I found this great web site COSMIC from a link off davidg's link to the chaos theory
Yeah l agree it is relevant to the thread as we all want to know if we will ever be able to crack the ENSO holy grail predictive code, so to speak, if there is one..
I remain confident it is possible and l think my first read about this topic from the link below just further strengthens my belief that it is possible
Here is a summary of some mathematical modelling from the 'chaos theory"
that indicates the order in chaos
You will have to go back to reading the latest KEN RING as much of these findings support order within the chaos
I really enjoyed this article
Here are the concepts you must
try on your ENSO data BILL ILLIS
l gather you and surly bond are mathematicians
I can see potential here to identify the order within the chaos of the ENSO cycle
I found a short introductory version on the chaos theory version COSMIC
as l hadn't read up on it l admit. I was really enthralled !!! about the findings
I found this site from Davidg's link
This is really good!!
You will have to get on to this BILL..
Applying some of these mathematical principles to ENSO variable ( equations)
EXTRACTS and quotes
An introduction to chaos theoryhttp://www.imho.com/grae/chaos/chaos.html
The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.
as KEN K has explained
Lorenz was a meteorologist
Lorenz had discovered something revolutionaryThe lorenz attractor
The equations for this system also seemed to give rise to entirely random behavior. However, when he graphed it, a surprising thing happened. The output always stayed on a curve, a double spiral.
There were only two kinds of order previously known: a steady state, in which the variables never change, and periodic behavior, in which the system goes into a loop, repeating itself indefinitely. Lorenz's equations were definitely ordered - they always followed a spiral. They never settled down to a single point, but since they never repeated the same thing, they weren't periodic either.
He called the image he got when he graphed the equations the Lorenz attractor. (See figure 2)
Now relating that to ENSO.
Does the ENSO sequence stay on a curve, is it a double spiral, is it periodic nina /nino pattern?
As Lorenz found that changing the initial base state of forecast will yield different outcomes
He proclaimed ..in that case the weather will never be able to be accurately forecast..
Now if you apply this to dynamical weather models , this infers they will always be inaccurate.and as to global warming models ,the same applies
However Lorenz was wrong ,if you read on...
However ,what about
the findings of Robert MAY the biologist
Past a certain growth rate, it becomes impossible to predict the behavior of the equation. However, upon closer inspection, it is possible to see white strips. Looking closer at these strips reveals little windows of order, where the equation goes through the bifurcations again before returning to chaos. This self-similarity, the fact that the graph has an exact copy of itself hidden deep inside,
came to be an important aspect of chaos.
and the work of
( finding order in apparent chaos)
" Each particular price change was random and unpredictable.
But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period
that saw two World Wars and a depression. (James Gleick, Chaos - Making a New Science, pg. 86)KOCH CURVE and fractal dimensions
One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve.
Fractal has come to mean any image that displays the attribute of self-similarity. The bifurcation diagram of the population equation is fractal. The Lorenz Attractor is fractal. The Koch curve is fractal.
was looking at the bifurcation diagram again. He was looking at how fast the bifurcations come. He discovered that they come at a constant rate.
He calculated it as 4.669.
In other words, he discovered the exact scale at which it was self-similar. !! WOW
Make the diagram 4.669 times smaller, and it looks like the next region of bifurcations. He decided to look at other equations to see if it was possible to determine a scaling factor for them as well. Much to his surprise, the scaling factor was exactly the same. Not only was this complicated equation displaying regularity, the regularity was exactly the same as a much simpler equation. He tried many other functions, and they all produced the same scaling factor, 4.669.
How about trying the scaling factor of 4.669 ,BILL ILLIS on your La Nina and El Ninos +/- 0.5 ?
or the SOI
Some mathematician on the forum should be able to crack the code..with one of those computations!!
This was a revolutionary discovery. He had found that a whole class of mathematical functions behaved in the same, predictable way. This universality would help other scientists easily analyze chaotic equations. Universality gave scientists the first tools to analyze a chaotic system.
Now they could use a simple equation to predict the outcome of a more complex equation.
Did you read that!!!
This UNIVERSALITY 4.669 would help scientists to analyze chaotic equations
Do the current climate models and forecsting programs use
fractal analysis and bifurcation diagrams??????? and the universal constant 4.699 WOW
The mandelbrot set..
The equation is simple: z=z2+c. To see if a point is part of the Mandelbrot set, just take a complex number z. Square it, then add the original number. Square the result, then add the original number. Repeat that ad infinitum, and if the number keeps on going up to infinity, it is not part of the Mandelbrot set. If it stays down below a certain level, it is part of the Mandelbrot set. The Mandelbrot set is the innermost section of the picture, and each different shade of gray represents how far out that particular point is. One interesting feature of the Mandelbrot set is that the circular humps match up to the bifurcation graph. The Mandelbrot fractal has the same self-similarity seen in the other equations. In fact, zooming in deep enough on a Mandelbrot fractal will eventually reveal an exact replica of the Mandelbrot set, perfect in every detail.
the enso pattern? can be found in a mandelbrot set?
Did you read that
PERFECT in every detail!!
It has even been speculated that the brain itself might be organized somehow according to the laws of chaos.
So the chaos has order !! The article says
THE LAW... of chaos
seems an oxymoron doesn't it... How about ordered chaos, chaotic patterns and constants, . This concept needs a new name!!
I liked the suggestion of the universality constant= 4.669 .. or is that term already taken..LOL