Jenna Miller
Professor Steiner
EAS 217
4 October 2013
Lab 3: Response to Perturbation in the Carbon Cycle
Introduction:
The focus of this lab is on determining the effects which different perturbations have in terms of
long term stability of the Carbon Cycle. This is accomplished in STELLA computer
programming, which provides the ability to create complex models including various conditions
and perturbations that may occur. The modeling of the carbon cycle is the third piece in a study
of dynamic systems and their possible representations. The Carbon Cycle in this lab is in many
ways simpler to model than the previous rock cycle, yet it requires the addition of a greater
number of outside factors which influence the state of the cycle. This requires a greater
knowledge of STELLA and shows another piece in system dynamics modeling. In this cycle
carbon accumulates in three reservoirs, the atmosphere, the oceans and limestone. The
equilibrium of this model can be undermined by a variety of changes in earth’s conditions. This
lab tests the results of increased tectonic activity, over both short and long periods of time, and of
an increase in sea level. I hypothesize that due to the vastness of the carbon cycle, a short term
increase in tectonic activity will not have long term effects on the model. Instead, for a short time
increased activity will increase melting of limestone and metamorphism, both of which release
carbon into the atmosphere. Thus that reservoir will display a short term increase in volume,
after which it will return to a steady state quickly. A long term increase in tectonic activity,
however, will have a greater effect on the carbon cycle’s stability. The continued increase will
make it more difficult for the cycle to regain stability and the increases of carbon released into
the atmosphere could alter the state of the system over a long time period. Likewise an rising sea
level could have a long term increase in the atmospheric CO2. As the sea level rises, the area of
land exposed to weathering will decrease. This will disrupt the important negative feedback loop
which removes CO2 from the atmosphere, and thus lead to a net increase in the volume of
carbon in that reservoir.
Materials/ Methods:
This lab requires a computer, STELLA software, a lab manual and a lab notebook. To begin the
lab open STELLA and set up a model of the carbon cycle. The model should include following
the reservoirs and volumes: atmosphere (600Gt C), oceans (3.8E4) and limestone (48E6), and the
processes and rates: weathering (=7E4*EXP(Delta_T/13.7)), sedimentation
(=7E4*(Oceans/3.8E4)) and melting, and metamorphism (=7E4*(Limestone/48E6)*tectonic
pulse). Also include the following converters: Delta_T (=4.6*(relative_atmos_C^.364)-4.6),
Relative_atmos_C (=Atmosphere/600), Rel_limestone (=Limestone/48_6), Rel_ocean_C
(=Oceans/3.8E4) and Tectonic_pulse (model as a graphic representation of a steady state at 1
over 2 units of time).Connect to appropriate reservoirs and processes (See fig. 1).
Figure 1- Carbon Cycle Model
Run the cycle over 2 Million Years (1 unit should equal 1 million years) and check to verify that
the model is in a steady state. Next, run the model with an initial atmospheric value of 1200 Gt
C. To simulate long term tectonic activity increase modify the tectonic pulse converter to 2 and
run the model over 2 My. To simulate short term tectonic increase return all values to 1, with the
exception of .4, which should remain at 2. Run this new model over 2 My.
Add sea level converter to the model and program it as a graphical function of Del_temp. Add a
ocean_area converter as well and define it as a graphical function of sea_level. Next, add another
converter for cont_area, connect to ocean_area and define as “cont_area=1-ocean_area”.
Redefine weathering and sedimentation to be effected by the new converters using the following
formulas:
-Weathering=(7E4*EXP(Delta_T/13.7)Cont_area/.29
-Sedimentation=7E4*(Oceans/3.8E4)*ocean_area/.71
Set Tect_pulse to 2 and graph over 2 My. Save all graphs and models.
Data/Results:
The data from this lab shows the response in the carbon systems to the three modeled
perturbations. However, before introducing these new processes, it was necessary to show the
response time to a one time change in volume in a reservoir in the cycle.
Figure 2- Response time in the Carbon Cycle
Here the volume of carbon in the atmosphere was changed to 1200 Gt (twice its initial value).
The carbon cycle returns to equilibrium after about .3 My. The one time increase has no long
term effect on the state of the cycle. The oceanic crust shows a slight increase which returns to
equilibrium rate after .6 My. There is no effect on the limestone reservoir. These responses to
change in volume represent the lag time of each reservoir (See figure 3).
Response time in Carbon Cycle
Oceans
Limestone
Lag Time
Atmosphere
0
0.1
0.2
0.3
0.4
0.5
0.6
Lag Time (My)
Figure 3- Response time of Carbon Cycle to Doubling in Initial Atmospheric CO2
After determining this response time, the first experiment was to model the response to a short
term increase (for 200,000 years) in tectonic activity. Tectonic activity was increased to twice its
normal value.
Figure 4- Pulsed Tectonism in the Carbon Cycle
The increase, which takes place from .4-.6 units of time leads to a spike in volume or carbon in
the atmospheric reservoir. The volume reaches its peak at .5 My and declines back to its normal
rate at approximately 1My. It is interesting to note that the volume of carbon in the ocean crust
also shows some change over this time period, rising slightly at .4 My for a period of about 1
My. The limestone reservoir shows no change.
The next experiment was to increase tectonic activity to twice its value for a sustained time
period of 2 My.
Figure 5- Sustained Increased Tectonism in the Carbon Cycle
With a long term increase in tectonic activity the volume of atmospheric carbon increased
rapidly and permanently (for the set period of time). The carbon increases exponentially until it
reaches about 23 times its normal volume at approximately 1 My, where it levels off. The ocean
crust also shows a lesser, but sustained, increase in volume of carbon (shown more clearly in fig.
6). Unlike the atmospheric reservoir, the carbon in the ocean crust has not leveled off by 2 My,
but continues to slowly increase.
Figure 6- Sustained Increase in Tectonism in the Carbon Cycle on a Smaller Scale
The last experiment was to introduce change in sea level. This model shows the effects of a rise
in sea level over a sustained period of time.
Figure 7- Sea Level Rise in the Carbon Cycle
This graph shows a similar increase in atmospheric carbon as does increase tectonic activity.
However, the volume of carbon continues to rise for longer, leveling out around 1.25 My. The
volume also is larger with the effects of the rising sea level, reaching about 30 times its normal
volume. The volume of carbon in the ocean crust shows slow, but continuous increase over 2
My.
In addition to these experiments, the carbon cycle was explored by calculating residence times
for a molecule of carbon in each reservoir. The longest residence time by far is in the limestone
reservoir. The other two reservoirs have comparatively very short residence times (see fig. 8)
Carbon Cycke Reserviors
Residence time
Oceans
Limestone
Residence time
Atmosphere
0
100
200
300
400
500
600
700
Residence Time (My)
Figure 8- Residence time of Carbon Cycle Reservoirs
Discussion:
The apparent correlation between these graphs is logically explained. Let us first compare
residence and lag times (fig. 3 and 8). The residence times of oceanic and atmospheric CO2 are
relatively very short, 0.543 and 0.009 My respectively, thus they show both quick responses to
short term change and quick returns to equilibrium. Predictable, the slightly longer residence
time of CO2 in oceanic crust (in comparison to atmospheric CO2) leads to a longer lag time, by
about .1 My. The incredibly long residence time of CO2 in limestone, 685.714 My, provides
reasoning for its steady state throughout each experiment.
These correlations are present in the results of the three experiments. The first experiment which
increases tectonic activity for a short period of time shows the more dramatic and brief increase
in volume of CO2 in the atmospheric reservoir. This is to be expected due to the short residence
and lag time of a carbon in this reservoir. When the tectonic activity increases, the reservoir
gains CO2 from the increase of the processes of metamorphism and the melting of limestone.
However, soon after tectonic activity returns to normal, the increase volume is cycled through an
the atmosphere returns to its stable composition. In this experiment the oceanic crust also should
in increase in volume that was smaller and for a more sustained period of time. This fits in with
the longer lag time of the reservoir. Limestone, a reservoir with incredibly large volume, and
long residence and lag times, shows no change at all with such a brief disturbance. The results of
the second experiment are similar to those of the first. The volume atmospheric carbon rises
exponentially and levels off after less than 1 mY. The volume of carbon in the oceanic crust rises
more slowly, and by less, but does not level off within the 2 mY that we tested. Again the
volume of limestone insulates it from effects of changes over only 2 My. It would be interesting
to see if there would be a response in the limestone reservoir if the time span was increased even
further.
The change in sea level produce similar to increased tectonism, yet larger in scale. While in the
second experiment the volume of CO2 in the atmosphere rises to approximately 23 times its
initial value, in the third experiment it reaches about 30 times that. The volume of CO2 in the
oceanic crust also rises here, and as in experiment two it does not level off by 2 My. This was
somewhat similar to my hypothesis, as I predicted that the rise in the ocean level would decrease
the feedback mechanism of weathering on land which takes CO2 out of the atmosphere.
However, I did not realize how large of an increase in volume this would trigger in the
atmospheric carbon. I was also surprised that the volume of CO2 in the ocean crust was effected
in both experiments, which I had not predicted.
There are many other factors which are not taken into account in this experiment. Sea level is
influenced by a complex network of causes. One of which is vegetation, which scientists believe
could be a negative feedback on atmospheric C02 and work to hold temperature constant (Volk).
This would help stabilize sea level change. A positive feedback which we did not discuss is ice
melt, as the ocean rises the atmospheric CO2 increases which leads to an increase in temperature.
This causes glacial melt which raises the sea level further. These are only two of the many
positive and negative feedbacks which had an effect on the carbon cycle. They begin to show
just how difficult it is to create an accurate model of this, or any, dynamic earth system. Despite
this, modeling a simplistic version of the carbon cycle did help to provide some basic knowledge
about the system and how it could respond to outside factors. I would have liked to explore the
system on a larger geologic timescale to see if any change would occur in the volume of CO2 in
limestone and to see the leveling out of the volume of CO2 in the oceanic crust.