                  Review Topics Home Carbon Dioxide Concentration Algebra with Functions Greenhouse Information

## Impact

This module examines the possible impact of changes in atmospheric carbon dioxide concentration.

### Comprehension

Questions

1. What are some possible effects of increase in carbon dioxide concentration?
2. What might happen if global temperature increases significantly?
3. Do you think that carbon dioxide concentration will continue to increase at the same rate that it has for the last fifty years?
4. How does increase in global temperature affect ocean levels?
5. What are some of the controversies regarding global warming?

Acquisition
Mathematical Topics
The mathematical topics required for this study are listed in the menu to the left. Click on the topics if you need to learn more or refresh your memory.

Information/Assumptions
Since the mid thirties, carbon dioxide concentration has increased. An increase in carbon dioxide concentration corresponds to an increase in average global temperature, and this in turn leads to increased ocean level. The exact mechanisms are very complicated and there is real disagreement among scientist as to exactly what the effect is. In this module we will make certain assumptions and see what consequences we can predict. You can then choose other assumptions and see what outcomes would follow. Since 1979, scientists have generally agreed that a doubling of atmospheric carbon dioxide increases the earths average surface temperature by 1.5-4.5°C (3-8°F) (http://www.epa.gov/global warming). There is less agreement about how this changes ocean levels, but we will use a "moderate" assumption that a 3°C increase in global temperature raising ocean levels approximately 0.3 meters (about one foot).

Assumptions
1. The trend in atmospheric CO2 concentration derived in the previous part continues. If you did not complete the first part, click here to retrieve the function which describes the trend.

2. Doubling the pre-industrial level of CO2 corresponds to a 3°C increase in average global temperature

3. The relation between CO2 concentration and temperature increase is linear.

4. A 3°C increase in average global temperature corresponds to a 0.3 meter (about 1 foot) increase in ocean level.

5. The relation between temperature increase and rise in ocean level is linear.

Objectives:
to predict the change in global temperature from pre-industrial time; and
to predict ocean level change from pre-industrial time.
Application
It is estimated that an increase in carbon dioxide concentration corresponds to a change in global temperature and a change in global temperature corresponds to a change in ocean level. The relations can be shown with this diagram, where CO2:

Recall (from module I) that according to our model carbon dioxide concentration was at the pre-industrial level of 280 ppm in 1935 (t = -65). This will be our base level for global temperature and ocean level:

Objective 1 First we will write a linear function to describe global temperature change as a function of atmospheric carbon dioxide concentration where the temperature change is 0°C when the carbon dioxide concentration is at the pre-industrial level of 280 ppm, that is, since 1935. Use a (C,GT) coordinate system, where

C = CO2 concentration in PPM,

and

GT = global temperature change since 1935.

GT measures how much the temperature changes from the pre-industrial times. According to our model for CO2 concentration, the concentration was at the pre-industrial level of 280 ppm in 1935 and so we assume that T = 0 and C = 280 in 1935.

1. To write the equation we need two points.

a. The first point comes from the pre-industrial level which was 280 PPM and corresponding global temperature change of 0°C. Write the coordinates of that point, using a (C,GT) coordinate system.

b. The second point comes from our doubling assumption: a doubling of the concentration corresponds to an average global temperature increase of 3°C. Write the coordinates of that point.

2. Write the equation of the line through the two points you determined in #1.

3. Interpret the slope of the line in #2.

Now we write global temperature change as a function of time.

4. Replace C in your equation by the function C(t) you derived previously. Call this function G(t). What does this new function describe?

5. What is the slope of this function?

6. What does this slope describe?

Objective 2 Now we will write a linear function to describe change in ocean level as a function of change in temperature (that is, if you know how much the temperature changes, predict the corresponding change in ocean levels. Use a (OL,GT) coordinate system, where

OL = change in ocean level since 1935 (in meters)

and

GT = global temperature change since 1935.

Here we assume that OL = 0 and GT = in 1935.

1. To write the equation we need two points.

a. The first point comes from the 1935 level which was an ocean level change of 0 meters and corresponding global temperature change of 0°C. Write the coordinates of that point, using a (C,T) coordinate system.

b. The second point comes from assumption #4: a 3°C increase in average global temperature corresponds to a 0.3 meter (about 1 foot) increase in ocean level.

2. Write the equation of the line through the two points you determined in #1.

3. Interpret the slope of the line in #2.

Now we write ocean level change as a function of time.

4. Replace GT in your equation by the function G(t) you derived previously. What does this new function describe?

5. What is the slope of this function?

6. What does this slope describe?

Reflection
Revisiting the Problem Although most scientists agree that there is a relationship between increased carbon dioxide concentration and rising global temperature, the relationship is complicated and there is not agreement on the amount of increase.

Scenario 2 Now assume that doubling of atmospheric carbon dioxide from the pre-industrial era level of 280 PPM increases the earths average surface temperature by 1.5°C. (This is the low assumption.) Redo the problem with this assumption.

Scenario 3 Now assume that doubling of atmospheric carbon dioxide from the pre-industrial era level of 280 PPM increases the earths average surface temperature by 4.5°C. (This is the high assumption.) Redo the problem with this assumption.  