New Computer Fund

Tuesday, December 11, 2012

Fractals and Climate

(a+b)/a = a/b yields ~1.618 is the golden ratio.  A. M. Selvam is big into the Golden Ratio and fractal. Self-organized criticality: A signature of quantumlike chaos in atmospheric flows is one of many papers by Selvam on Self-Organized Criticality (SOC) which uses the golden ratio to estimate the frequency of occurrence of SOC.   The Koch Snowflake animation above from Wikipedia is just one of many examples of fractals.  Recurrent patterns in time series also produce fractal like behavior.  Nature produces quite a few examples of fractals, snowflakes, ice crystals, hexagonal close packed latices and others.  Relating climate to SOC and fractals is to me about as convincing as pyramid power razor sharpeners.  There needs to be mechanisms to explain the occurrences.  

Tuning, like adjusting shocks, is more up my alley.  Following a perturbation, like a speed bump, your car bounces and the better your shock absorbers are tuned to you car weight, the less time the bouncing continues.  

The Tierney Lake Tanganyika plot above with the rough solar enegy curve above is one I have used before.  The recurrent pattern has some similarity to the Elliot Waves used by the stock market gurus that want to help you lose money.  In fact, Wikipedia has an illustration of a typical Elliot wave pattern.

This pattern is pretty similar to the global temperature average with the rise and fall of temperatures every decade or so.  Unlike the pattern above, the temperatures have changing slopes for the "Saw Tooth" waves where the down slope generally decreases as a peak is approached.  

In climate, the change in the slope would be related to the change in energy which is somewhat like changing the load on your shocks.  The "damping coefficient or ratio" changes with load.  So whether Selvam and Elliot have discovered the secrets of the universe or not, there is a relationship that can be used to fine tune our understanding of climate.  

This curiosity of nature lead me to the Southern Hemisphere and the Drake Passage.  Since the Drake Passage is the nozzle that adjusts the flow of ocean heat uptake, changes of the Drake Passage flow would influence the slope of the waves on some time scales by changing the efficiency of deep ocean heat uptake.  

Since I am slower than molasses in winter time, quite a few climate scientists have noticed that the standard climate models are not performing as expected and have turned their attentions to the Southern Hemisphere and Self-Organized Criticality.  Some without really knowing that they have.

Vaughan Pratt, a professor at Stanford University had a AGU poster called Multidecadal Climate to a Millikelvin which he posted also on Judith Curry's blog.  

The SAW in this chart is similar to the damped Elliot Wave I would expect in climate.  The question I would think is the cause of the damping?

From the Selvam Link, "Man-made greenhouse gas related atmospheric warming would result in intensification of natural climate variability, seen immediately in high frequency fluctuations such as QBO and ENSO and even shorter timescales." but, that ain't necessarily so.

In a bi-stable system with two strange attractors or semi-stable setpoints, the damping coefficient would change as the system approached an attractor or semi-stable condition.  

Using the same Tierney data set with the full length I have drawn in what may be semi-stable preferred states which would increase the damping of the pseudo-cyclic oscillations.  The "setpoints" are likely related to the average total energy of the "system" which would be the deep oceans, IMHO.  A Tale of Two Greenhouses is a quick post of mine indicating there is a competition between the SW dominate Deep Blue Sea greenhouse and the LW dominate much lower thermal mass atmospheric greenhouse effect.  Since the average lag of the Deep Blue Sea temperature with respect to atmospheric temperatures is roughly 1600 years, the longer term Deep Blue Sea "Elliot Waves" or recurrent decay patterns should be considered before screaming "eureka!".

So Webster, Phttt!

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