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CO2 Levels (a depressing story)

Posted by Patrick on November 27, 2011

A few days ago, I listened to an ABC radio podcast on All in the Mind entitled “The case for moral enhancement”. [1] I was expecting the ethical minefield of eugenics to be discussed (which it was), but I was surprised by the turn of the conversation towards the end: 0ne of the reasons why we’d want to enhance our moral compass is because we didn’t evolve to deal with problems that affect the entire population of the planet.  In particular, one of the professors grimly said that “it’s wishful thinking to think that people are going to voluntarily deal with climate change”.  Heavy stuff!

Today it was CBC radio’s Quirks and Quarks turn to tackle the issue of climate change. [2] Again, it was nothing short of depressing.  Very…  Depressing…  One of the guests said that our inability to deal with the problem not only means that we’ll face catastrophic repercussions, but it also says something pretty grim about ourselves: “Can we not deal with an ethical issue about the lives of billions of people around this planet?”

Because I like to understand the information contained in graphs, I clicked on the one posted on the Quirks page [2], which led me to its source on wikipedia [3], which lead me to the source of the raw data [4].  I decided to import that data into a spreadsheet to see what information I could extract from it.

Using two simple functions, and a method called “least squares” [5] to scale them properly, I managed to find the proper parameters that model the CO2 concentration as a function of time.  Visually, the orange graph (the model) follows the blue graph (the data) pretty well, so the model I found is pretty good (within that range of time anyways).

I found the equation of the model (the orange graph) to be:

It looks complicated, but there’s basically three pieces to this function, each with their own particular meaning.

The first part is just the number 270.  What it means is that if we go back in time by more than a few hundred years, the average CO2 concentration in the atmosphere would have been around 270 ppmv (compare that to today’s 390 ppmv !)

The second part is responsible for the oscillation of the concentration due to seasons.  The number 2.7 in front of the sine function means that the concentration increases from its average value by 2.7 ppmv in the winter and decreases by 2.7 ppmv in the summer.  So the total variation (of about 5.4 ppmv) is pretty small (compared to the average increase).

The third part is what we’re responsible for.  It says that the difference in CO2 from the ancient average of 270 ppmv will double every 37 years.  This is a bit tricky so here it is again: if you look at the concentration of CO2 today and subtract that from what it was hundreds of years ago, that difference will double in 37 years time.  For example:

  • The concentration was around 315 ppmv in 1958, which is a difference of 45 ppmv from 270 ppmv.
  • 37 years later (in 1995), the concentration was 360 ppmv, which is a difference of 90 ppmv from 270 ppmv (double the previous difference of 45 ppmv)
  • Another 37 years later (in 2032), the concentration should be (if the trend continues) 450 ppmv, because there should be a difference of 180 ppmv from 270 ppmv ( double the previous difference of 90 ppmv)
  • And in 2069? 720 ppmv, because it’ll be 360 ppmv more than 270 ppmv…

So according to this model, if the trend continues (ie, we keep doing what we’re doing now), the atmosphere will reach levels of CO2 comparable to that of the Eocene–Oligocene extinction event 34 million years ago (which were around 760 ppmv) [3] in a time scale of a few 37-year periods!  And I thought the podcasts were depressing…  The next graph shows this extrapolation in both direction.  The model (in orange) is graphed (without the seasonal variations) between 1750 and 2100 with the actual data (in blue).  The future looks completely crazy, but other data suggest that the past is actually pretty spot on. [3]

Now, to be fair, the assumption that “we keep doing what we’re doing now” implies at least two things that are very unlikely:

  1. Our population will continue to grow exponentially.
  2. Our resources of fossil fuels will continue to match our growing demands.

In reality, we’ll either find ways to turn this around, or we’ll suffer from other problems that will curb our population explosion and our ability to consume so much fossil full.  One thing is certain: we can’t let that orange curve go that high.


  1. All in the Mind, The case for moral enhancement,
  2. Quirks and Quarks, The Rocky Road to Durban,
  3. Wikipedia, Mauna Loa Carbon Dioxide-en.svg
  5. Wikipedia, Least Squares,

One Response to “CO2 Levels (a depressing story)”

  1. […] then so happened that I turned to my RSS reader and found Patrick Truchon’s latest post which explained the math behind forecasts about the incredibly fast growth of atmospheric CO2 which […]

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