## Carbon Dioxide Concentration
Impact

### Comprehension

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

### Comprehension

**Questions **
- What are some possible
effects of increase in carbon dioxide concentration?
- What might happen
if global temperature increases significantly?
- Do you think that
carbon dioxide concentration will continue to increase at the
same rate that it has for the last fifty years?
- How does increase
in global temperature affect ocean levels?
- 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://yosemite.epa.gov/oar/globalwarming.nsf/content/ClimateFutureClimate.html).
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 raises ocean levels approximately 0.3 meters
(about one foot).

**Assumptions**

- 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.
- Doubling the pre-industrial
level of CO2 corresponds to a 3°C increase in average global
temperature
- The relation between
CO2 concentration and temperature increase is linear.
- A 3°C increase
in average global temperature corresponds to a 0.3 meter (about
1 foot) increase in ocean level.
- 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 assumed 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:

t = years from 2000

CO2 = atmospheric carbon
dioxide concentration

GT = average global
temperature change

OL = average global
change in ocean level

Recall (from module I)
that according to our model carbon dioxide concentration was at
the pre-industrial level of 280 ppm in 1932 (t = -68). 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 1932.
Use a (C,GT) coordinate system, where

C = CO2 concentration
in PPM,

and

GT = global temperature
change since 1932.

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 1932 and so we assume that GT
= 0 and C = 280 in 1932.

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

Now we write global temperature change as a function of time.
- Replace C in your
equation by the function C(t) you derived previously. Call this
function G(t). What does this new function describe?
- Estimate the annual
increase in G(t) for the year 2000; for the year 2010.

**Objective 2** First
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 1932 (in meters)

and

GT = global temperature
change since 1932.

Here we assume that OL
= 0 and GT = in 1932.

- To write the equation
we need two points.

**a**. The first point comes from the 1932 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.
- Write the equation
of the line through the two points you determined in #1.
- Interpret the slope
of the line in #2.

Now we write ocean level change as a function of time.
- Replace GT in your
equation by the function G(t) you derived previously. What does
this new function describe?
- Estimate the annual
increase in G(t) for the year 2000; for 2010.

**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.

**Additional Questions**

- What assumptions went
into your model(s)?
- How valid do you
think these assumptions are?
- What events would
change your prediction(s)?