MATERIALS:

• The Very, Very Simple Climate Model (online interactive activity)
  • eo.ucar.edu/staff/rrussell/climate/modeling/co2_climate_model.html
• Computers with Internet (web) access
• Adobe Flash plugin/player installed on computers
• Paper and pencils, poster board and markers, or PowerPoint for optional assessment

DIRECTIONS:

Introduction:

1. Ask students what they have heard about future climate change from newspapers, the Internet, and television. If time allows, have students find and then share articles about future climate change. Discuss how greenhouse gases, such as carbon dioxide, that are emitted to the atmosphere are, in large part, causing recent climate change. The Windows to the Universe page entitled "Global Warming: Scientists Say Earth Is Heating Up" provides a summary.
2. Tell students that models are used to predict how Earth's climate will change in the future. In general, a computer model uses math to describe how the Earth works. Have students read the Windows to the Universe page entitled "What Is a Climate Model?" and then discuss what models are. (You may wish to have your students continue on and read "How Climate Models Work" and "Accuracy and Uncertainty in Climate Models" too.)

Interactive Activity: Part 1 - Learning how the model works

1. Tell students that they will use a model to test what will happen to the atmosphere and climate over this century depending on the amount of carbon dioxide released into the atmosphere.
2. Tell students that they will use a model to test what will happen to the atmosphere and climate over this century depending on the amount of carbon dioxide released into the atmosphere.
3. Introduce the variables to the left of the graph (see figure below) that students can manipulate as they run the model. The carbon dioxide emissions rate is measured in gigatons of carbon dioxide per year. Depending on your students' math skill level, you may wish to introduce the concept of rate at this point.

4. Ask students what would happen to Earth's temperature in the future if each year we released the same amount of carbon dioxide into the atmosphere as we did in the year 2000. That rate was around 9 gigatons of carbon per year (9 GtC/yr). Instruct students to set the carbon dioxide emissions rate to 9 gigatons (it should be set around 9 as the default.) Instruct students to set the "Timestep size" to 10 years using the popup menu. This means that every time they tell the model to advance, it will move ahead 10 years of "model time."
5. Instruct students to click the "step forward" button 10 times to get data to appear through the 21st Century. Each time they click the button three points will appear on the graph. The color of these points correlates with the colors of the three y-axis measures. (The figure above shows the resulting graph.)
6. Discuss as a class what this graph is showing.
   • The blue triangles (emissions rate) represent how much carbon we add to the atmosphere each year. Since the rate stayed the same for this model run, the blue triangles form a horizontal line on the graph.
   • Black dots represent how much carbon has accumulated in the atmosphere over time. Units are "parts per million by volume" (ppmv). For reference, the actual concentration was around 368 ppmv in the year 2000. In this run, the concentration rises from less than 400 ppmv to over 500 ppmv by the year 2100.
   • Red dots represent average global temperature in degrees Celsius. For reference, this value was around 14.3° C in the year 2000. In this model run, the temperature steadily rose to about 16° C by the year 2100. In this simple model, the temperature is determined entirely by the atmospheric CO₂ concentration via greenhouse warming of the atmosphere.

Interactive Activity: Part 2 - Testing different scenarios of climate change

1. Ask students if they think the first model run will reflect what people will do over the 21st Century. The actions of humans are the largest unknown when it comes to future climate change. Survey student opinions: Will we release the same amount of carbon dioxide into the atmosphere that we do now? Will we release less? Will we release more?
2. Brainstorm how and why carbon emissions may change in the future. For example, carbon emissions will go up if more power plants are created that burn fossil fuels, yet carbon emissions will go down if more technologies are invented that reduce the use of fossil fuels.
3. Based on the survey and brainstorms, have students work in groups to come up with a scenario that they would like to test. (Example: carbon dioxide emissions rise through the middle of the 21st Century, and then decline after that.) To be somewhat realistic, they would need to start with emissions around 8 GtC/yr since that is what it was in the year 2000. To help students focus as they run the model, have student groups write out their scenario in a paragraph before they begin.
4. To reset the model so that it can be run again, instruct students to click the "Start Over" button (near the lower left corner). Instruct students to set the timestep as 10 years as they did before. Demonstrate for them how they can change the emissions rate during the Century by changing the rate, clicking "step forward", and then changing the rate again. (For example, if you had decided to increase emissions for the first half of the century and then decrease them for the last half, you would need to increase the rate for each timestep for the first 50 years and then decrease the rate for each timestep for the last 50 years.)
5. Discuss as a class the results of various student scenarios: What happened to temperature and carbon dioxide concentrations over time? Is some global warming enevitable? Which scenario had the least warming? Which had the most?

SUGGESTED ASSESSMENT:

You may wish to have students (or student groups) present their results from Part 2 to the rest of the class in an oral report, posters, or PowerPoint slides.

SUGGESTED EXTENSIONS:

Have students make an experiment using the Very, Very Simple Climate Model by testing whether there is a difference in resulting global temperature between two scenarios.

Have students read the page "Tackling the Global Warming Challenge" and then brainstorm things they could do to reduce the amount of greenhouse gases that are released into the atmosphere.

Combine this activity with "Carbon Dioxide: Sources and Sinks" and the "Carbon Cycle Game" to develop student understanding of where atmospheric carbon dioxide comes from, where is goes, and how long it stays in the atmosphere.

BACKGROUND INFORMATION:

Climate scientists use models to understand how the Earth is changing. Models of Earth can be experimented upon to assess the impact of various perturbations on the planet. Climate models describe our planet with mathematical equations. Because Earth is complex, it takes hundreds of very complex equations to model the atmosphere, oceans, and land surface. Because of the complexity, climate models are usually run on powerful computers.

The Very, Very Simple Climate Model is, as the name implies, very simple. In this model, average global temperature is determined entirely by the atmospheric carbon dioxide concentration via greenhouse warming of the atmosphere. The impacts of the Earth's biosphere, changes in land use, wind and precipitation patterns, other greenhouse gases, uptake of carbon dioxide by the oceans and other factors are not considered by this very simple model. Many of these factors decrease the amount of carbon dioxide in the atmosphere over time.

George E.P. Box once said, "all models are wrong, but some models are useful." The more a complex system like Earth is simplified in a model, the more wrong the model is. However, in simplifying this model to temperature and carbon dioxide, The Very, Very Simple Climate Model allows students to focus on the cause and effect relationships of greenhouse gases and climate change. A major educational point embodied in this model is that temperatures depend on concentration, which rises whenever emissions are greater than zero. When you hear world leaders saying that they are working hard to reduce the rate of growth of greenhouse gas emissions, remember that reducing the rate of growth does not lead to reduced temperatures. Instead, the amount of greenhouse gases continues to grow in the atmosphere whenever emissions are greater than zero.

The assumptions behind this model, though rather limited, are valid as far as they go. The starting values for concentration, emission rate, and temperature are right around actual values for the year 2000. The ranges for emission rate choices are in line with predictions scientists think we are likely to see in this Century. The relationship between atmospheric carbon dioxide concentration and temperature is well-established; basically, temperature rises about 3° C for each doubling of carbon dioxide concentration. So, for example, if the concentration goes from 400 ppmv to 800 ppmv, we expect to see temperature go up by 3° C.

According to the Intergovernmental Panel on Climate Change and their 2007 Assessment Report, Earth’s average temperature rose 0.6° Celsius (1.1°F) during the 20th Century. Based on the results from about a dozen computer models, the IPCC projects that global warming will continue. Model results project that Earth's average global temperature will rise between 1.8° and 4.0° Celsius (3.2° and 7.2° F) depending largely on how humans change the ways they live on the planet.

Details of the Math Behind the Model

Based on a mix of theory and observations, scientists now know approximately how much Earth's surface temperature as CO₂ levels increase... everything else being equal, which is, of course, never the case. Stated simply, a doubling of the atmospheric concentration of CO₂ is expected to produce about a 3° C (5.4° F) rise in average global surface temperatures.

An example: the CO₂ level in the year 2000 was 368 parts per million (ppm), while the average global temperature was 14.3° C (57.7° F). If, in the future, the CO₂ concentration were to rise to 736 ppm ( = 2 x 368 ppm) we would expect global temperatures to rise roughly 3° C (5.4° F) to 17.3° C (63.1° F). CO₂ concentration would have to double again to 1,472 ppm ( = 2 x 736 ppm) to cause another 3° C (5.4° F) temperature rise to 20.3° C (68.5° F).

Mathematically, here's the formula which expresses this relationship:

Let's look at an example calculation. What would we expect the average temperature (T) to be if the CO₂ concentration rose to 600 ppm? Let's use 14.3° C for T₀ (in 2000) and 368 ppm for C₀.

T = T₀ + S log₂ (C / C₀) = 14.3° C + [ 3° C x log₂ (600 ppm/ 368 ppm)]
= 14.3° C + [ 3° C x log₂ (1.63)] = 14.3° C + [ 3° C x 0.705] = 14.3° C + 2.1° C = 16.4° C

The "climate sensitivity" factor, S, is actually an estimate. According to the Fourth Assessment Report by the IPCC (Intergovernmental Panel on Climate Change), the climate sensitivity value is "likely to be in the range 2 to 4.5° C with a best estimate of about 3° C, and is very unlikely to be less than 1.5° C. Values substantially higher than 4.5° C cannot be excluded, but agreement of models with observations is not as good for those values." We have used 3° C for climate sensitivity in this simple model.

How does the CO₂ emission rate affect the CO₂ concentration level? Based on estimates of the total quantity of CO₂ in the atmosphere (in gigatons, abbreviated GtC) and of the CO₂ concentration, every 2.3 GtC of emissions would be expected to raise atmospheric CO₂ concentration by 1 ppm. So, if emissions in a given year were about 7 GtC, we would expect CO₂ concentration to rise by almost 3 ppm ( = 7 GtC ÷ 2.3 GtC) that year. Total global carbon emissions were around 8.2 GtC in 2000, and had climbed to 9.2 GtC by 2006.

To keep this model simple, a couple of major factors were left out. We intend to add them as optional elements in the simulation in the future.

• Ocean Absorption of CO₂: Sea water absorbs carbon dioxide from the air, creating carbonic acid in the water. Scientists estimate that roughly a third of the anthropogenic CO₂ released into the atmosphere is (currently) absorbed by Earth's oceans. Thus, only about 2/3rds of emissions actually go towards increasing the atmospheric concentration of CO₂. Over time, as more carbon is sequestered into the oceans and the oceans therefore become more acidic (as a result of the carbonic acid produced), scientists expect that the oceans will be able to absorb less and less CO₂ from the atmosphere. Thus, in the future, we expect a higher percentage (than the current 67%) of emitted CO₂ to remain in the atmosphere... thus promoting greenhouse warming.
• Residence Time of CO₂ in Earth's Atmosphere: Carbon dioxide is constantly cycled between the atmosphere, oceans, soil, living creatures, rocks, and so on. Every year, some of the CO₂ humans have emitted into the atmosphere is naturally absorbed by other elements of the carbon cycle, reducing atmospheric CO₂ concentration and thus greenhouse forcing. However, it takes a very long time for excess CO₂ in the atmosphere to naturally migrate to other carbon reservoirs. As an example, if we had completely eliminated all anthropogenic carbon dioxide emissions in 2000 (and every year hence), scientists estimate that by the year 2100 CO₂ concentration in the atmosphere would drop to about 12% below year 2000 levels. Because of this long residence time of CO₂ in the atmosphere, the omission of this factor from our simple model is a relatively minor source of inaccuracy.

More Sample Model Runs

There a few common types of carbon emission level scenarios your students might try with this simple model:

• What if carbon emissions were held at current levels? (This is illustrated in the graph in the "Interactive Activity: Part 1 - Learning how the model works" section above.)
• What if carbon emissions continue to rise?
• What if carbon emissions continue to rise during the first part of the 21st century, then are held stable or even reduced in the latter part of the century?

The latter two scenarios are illustrated in the sample model runs below. There are some important features of each of these scenarios, largely independent of the exact values used, that you might want to point out to your students.

1. When CO₂ emissions rise steadily, atmospheric CO₂ concentration rises at an accelerating pace (its curve "bend upwards").
2. Temperature rises less sharply than atmospheric CO₂ concentration. This is because one must double the CO₂ concentration in order to generate a fixed 3° C (or whatever climate sensitivity value you employ) increase in temperature.
3. Even if emissions are reduced to zero, in this model the atmospheric CO₂ concentration and temperature will not go back down. This simple model has, effectively, an infinite residence time for CO₂ in the atmosphere.

Sample Scenario: Continuously Rising CO₂ Emissions

Sample Scenario: Emissions Rise During 1st Half of Century, Then Fall to 1990s Levels

This writeup is available online at:

http://eo.ucar.edu/staff/rrussell/climate/modeling/co2_climate_model_activity.html