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Teaching Notes

In this Section

Grade Level

The mathematical calculations and manipulations are designed for upper level high school or college student (multiplying and unit conversion), although younger students should also be capable of the general concepts if the spreadsheet calculations are more fully prepared for them.

Learning Goals 

After completing this unit, users will be able to:

  • Manipulate emission data in a spreadsheet to model future CO2  concentrations.
  • Perform basic carbon cycle mass balance calculations.
  • Interpret results from pre-generated maps and graphs.
  • Gain familiarity with the lexicon of climate research vocabulary.
  • Indentify and select actions necessary to mitigate climate change.

Rationale

Global climate change is recognized by scientists as a significant threat to the health of our planet. Carbon dioxide emissions have increased dramatically in the past decades, resulting in accumulation of this long-lived molecule in the environment, leading to global warming and other climate changes.  Current goals for limiting climate change can address the CO2 emissions directly (e.g., 80% reduction of 1990 emissions by 2050 “80x50” ), or set a goal for the maximum permissible CO2 concentrations in the atmosphere (350 ppm)   or maximum acceptable temperature change (2°C).  Methods to reduce carbon dioxide emissions include energy efficiency and energy conservation, the use of alternative energy resources, and reforestation.  An approach to understanding which of these actions and the extent of the changes required has been developed at Princeton University. This concept uses “stabilization wedges.”  If the entire world contributes to implementing these wedges, current emissions or climate goals could be achieved, thereby slowing further climate changes. However, this is not without cost. It will take a great deal of effort to successfully slow climate change. 

Key Concepts and Vocabulary

350 Challenge: This concept is based on the scientific evidence that the average atmospheric CO2 concentration should not be higher than 350 ppm. At concentrations above this level serious and irreversible environmental and social effects will occur.  http://www.350.org/

Copenhagen Accord: Many heads of states came together at the Intergovernmental Panel on Climate Change (IPCC) meeting in December 2009 in Copenhagen to form a cooperative agreement on limiting global climate change. One component of their end result was the recommendation that average global temperature rise should not exceed 2°C relative to pre-industrial values. http://unfccc.int/resource/docs/2009/cop15/eng/11a01.pdf

80x50 Policy: Former New York Governor Paterson issued an Executive Order stating that by the year 2050, New York State’s carbon emission levels should be reduced to 80% of the levels emitted in 1990.  http://www.nyclimatechange.us/ 

Atmospheric CO2 Concentration: This is the average concentration of CO2 in the atmosphere. It could be the result of CO2 directly emitted into the atmosphere by human or natural processes, or emissions of other carbon molecules (volatile organic compounds or CO) that react with oxygen to form CO2. CO2 concentrations are measured in parts per million by volume (ppm). 

Business as Past: This concept is one projection of possible future carbon emissions and atmospheric concentrations. Researchers analyze how humans have used carbon emitting sources in the past, and model scenarios in the future based on these past trends. Similar to this, Business as Usual assumes that current trends in increased annual greenhouse gas emissions will continue into the future. This is not necessarily the most accurate prediction, as this assumes no change in the energy sources we use or other new trends. Business as Past takes into account how the growth of different technologies has increased in the recent past, as well as predictions of available sources of energy.

Key Concepts:

  • A mass balance on the atmosphere can be used to relate atmospheric CO2 concentration to emissions.
  • Burning of fossil fuels is a major contributor to climate change.
  • Because of the long lifetime of CO2 molecules in the atmosphere, there is a long lag period between our efforts to reduce CO2 emissions and an actual reduction in atmospheric CO2 concentrations.
  • Sometimes the goals set in place by policymakers are not achievable given realistic conditions.

Backgroud Information

Fossil fuel emissions around the world continue to increase. Currently, the U.S. is the second highest emitter of greenhouse gases; China is first. Global emissions in 2010 were approximately 9.7 Gigatons carbon. If no efforts are made to reduce these high emission levels, atmospheric CO2 concentrations will continue to rise at an unprecedented rate and will have negative consequences on our world’s ecosystems and social systems. Many groups and organizations have released appeals and challenges to nations around the world in an effort to mitigate global climate change. The mitigation efforts required to stabilize our climate are significant.  Policy makers have been working to establish goals for a stabilized climate.  There are three basic approaches:

Reduce the total emissions by a specified value: For example, former New York Governor Paterson issued an Executive Order stating that by the year 2050, New York State’s carbon emission levels should be reduced to 80% of the levels emitted in 1990.

Set a goal to limit the maximum change in our global average temperature: The Nations signing the Copenhagen Accord agreed on a safe temperature change on a global scale of no more than 2°C above pre-industrial values. 

This project module uses the Copenhagen Accord’s 2°C maximum global temperature change and the 350 ppm challenge goals to define the necessary changes to limit climate change. The mitigation strategies used should not surpass these two values in terms of global temperature and atmospheric CO2 concentration, respectively. 

Figure 1

In an effort to accelerate mitigation efforts taken by nations, the IPCC has released several Assessment Reports on the future of our climate. Its most recent report in 2007 (AR4) lists 40 possible scenarios for our future. These scenarios are based on many different factors, including population, technology development and global dissemination, which can lead to a wide range of predictions of our climate future. Figure 2 shows predicted future temperatures for several of the IPCC scenarios. Clearly, the particular policies and technologies implemented throughout this century will have a significant impact on the range of carbon emissions. This project uses scenario A1G for the Business as Past model. The IPCC states that A1G is an “‘oil and gas’ rich future with a swift transition from conventional resources to abundant unconventional resources including methane clathrates.” This scenario does not assume ridiculously high levels of carbon emissions, but neither does it rely heavily on renewable energy sources. It’s a realistic estimate of our future fossil fuel emission profile.11

Figure 2

So how exactly does the world go about reducing emissions to prevent this projected significant change in our future climate? To visualize this process, Pacala and Socolow  developed what is known as a system of stabilization wedges (Figure 3), which is a concept for reducing carbon emissions over a 50 year timeframe. Multiple options for reducing emissions are possible, with each option symbolized as one ‘wedge.’ Each carbon-cutting strategy wedge is a triangle shape, indicating that the strategy starts initially with zero emissions reduction at the onset, and will increase to avoid 1 billion tons of carbon emissions per year by 50 years, with a cumulative savings of 25 billion tons of carbon (25 Gigatons) over the 50 years from the start point (Figure 3).

Figure 3

To effectively reduce emissions over 50 years, multiple wedges are needed.  The collection of these wedges is referred to a stabilization triangle (Figure 4). As actions associated with more wedges are implemented, climate change will be mitigated to a greater extent.  The stabilization wedge project of the Princeton Carbon Mitigation Initiative lists 15 different wedges available for implementation (Figure 5). There are four different categories of actions that can be taken:

  • Energy conservation and efficiency
  • Nuclear Power
  • Fossil-fuel strategies
  • Renewables and biostorage

Figure 4

The Princeton Carbon Mitigation Institute website has multiple documents and a teacher’s guide that provide more detail about each of the wedge options.  Some examples of wedges include building a certain number of wind turbines, increasing the efficiency of existing power plants, and reforesting a region. Some wedges are more feasible than others to implement and some cost more than others. There are wedges that can only be used once and others that can be used multiple times (with a blue star next to them).

Figure 5

Scientists have worked to predict climate changes that result from vairous modifications in our greenhouse gas emissions. There are four primary steps in this process:

  1. Predicting global fossil-fuel related carbon emissions.
  2. Correlating these emissions to increased concentration of CO2 in the atmosphere.
  3. Using a global circulation model (GCM) to predict the future climate around the world.
  4. Determining what specific actions are required to meet the climate, emissions or CO2 concentration goals.

In this lesson, a very simple carbon mass balance equation is used to calculate average CO2 concentrations that result from a specified carbon emission rate. Figure 6 illustrates the factors that affect atmospheric CO2 concentrations resulting from carbon emissions (represented by “carbon” in the figure). The tub represents the atmosphere, while the faucet represents carbon emissions from fossil fuel combustion and the drains represent sinks (losses) for carbon dioxide. When fossil fuels are emitted at a high rate, CO2 accumulates in the atmosphere faster than it is depleted – the bathtub is filling up. Thus, the atmospheric concentration of CO2 increases over time, leading to an increased greenhouse effect and higher global temperatures. 

Figure 6

The mass of carbon dioxide in the atmosphere changes every year. CO2 is represented here as only the mass of carbon associated with the carbon dioxide,  If we start with 800 billion tons of carbon (BtC) in the atmosphere, then we add 8 billion tons more by burning fossil fuels, but lose 4 billion tons to the ocean and biosphere, we end up with 804 BtC in the atmosphere after one year (800 + 8 – 4 = 804).  After another year with the same sources and sinks, we would have 808 BtC in the atmosphere.  The overall mass balance can be written as:

Mass of C in atmosphere at the end of the year = Mass of C in atmosphere at the beginning of the year + carbon sources (fossil fuel emissions) - carbon sinks (ocean and land)

There are 1000 kg per metric ton, and 1000 g per kg (= 106 g/ton), so 800 BtC can be converted to 800x1015 g C.

CO2 concentrations in units of parts per million by mass can be calculated from the mass of carbon in the atmosphere by assuming that the mass is equally distributed throughout the mass of the atmosphere (5.13x 1018 kg) (From Atmospheric Chemistry and Physics by Seinfeld and Pandis):

Atmospheric concentration: ppm by mass (ppmm):

Equation 1

Atmospheric concentration units of ppm by volume (ppmv) are equal to ppm by moles, so that mass ration can be converted to a mole ratio with the appropriate molecular weights (MWatm = 28.7 g atm/mol):

Equation 2

These calculations are included here for teacher understanding since they are included in the calculations that are automatically performed within the spreadsheet that the students will use. They are not required for student learners, however.

Instructional Strategies

General Approach

This unit takes students through the process of predicting and interpreting our future climate based on changes in the estimated future emissions of CO2.  The students start with one of the predicted future emission profiles (IPCC SRES A1G – global economic focus with a high rate of gas use), and then determine what mitigation efforts are required to meet climate goals that are based on the following:

  • reduction in carbon emissions (NYS' 80x50 plan);
  • limit to acceptable atmospheric CO2 concentration (350 ppm); and
  • limit to acceptable increase in temperature (2°C higher than pre-industrial levels).

An overview of the logical flow of this unit is shown in Figure 7. The students use a prepared MS Excel spreadsheet that has predicted CO2 emissions.  They choose the number of stabilization wedges they would like to implement and the future CO2 concentrations are calculated automatically within the spreadsheet through mass balance equations.  The students can check if they meet the 350 ppm and 80 x 50 goals based on the MS Excel spreadsheet.  Determination of the predicted temperature change associated with these predicted emissions requires the use of a global circulation model.  The educational model EdGCM was run during the development of this project and model results are available to students as contour maps of predicted temperature and global average temperature anomalies.  The model is available to students through a free 30-day demonstration period and could be used in the classroom by advanced students.  However, due to the slow computation times, we have chosen to provide the results of this model rather than expecting students to run the model themselves.

Figure 7

Prior to completing this project, students should be introduced to Pacala and Socolow's stabilization triangle concept. Knowledge of the general global carbon cycle and the changes in this cycle due to anthropogenic emissions over the last century is also recommended. The instructions tell the user to calculate all the reductions for all scenarios, along with resulting concentrations. To save time or to make it challenging, ask the students to calculate only one or two scenarios (number of wedges) and compare results at the end of the lesson. 

Implementation

Anticipatory Set Present a plot of carbon dioxide (or carbon) emissions over the last century (Figure 8) to provide a basis for discussion:  (see mitigation.ppt file for this and other graphics to use in class)

Figure 8

  • What does nearly 10,000 million metric tons really mean? (1x104 x 1x106  x 1x103 kg/ton = 1x1013 kg; a large man (220 lbs) ~100 kg, so this would be the equivalent of 1x1011 “men” emitted as carbon each year. Current population ~7 billion people (7 x 109), so that is more than the weight of 10 large men of carbon emitted for each individual on this planet.  In reality, this value would be closer to 100 large men worth of carbon emitted for every U.S. citizen.
  • What has contributed to the increased carbon dioxide emissions due to fossil fuel consumption?  (increased global population and affluence, energy consuming technologies such as cars, air conditioners, electronics….)
  • Are we concerned with the significant emissions (and accumulation) of carbon in the atmosphere? Why or why not?(yes – climate change – increasing temperatures, droughts/floods, habitat destruction…)
  • What happens to the carbon dioxide that is emitted to the atmosphere?
  • Present the bathtub concept and simple mass balance to show why we are concerned with CO2 accumulation. Note that the sinks are the ocean and land uptake (mostly photosynthesis), but when emissions (sources) are greater than sinks, the bathtub (atmosphere) will fill up with more CO2 molecules.
  • If we are concerned about these numbers and want to decrease carbon dioxide emissions, what do you think we can do? (energy efficiency and conservation, public transportation, renewable energy, nuclear energy, etc.)

Introduce the concept of “wedges” and that some number of wedges is needed to reduce our carbon emissions.  Project graphics of wedges or print and hand out paper “wedges” as a manipulative from the teacher guide (pp. 15-16) prepared by the Princeton Carbon Mitigation Institute.  Have each student select five wedges that they think would be feasible.

  • Do they think this will be enough action? If not, any guess about how many needed?
  • How do we know what is enough? (Introduce climate goals - 80% reductions (relative to 1990 values by 2050; Atmospheric CO2 concentration < 350 ppm; and/of global average temperature anomaly ≤2°C over pre-industrial levels)

Indentify the goal of this module: to estimate how many wedges are required to meet the climate change mitigation goals and to indentify which wedges should be used.

Procedure (Students may work in groups of 2 or 3)

  1. Open the MS Excel spreadsheet and change the number of wedges (in increments of 5, up to 25) to assess if you can reach the 80x50 or 350 ppm goals with 5 wedges.  If not, try other values. Note the desired number of wedges.
  2. Review the EdGCM results (printed or electronic version of contour maps and global average temperature anomalies) to evaluate the effectiveness of the chosen number of wedges in meeting the 2°C maximum temperature increase.
  3. Revisit the stabilization wedges chart and develop a plan by selecting which wedges or combination of wedges should be implemented on a worldwide basis. The US does not need to do all of it.

Closure At the end of the activity, students should discuss what was necessary to achieve the goals. They should learn that it takes a lot of effort (in the form of many wedges) to mitigate global climate change. Review what their choices were and total $ sign value of their selections. The consequences, or cost, of implementing these wedges should also be discussed here – relative to the cost and feasibility of not doing anything to mitigate carbon dioxide emissions. It might be easy to do in theory, but in the real world getting society to cooperate on a scale such as this is difficult. 

Suggested timeline:

  • Day 1: Introduction - carbon cycle/mass balance examples, mitigation brainstorm, climate goals, introduction to project statement (two days may be required depending on extent of material previously covered).
  • Day 2: Group work with spreadsheet to evaluate how many wedges required to meet 350 ppm and 80 x 50 emission reduction goal
  • Day 4: Review EdGCM to evaluate the predicted temperature anomalies for the number of wedges selected.
  • Day 5: Evaluate which wedges to choose
  • Reporting out - discuss results as a class

Learning Concepts

This module was developed for an AP Environmental Science class. While the basic concept of mitigation through emission controls is not overly complex, the mathematical calculations and manipulation of spreadsheets may present challenges.

This project includes aspects of technology (mitigation technologies), science and mathematics.  It could be adapted with a greater focus on mitigation technologies for a technology or pre-engineering class.  The project could also be coupled to a civics or government class with a focus on the policies and changes to society that would be necessary to implement the extensive changes to our energy and social systems as shown in this project.

The module is also appropriate for upper level Mathematics classes. Solving a real-world problem would bring relevance to data manipulation and /or database work. 

It should also be pointed out that the spreadsheet manipulation could be limited or adjusted so that this lesson could be used with lower level/grade level students.  The basic premise and mitigation strategy has merit and lends itself to discussion.

STEM Standards

The following New York State Mathematics, Science and Technology (MST) Standards are supported by this unit: (http://www.p12.nysed.gov/ciai/standards.html )

Standard 1: Students will use mathematical analysis, scientific inquiry, and engineering design as appropriate, to pose questions, seek answers, and develop solutions.

  • The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing creative process.
  • Engineering design is an iterative process involving modeling and optimization finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints. 

Standard 4: Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

  • Explain how living and non-living environments change over time and respond to disturbances

Standard 7: Students will apply the knowledge and thinking skills of mathematics, science and technology to address real-life problems and make informed decisions.

  • Design solutions to real world problems on a community, national, or global scale, using technological design process that integrates scientific investigation and rigorous mathematical analysis of the problem and the solution.

Standard 6: Students will understand the relationship and common themes that connect mathematics, science, and technology and apply the themes to these and other areas.

  • Models are simplified respresentations of objects, structures, or systems used in analysis, explanation, interpretation, or design.
  • Indentifying patterns of change is necessary for making predictions about future behavior and conditions.

Standard 7: Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real life problems and make informed decisions.

  • The knowledge and skills of mathematics, science, and technology are used together to make informed decisions and solve problems, especially those relating to issues of science/technology/society, consumer decision making, design, and inquiry into phenomena

Mathematics Standards

The following National Common Core Mathematics Standards are supported by this module:

(http://www.corestandards.org/the-standards/mathematics )

Students will be able to:

A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

S-ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

Assessment

The student worksheet should be completed by all students and submitted as part of the assessment of this module. The module could also be treated as a laboratory with a formal (or informal) laboratory report.

Resources and Files:

Student Worksheet

Student Spreadsheet

Wedge Choices

EDGCM climate modeling results

Mitigation strategies powerpoint presentation

Princeton University Carbon Mitigation Initiative's Wedges Game