From the Carbon Footprint to the Temperature Anomaly in 2100

Calculation note


Click for PDF version

Introduction

Estimating the future of climate change is by far not an exact science, albeit a very active research domain. In this application, the temperature anomaly estimation is based on a study published in 2000 by the Intergovernmental Panel on Climate Change. This study presented the estimations based on six different scenarios, six different possible futures of the human society.
The scenarios varied on wether the earth’s population peaked around 2050 or increased continuously, wether low-carbon policies were adopted world-wide and wether the economy of the countries became increasingly regional or, on the contrary, that the development gaps between countries tended to fade out with globalisation.

The report is available at this address :

https://www.ipcc.ch/publications_and_data/ar4/wg1/en/spmsspm-projections-of.html

I just took some of the outputs of those six models :

The goal was to link cumulative emissions to the temperature anomaly, and then use the population evolution to say such things as :
      “If everyone (the world’s population in the XXIst century) emitted the same amount of greenhouse gases as you do until the next century, the temperature would rise by X degrees”
Although such a thing will never happen, because inequalities exist and will persist for quite some time, it is a striking thought for a conclusion, and a scientifically acceptable one too.

Calculation

I took from this figure from the IPCC report the average values of cumulative emissions for the scenarios :

Associated with the reported temperature anomaly estimations here :

Finally, the extracted data from the report can be summarized as such :

Note : One ton of Carbon equals 3,67 tons of CO2.
There is a good linear dependence between the cumulative emissions of Carbon Dioxide and the temperature anomaly : The computed coefficients from the regression are : Degrees = 0,4764*CO2 + 0,2212
Now to compute the temperature anomaly in sentence like the one mentioned before, we need the average population over the century. The following figure of the report provides the population evolution for the different scenarios, and I chose to use the curve corresponding to the A1T, A1B, A1FI, B1 scenarios, because it is the most optimistic one.
By computing the integral of this curve (the green one), we obtain that the average population of the world over the 1990-2100 period is 7,77 billion.
Finally, given a personal carbon footprint of X tons of CO2, the temperature anomaly is :

T = 0,4764*( 7,77 billions * X tons of CO2 * 110 years ) + 0,2212