One Hundred Planets & One Thousand Years

Global Warming has been a subject much in the news over the last few years.  Al Gore has done a lot to bring the issue to the attention of the world.  There are really two subjects intermingled in my mind, anyway.  One is the possible warming of the planet and climate change that results and the other is pollution both from fossil fuels and from man's folly.  We have to remember that the ice core and tree record shows temperature shifts in the past from a number of causes.  It is hard to sort all this out, when discussing the environment with well meaning people. 

Communicating with a group of mathematicians and scientists across the globe, I've discovered that many climatologists  believe that man induced CO2 is connected with the apparent climate change and the decrease in the polar ice caps.  Others feel this is just part of a natural process that has gone on over geologic time

It's very difficult to make an exact connection between CO2  and the warming trend.  This is hard to understand for the general public because many scientists believe it to be true, but have not convinced all their peers. 

As the great Nobel Prize winner Richard Feynman says :"... it is of paramount importance, in order to make progress, that we recognize this ignorance and doubt.  Because we have the doubt, we then propose looking in new directions for new ideas".  In this way things eventually become clear.  This is common in Science.  For example Einstein's 1905 work was not fully accepted  until the 1920s, when the rest of the science community finally caught up.. 

Working with a talented scientist in the UK, I developed a model based upon the temperature variations from 1850 until August 2007.  At his suggestion I took the mean of the temperatures as recorded at the University of East Anglia database.  Currently there are 3000 stations reporting world-wide on a monthly basis on a 5 degree x 5 Degree approximate grid.

The earth's temperatures are shown in the database at East Anglia as deviations from a mean.  You can establish trend lines and do work that can be shown on graphs that seem to correlate with some of the presentations in Al Gore's movie "An Inconvenient Truth", wherein he superimposes CO2 increase to temperature increase.  These graphs are compelling, but they are of different scale and are attacked by "doubters" for that reason.  I decided to take another tack. 


I wanted to see what 100 earth like planets would do over 1000 years, if left to purely random processes.  I took the first differences of the deviations from the mean and found the Standard Deviation of the entire sample from 1850 to 2007.  Computing a Standard Deviation is a way to capture the 'heartbeat' of a process and is an indicator of a distribution's concentration or dispersal.  We are familiar with this when the STD is used to compute a Bell Shaped Curve or Gaussian Distribution from our school days.  STD is a good measure of the spread of a distribution and can be used to define the "bell curve" of a Gaussian or Normal Distribution.

I then kept track of what would happen if I selected random temperature deviations from the mean over a 1000 year period for 100 planet earths using the STD from 1850 to 2007.

Now you must understand that I did not exert any dampening effects on the distribution that might come from earth's ability to adapt and correct climate 'swings'.  For example, the biosphere is capable of absorbing CO2 over a long period of time (centuries in the case of water and forests and longer for rock).  We know that CO2 is easily absorbed by plants, but data now shows that man is producing twice as much as earth can absorb and on average the absorption rate is very slow.

My model's lack of dampening is not to be considered fatal to what I want to show.  I want to show you what can happen when purely random processes are at work.  This is much misunderstood and the results might shock you.  I've shown the interesting graph above.  The colours are interpolated from red to violet to indicate visually the changes in temperature

You will note the cone like growth of the maximum and minimum deviations. It looks like a Bell Shaped Curve placed on its side. This is caused by the random stochastic process that is not dampened by unknown responses of the biosphere.  It is interesting to note that once a curve of this type starts to move either to cold climate or warm climate, it does not recover quickly in a purely random experiment nor does a well behaved curve move to become deviant rapidly.

One could prove that if we left this random process go for millions of years, even the lines that are deviant would recover and go to the opposite extreme, but some that were close to the mean would also move inexorably to cold or hot.  The earth is indeed fragile and the nature of randomness magical.

Mike Sterling December 2007 for the Saugeen Times

The Graph below is from the University of East Anglia with worldwide reports driving the bar chart.  It show a steady climb in the last fifty years of data aquisition.