Calculus Project – Modeling Climate Change
Global warming is a big deal, but it can be difficult to predict the weather ten days from now, let alone
twenty years into the future. One way scientists study climate change is using computer programs that
model weather patterns.
In this assignment, you will use a computer model that simulates the greenhouse gas effect responsible
for climate change. You will employ your knowledge of calculus to study this model and draw
conclusions from it.
The model we will be using is described in the Tutorial section below. You should work through the
tutorial first before returning here to finish the rest of the assignment.
In Calculus, we study rates of change in a context where the answers are always neat and tidy. The real
world is messy, and this assignment is about exploring rates of change in that messy environment. Write
up a well-organized essay that answers each of the questions below. The essay should be at least 1000
words although I care less about the length of your essay and more about how effectively and
thoroughly you answer each question.
1. What is the greenhouse gas effect, and how does the model we’re using simulate it? Make sure you
include proper citations (both inline citations and a works cited page at the end of your essay). You can
find citations for the model itself by clicking on “Model Info” at the bottom of the page and scrolling
down to where it says “How to Cite”. For some terms like albedo, you will have to find citations
elsewhere. You can use Wikipedia as a starting point, but you should cite a different source in the final
2. Find a model with no clouds and no CO2, where the average global temperature does not go above
25°C in the first 5000 ticks. What were the settings for this model? Use Excel or Google Sheets to find a
quadratic trendline for this model.
3. Find the derivative of your quadratic trendline, and use this to answer the following questions.
• How fast is the average global temperature increasing (or decreasing) at 1000 ticks?
• How fast is the average global temperature increasing (or decreasing) at 4000 ticks?
• Is the rate of change in the temperature speeding up or slowing down? What does this say
about the second derivative?
• What will be the highest average global temperature that this model will reach? At how many
ticks will this happen? Or is there a highest average global temperature? Justify your answer.
• In the paper, make sure you explain how calculus was used to answer these questions. If there
are graphs, include them in your answer and where appropriate, try to connect them to your
explanations of the calculus.
4. Is a quadratic trendline really appropriate for modeling climate change? What could be problematic
about it? Are there other types of trendlines like exponential, logarithmic, or a higher degree polynomial
trendline that would be more appropriate? Pick another type of trendline that you think is a better fit
and explain why. Create this trendline in Excel or Google Sheets and answer each of the questions from
the previous problem again using this new trendline. How are your answers different than before?
5. Now add 100 CO2 to your model. Run the simulation again, and use Excel or Google Sheets to create
two trendlines as before (one quadratic and one of another type of your choosing.) Find the derivatives,
and answer the same questions as before. How does the additional 100 CO2 change your answers to
6. What assumptions has this model made? What are some factors in global warming that are not
accounted for in this model? Do you think this model is realistic?
7. What is the average global temperature in degrees Celsius right now and by how much do scientists
think this temperature could rise before producing catastrophic global warming? What would this model
and your calculations say about this? Make sure you include proper citations for this answer. Again, this
includes both inline citations and a works cited page at the end o fyour essay.
• A rough draft of your essay is due by 11:59pm on Friday, May 29 in the “Project” section on
• The final draft of your essay is due by 11:59pm on Thursday, June 4 in the “Project” section on
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