2011-08-06 03:57:40Mathturbation 101 - A How-to Guide
George Morrison

Bumped into this handy link on the great Curry "Carbon cycle questions" thread.

Do you ever find you have a pesky climatological metric that you need to explain by fitted-cycles/not-the-IPCC? Then  this is the guide for you!

Whether it is - atmospheric CO2, sea ice, temperature, sea level, isotopes, deuterium depletion in ice cores, solar radiation, WHATEVER!!!... If you need to find some obscure cycle that fits what is happening and therefore disproves the CCCP, this guide shows you how.

It starts with a discussion of some basic principals that will be used:

Plots of the data as a function of time reveal a common yet distinctive characteristic. Each set of data presents a cyclical distinctive, but not unique wave form. Wave forms can be digitally generated using a mathematical infinite series and can be approximated by the first few harmonic terms. The mathematical technique most often used to analyse physical relationships is the normal statistics least squares fit. This works well when the independent variables are truly fixed (accurately measured) and not functionally related to each other. In the real world of researching global climate change with so many possible variables that must be considered, it is unrealistic to expect that a relationship so calculated establishes cause and effect. At best it is an indicator and at worst it is literally lunacy...

But then it quickly moves the student forward into advanced applications. E.g., Western Pacific Equatorial SST:

I calculated SST for 160 East using the Nino rate of warming data. Least squares regressions on these data yield fours tatistically significant natural cycles. The annual cycles are approximated by a triangle wave form with one harmonic (cos(x)+cos(3x)/9). The three other cycles are sine waves with lengths of 11.11, 39.05, and 79.01 years. The regression accounts for nearly 60% of the variability.

Cool. I love the the precision. Not 79 years. 79.01 years. Ok, but how about the Western Pacific Equatorial SST? (Wait, didn't we just do that one? Never mind, let's continue.):

The results for the long term data are shown above. The shape of the cycles is a sawtooth wave form approximated by sine(x)-sine(2x)/4+sine(3x)/9 where x=2Pyears/b+a. The terms a and b are determined by trial and error in a multiple linear regression. The term b is the wave length and a is a positioning constant. I found five statistically significant wave lengths. They are 101,000, 43,050, 24,840, 9942, and 5014 years. The first three correspond to the Milankovitch cycles. The fit accounts for 80% of the variability in the data back to 400,000 BC

Ok, so it works for Western Pacific Equatorial SST. Anything else? Of course! How about 13C/12C isotope changes?:

Five sine wave cycles are statistically significant, accounting for better than 84% ofthe variability. The standard deviation is 0.023. The cycles in the regression are 307.9. 88, 19.98, 9, and 5.5 years. Three of these cycles are common with regression fits for concentrations of carbon dioxide.

The crazy thing is, this guide is FREE!!! The intertubes are the best.

2011-08-06 04:17:51
Daniel Bailey
Daniel Bailey

I read about half of it before my head started to hurt, whereupon I skipped to the end...and my brain promptly cramped up hard enough to throw a rod...

...and I'll never get those last 15 minutes of my life back (that's the worst part).