Wednesday, 15 June 2011

Bifurcations and Forecasting Scenarios - in CO2 emissions

I was quickly reading over a new paper on renewable energy policy [Krey and Clarke 2011], and realized that there is a visual link between global CO2 emission predictions and a bifurcation diagram.

The bigger plot below shows "Historic and projected global fossil and industrial CO2 emissions across all scenarios between 1900 and 2100",  Figure 1 in Krey and Clarke 2011. The red-frame insert is the bifurcation diagram of the the logistic equation taken from here.
 

From Wikipedia: bifurcation diagram shows the possible long-term values (equilibria/fixed points or periodic orbits) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable solutions with a solid line and unstable solutions with a dotted line.

Granted that the link is more visual than fundamental, and requires an artistic licence of some degree. Note that the first bifurcation starts at the point separating historical values from projected (aka predicted) values. Thus, history is the stable solution, and forecasts are unstable solutions, the source of the uncertainty. This could hint towards a new topic for the application of NKS (New Kind of Science) approach and his reliance on cellular automata similar to the logistic equation to explain complex systems.