Super exponential growth of atmospheric CO2

Graphs taken from forthcoming book -  The Vortex of Violence, and why we are loosing the battle against climate change.

Take atmospheric CO2 data from Manua Loa, and plot a straight line through it and you can see more clearly that the rate of increase increases with time:

To simplify the graph further we remove the monthly cyclic data by plotting a 12 month moving average. Rather than drawing a line of best fit through the data, we simply draw a line from the first point to the last. 

This graph shows the highly defined convex nature of the graph and the rate at which the gradient has has changed over the this time period. 

As all the things driving the graph are exponential such as economic growth, fossil fuel consumption, population growth, etc and given the graph above it stands to reason that an exponential function should be able to model it which will be of the general form CO2=Ae^kt, however:

The blue line, shows the 12 month moving average and the red line is the best fit exponential data.  The red line looks straight-ish, simply because of the values used in the best fit exponential function, but these values represent the best approximation that an exponential function can give to the data over this range. It is clearly unable to provide a decent fit, with an increasing underestimate with recent data. It leads to the proposition that k in the equation above is over time.

So we plot k against time. To calculate k for any date, we need just two data points on the curve. One of these we fix as of today and the other starts at 1959 and slides towards today's data point. From these two points we can easily calculate k for each specific date. If the data was a perfect exponential curve, then the value of k would not be affected by our choice of points, and that is largely what we see until 2009. However, after 2009 then k starts growing explosively. This lays out the nightmare of super exponential growth; exponential growth on exponential growth. 

Finally given the changing value of k, we can plot how the date at which we expect atmospheric CO2 to go through 450 ppm for any date and we see this coming forwards. So based on the data back in 1960 we would have expected to go through 450 ppm around about 2042, which was bad enough. But recalculating this using data over the last couple of years suggests that we could be going through 450 ppm by 2030.

After 450 ppm, the worst nightmares of runaway climate change are impossible to avoid. Given these graphs, any talk about getting emissions down to 350ppm to give us long term hope of avoiding runaway climate change is pie in the sky. It means that we must contemplate a much more drastic change to business as usual.

These graphs will be updated as new data comes from the Manua Loa observatory.