Fifty Years From Now…

From the official NASA climate site it is easy to download global temperature time series data. The data refer to absolute changes of global surface temperature in Celsius with regard to a “Base”. The Base is defined as the average temperature between 1951 and 1980. The series, that starts in 1880, is depicted below:


Global warming, surface temperature deviation from Base (average 1950-1981) in Celsius. Source: NASA,

The picture shows a clearly identifiable upward trend after 1960. In the graph below we focus on the time window starting in 1960.


Global warming, temperature deviation from Base (average 1950-1981) in Celsius. Source: NASA, Window: 1960 – 2014. Linear fit (blue line) and quadratic fit (red line)


On the graph we have applied a linear fit (the blue line) and a quadratic fit (red line). Both lines provide a good model fit to the data. Within the chosen time window both models do not differ significantly from each other. The level of curvature within the given time window is negligible.


At the COP21 United Nations Conference on Climate Change in December 2015, the participating 195 countries have agreed that temperature levels should remain “well below” 2 degrees Celsius above the pre-industrial levels. Also, efforts need to be pursued to limit the temperature increase to 1.5 degrees Celsius above pre-industrial level. The 2 degrees limit is considered to be critical for a sustainable environment; increases above that limit will lead to a dangerously rising sea water level, the possible disappearance of island groups such as the Marshal islands and Tuvalu and extreme weather events.

Suppose that, for this analysis, we equate the pre-industrialized level with the Base as defined by NASA. In that case we can extrapolate the two model fits shown above and determine when the 2 degrees Celsius increase will have been reached, if the fitted trend would persist in the future.

For the linear trend we find a yearly temperature increase of 0.0158. The 2 temperature increase will then be realized in 2092.[1] For the quadratic fit this event will be realized in 2065.[2] So when extrapolating, the curvature leads to a significant difference between the quadratic and the linear fit.

Running out of time

The curvature means that global warming will follow an accelerating pace rather than a constant pace. Of course whether or not the future development of global warming will follow a quadratic process is impossible to predict. However, given the fact that climate changes such as the melting of the arctic sea ice can be self-reinforcing, a quadratic scenario might be more probable than the linear one.

Our analysis shows how time is running out. The year 2065 is quite close, many of us will still be around by then, our children will not yet have reached pension age and our grandchildren will be growing up.

If the quadratic trend is indeed the true one, immediate and drastic measures are needed. A huge change in mindset is required on how we live our lives, what we consume and where we travel.

Also risk management will change dramatically. Actuarial life tables that do not take the consequences of extreme weather conditions into account are obsolete. The way these tables are built needs to be reinvented. In the COP21 agreement it is said that a clearinghouse for risk transfer should be established (apparently for insurance and reinsurance of losses related to extreme weather events) and also a task force to develop recommendations for approaches to address displacement related to extreme weather events.

Additionally, the financial industry can make a difference by triggering a fundamental change in investments towards clean companies that use renewable energies.

Only concerted efforts at governmental, business and personal level can save our planet. The year 2065 is right around the corner.

[1] We define MidPoint Base as 1965. Then MidPoint Base + 2/0.0158 = 2092.

[2] For the quadratic fit we derive the following equation (with C the deviation in degrees Celsius to the Base and Y for the year): C(Y)=8.2768 * 10^-5 * Y^2 – 0.3131 * Y + 295.7132. Solving the equation for C(Y)=2 gives Y = 2065.


Over Folpmers
Financial Risk Management consultant, manager van een FRM consulting department, bijzonder hoogleraar FRM

One Response to Fifty Years From Now…

  1. Erik Daae says:

    Dank voor deze verontrustende visie. Laten we hopen dat de beleidsmakers in de wereld dit ook lezen en in actie komen.

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