or in the lithosphere (in groundwater, soil, pore spaces in bedrock, or even within "hydrous" mineral grains in solid rock). Water moves from one sphere to another through a wide variety of processes. Any place water can be stored is a called a reservoir; the motion of water from one reservoir to another is called a flux. On the diagram to the right, the words and arrows represent fluxes. More generally, any cycle can be depicted as a collection of reservoirs with a set of related fluxes. The water cycle is a small, but significant, part of the Earth system. Learn more about what constitutes Systems Thinking from InTeGrate.

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Feedback Loops Can Amplify or Dampen Change

Feedback mechanisms have been described as a threshold concept for understanding complex systems, a concept "difficult to learn but transformative once mastered" (Kastens et al., 2009). A feedback loop is a mechanism by which change in a variable results in either an amplification (positive feedback) or a dampening (negative feedback) of that change.

We are familiar with feedback in our everyday lives in many contexts. For example, a thermostat uses feedback to regulate air temperature within a building. During the winter, a rise in temperature to the desired level signals the thermostat to turn off the furnace (dampening the increase in temperature = negative feedback). This causes the temperature within the building to stabilize, and then to begin to cool as heat is lost to the exterior. This signals the thermostat to turn the furnace on again (also a negative feedback, because it reverses the decrease in temperature). Negative feedbacks act to maintain a system's current, stable state.

Positive feedback mechanisms, in contrast, act to amplify change. For example, when the Earth's atmospheric temperature rises, evaporation increases, which causes an increase in atmospheric water vapor concentration, which causes an additional rise in atmospheric temperature through the greenhouse effect, which causes more evaporation, and so on. If there were no other factors contributing to atmospheric temperature, this rise in temperature would spiral out of control. Fortunately for life on Earth, there are many factors that affect the temperature of our atmosphere.

In addition to the challenges presented by the concept of feedback loops, the terminology itself can confuse students, who may think that "positive" feedback is good and "negative" feedback is bad. This misunderstanding is exacerbated by common (mis)usage of those terms ( Kastens, 2010 ).

Strongly Interdependent Variables: Changes Can Have Unintended Consequences

In a complex system, there are many variables, and they are strongly interdependent. This makes it difficult to know exactly which inputs contribute to an observed output, and the extent of each factor's contributions. For example, an increase in the average global temperature can be caused by changes in the solar radiation budget, changes in the composition of the atmosphere (such as a change in the concentration of water vapor), changes in the Earth's albedo (the amount of solar radiation reflected by snow and ice cover), or a combination of all of those factors. Moreover, those factors are not independent of one another: changes in atmospheric composition can lead to changes in precipitation rates, which can lead to changes in the percentage of land covered by snow and ice, thus changing the Earth's albedo.

Because the variables in a complex system are so strongly dependent on each other, changes to system inputs can have unintended, unanticipated consequences. This is one reason why accurate prediction of the behavior of complex systems is so difficult. (Some climate change deniers use this to argue that human impacts on climate are still debatable. Climate scientists, however, overwhelmingly agree that our global climate is changing as the result of human activities ( IPCC, 2007 ( more info ) ).) Examples of such unanticipated consequences brought about through human interaction with complex systems range from the proliferation of antibiotic-resistant bacteria to fluctuations in the global economy.

Complex Systems Exhibit Chaotic Behavior

Chaotic behavior is characterized by extreme sensitivity to initial conditions, fractal geometry, and self-organized criticality (Turcotte, 2006).

Sensitivity to initial conditions

The concept of sensitive dependence on initial conditions has been popularized in the so-called "butterfly effect": the idea that a butterfly flapping its wings in Brazil could change the weather in Texas. Minute differences in the initial conditions for such a system result in extremely different outcomes. Edward Lorenz discovered this property while studying thermal convection (Lorenz, 1963), and from it correctly inferred the difficulty of long-term weather prediction. The butterfly effect refers to the idea that the flap of a butterfly's wings would be enough to change the initial conditions of the Earth's atmosphere, thus having a profound effect on global weather patterns. While this may seem far-fetched, it begins to make sense when you consider the strong level of interdependence of the system, its nonlinearity, and the possibility for signal amplification via feedback .

Fractal geometry

Benoit Mandelbrot coined the term "fractal" to describe a special set of self-similar curves. Self-similarity implies that an object looks the same at any scale. Many natural objects approximate fractal geometry, such as clouds, snowflakes, river drainage systems, and coastlines. In fact, geographic coastlines are "so involved in their detail that their lengths are often infinite or more accurately, undefinable" (Mandelbrot, 1967). Mathematically, self-similarity requires a power-law distribution of representative objects. In other words, as the size of an object decreases, there is a corresponding power-law increase in the number of objects of that size. For example, the ratio of second-order streams to first-order streams in a drainage basin is very nearly equal to the ratio of third-order streams to second-order streams, or to the ratio of fourth-order streams to third-order streams, and so on (Turcotte, 2006).

Self-organized criticality (SOC)

Self-organized criticality is the concept that a dynamic system will move toward a critical, or emergent, state, by natural processes. It is perhaps most easily understood via an example. This concept was introduced by Bak, Tang and Wiesenfeld in 1988 to explain the behavior of a cellular automaton (CA) model. In their model, sand is dropped randomly into a square array of boxes (cells). Sand grains accumulate in each box until it holds four grains. At that point, the four grains are redistributed: one to each of the four nearest neighboring boxes. If the addition of those grains to the neighboring boxes triggers another redistribution, the chain reaction is referred to as an avalanche. Simulations of this model show that the size of the avalanches (number of boxes involved in chain reaction events) follows a power-law distribution. Moreover, many natural events (including avalanches, landslides, forest fires, and earthquakes) have been found to exhibit power-law frequency-area behavior (Bak et al., 1988, cited in Turcotte, 2006).

The critical, or emergent, state of a natural sand pile is a circular cone where the sand surface has reached the angle of repose. In that state, the addition of sand will lead to an avalanche of some size, thus maintaining the angle of repose (and the conical shape of the pile). The system, or sand pile, achieves this state -- a metastable, or "critical" state -- through a series of avalanches, without any interference from external forces or processes. This is what is meant by "self-organized" criticality (Herbert, 2006).

Multiple (Meta)stable States: Small Changes Can Cause Major Consequences

Metastability describes a system that is in a delicate state of equilibrium -- a state where a small change in conditions may precipitate a major change in the system. The chaotic nature of complex systems -- and particularly their sensitivity to initial conditions -- means that they are often either not in equilibrium or are metastable. The alternation of Ice Ages and Interglacial periods over the past two million years of Earth's history suggests that these two climactic conditions are metastable states for our planet.

A Non-Gaussian Distribution of Outputs: "Unlikely" Events Are Less Unlikely

A "normal," or Gaussian distribution is a bell-shaped distribution clustered around an average, such as that shown in the graph on the right. A non-Gaussian distribution is, literally, any distribution that is not Gaussian. However, it often refers to a distribution with "heavy tails," where those outcomes that are far away from the average are more likely than they would be in a Gaussian distribution. Complex systems exhibit non-Gaussian outputs.

What this means in practice is that "improbable events are orders of magnitude more likely than events that follow the Gaussian distribution. Estimates and predictions of system future behavior, particularly Gaussian estimates, formed by observations collected over short time periods provide an incorrect picture of large-scale fluctuations" (Herbert, 2006). This is true for all kinds of complex systems, from financial systems to Earth systems.

Bak, P., Tang, C. & Wiesenfeld, K. 1988. Self-organized Criticality, Phys. Rev. A, v. 38, p. 364-374.

Herbert, 2006. Student Understanding of Complex Earth Systems. In C. Manduca and D. Mogk (Eds.), Earth and Mind: How Geologists Think and Learn about the Earth : Geological Society of America Special Paper 413, p.95-104.

Intergovernmental Panel on Climate Change, 2007. Climate Change 2007: Synthesis Report ( more info ) . Online at http://www.ipcc.ch/publications_and_data/publications_ipcc_fourth_assessment_report_synthesis_report.htm; accessed 4 December, 2009.

Kastens et al., 2009. How Geoscientists Think and Learn. Eos, Transactions, v. 90, n. 31, p. 265-266.

Kastens, 2010. Going Negative on "Negative Feedback." Earth and Mind blog: http://serc.carleton.edu/earthandmind/posts/negativefeedbac.html. Accessed February 17, 2010.

Lorenz, 1963. Deterministic Nonperiodic Flow. Journal of Atmospheric Sciences, v. 20, p. 130-141.

Mandelbrot, 1967. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science, v. 156, p. 636-638.

Roe, 2009. Feedbacks, Timescales, and Seeing Red. Annual Review of Earth and Planetary Sciences, v. 37, p. 93-115.

Turcotte, 2006. Modeling Geocomplexity: "A New Kind of Science." In C. Manduca and D. Mogk (Eds.), Earth and Mind: How Geologists Think and Learn about the Earth : Geological Society of America Special Paper 413, p.39-50.

USGS, The Water Cycle . Online at https://water.usgs.gov/edu/watercycle.html; accessed 16 September, 2009.

Winslow, 1997. Introduction to Self-Organized Criticality & Earthquakes. Online at ftp://ftp.ingv.it/pro/terrasol/materiale_consultazione/SOCEQ.pdf; accessed 07 July, 2016.

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