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 theory
http://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
Lorenz was a meteorologist
Lorenz had discovered something revolutionary


The 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
MANDELBROT..Bifurcation mathematics
( 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.



Feigenbaum

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

Hi crikey,

Funny you mention that - I've long had a suspicion over the years that fractals might be part of the ENSO (& other climate oscillations) story because there's so many oscillations which consist of smaller oscillations which in turn consist of even smaller oscillations. The diurnal variation of temp being part of multiweek oscillations of temp being part of multiseasonal/multidecadal oscillations I mentioned in a previous post being one of my thoughts. Fractals have been observed in many aspects of our world including ratio of number of branches to tree species numbers in rainforests, etc. I've also long mused about their involvement in things like tornadoes.


As for chaos theory, there's examples all around us & many happen every day which most people aren't even conscious of. For example, we can be pretty certain about our health in the next few seconds. Look further ahead in time to the next few hours & we can still be fairly confident about it but the probability is a bit lower. Look even further ahead out to weeks, months or years & we become more unsure. Why? Because of chaos theory i.e. with increasing time, even the smallest of things can magnify to have a big effect. Your friend might have a big night & as a result, get on their bus late the next day... the same bus in which a person with a cold is sitting... who then infects your friend who ends up infecting you weeks down the track.

Or you're commuting to work in the morning & the traffic ahead of you is light. We can assume with very high confidence it'll stay that way for the next few seconds. If we look further ahead in time to the next few minutes, it's still very likely the traffic will stay light but the probability is lower. Look even further forward to the next 45mins & we become unsure. A driver might be late leaving home because the battery on their alarm went flat... as a result they're in a rush, tailgates someone who's driving slowly then an accident occurs, suddenly causing a traffic jam.

In most, if not all of these cases, there can be all sorts of oscillations & background predispositions to make certain states more likely e.g. peak hour in traffic... or easing of traffic during school holidays, our genetic and lifestyle dispositions to getting diseases, etc. But the very fact that it's far easier to predict events in the near future compared to the distant future is due to chaos theory. As mentioned previously, if this wasn't the case, you'd be able to predict the exact temperature for say 1:45pm on the 1st Jan 2090 with the same accuracy as for the minute after I type this.

30 day SOI has rebounded back up and is currently +1.3

The point is that much of what can be claimed as chaos, that supposedly magnifies small errors from the weather and climate and ENSO models from the initial state to forecast state with time, is that is there are no solar inputs of which there are many(visual, x ray, infra-red, magnetic, particle, magnetic, solar wind, 10.7cm, etc, etc), plus various lunar inputs to a much less extent, plus effects from atmosphere-ionosphere changes and other layers above, and the forecasts of these various changes that could also be incorporated into the various global models...therefore, as they do not put any of these in(or try to research them as they should, as many of the connections are still not known,& most money goes into AGW research these days it appears) they go off beam with time a lot, not because of chaos, but because of a lack of this extra initial data input and a lack of forecast of this extra data input. The physical world is only really looked on as chaos because we do not use all the data avaliable, and we do not understand or fully understand all the various connections. Now a lot of these smaller interactions we will likely never figure out and one could leave those in the "chaos basket" if you wish, but there an awful lot of medium bits out there now to discover. But, we have not and do not really appear as if we will put the research dollars to these extra solar-lunar-climate-weather-ionosphere type connections as we just say the models climate and weather go off beam with time because of chaos...maybe it is more because we have still so much to learn and we are still so far away from getting there as we think that we have finished our weather climate research with just oceans and atmosphere, and leave all other connections in the "have no effect basket of chaos".

Good to see Johnno...yes, back to the current and future ENSO discussion at hand!

Very well said BD, I think tho it is only a matter of time before some really smart bastard comes along and ties it all together as an independent, irrespective of the funding side of things. There are many individuals even here on this thread on Weatherzone taking a keen interest and trying to piece all the parts of the puzzle together. Given the drive of some people and the wealth of information available at ones fingertips today it surely is just a matter of time before the Wegener of weather comes along and slot's nearly everything into place for the rest of us.

I for one have learned a wealth of information from the various posters on this thread, ironically from the people who disagree with each other mostly and have been given a few AHA moments from such dialogue.

Weather and Climate as such is a very new science and the serious science is realistically only fifty years old at most. Given the individual interest and the wealth of new technology available to people who live and breath such things it really is only a matter of time until the keys of the supposed chaos are unlocked.

KK you argue that
"It (Chaos Theory)refers to the extreme sensitivity of the initial state of the weather/climate system to different influences."
That sounds like another way of saying it is unpredictable. But there is a difference between saying something is unpredictable by nature and saying it is only unpredictable at the moment because of our limited exploration or understanding.

Then
"If ENSO was truly non-chaotic, we would be able to predict with 100% accuracy, the precise timing & amplitude of all upcoming phases for the next 5 billion years."
Wow, you like thinking big - impressive! But how about we start with 5 days - even that's beyond capabilities of meteorology at the moment.

Then
"If the above wasn't true, you would be able to predict the min/max temp for tomorrow with as much certainty & accuracy as the min/max temp for a particular day one million years from now. Or that a shower of rain will start at location X from 3:26pm and end at 3:42pm on the 1st Jan 2090."
Theoretically yes, but you would need super computers tuned to every cycle. It could be achieved to a point of usefulness, yes, with micocomputers embedded in dust and covering the planet's surface. Adding in all known solar, lunar, planetary and tidal cycles would get close to such a predictive system. It would have to operate under wraps and wait for about a century to gather reliable means on trends before going public, but it could be done.

What is considered possible is a function of willingness, information and imagination. The idea of chaos closes doors because it factors-out data considered immaterial.

"At no stage has the BoM actually said, "An El Nino will not occur".
Well no, this is a nonsequator. They have said it is a condition. That means they cannot call it until after it has occurred, so they cannot say will.

"Because of chaos theory i.e. with increasing time, even the smallest of things can magnify to have a big effect."
Not necessarily. Cause cannot ever be verified from a small number of variables, because everything is always in flux and there is no beginning frame of reference unless we make one up. That puts the subjective in, and the arbitrary, and that makes a sequence nonrepeatable and therefore no longer in the realm of science.

Science is never precise but aims for precision. Science is an approach, not a destination. Naming a temperature at 2pm a million years from now in Ballarat is not the idea of science. Finding a possible series of different ways of being able to name it, is. It is the method that rides supreme, not the result because there may be variables no one has thought of or discovered yet that could change an outcome either now or down the track. Some factors come and go on large cycles, for which we haven't yet built instrumentation to detect. We don't know the answers to questions we have not yet learned to ask. It is why we talk of the scientific method, that may or may not lead us to a scientific 'outcome'. Outcome or not, we still do the method.

Lorenzo's work held science back IMO. There will always be constants because the human mind cannot recognise anything other than patterns. Therefore true random cannot exist in our understanding, but as a function of laziness or naivety around that understanding. We are purpose built and mass produced. For example, our legs are built to walk, not to flap the air. Our eyes will only work with repeat retinal firing, without which we stop seeing anything. We see not the "real" world, whatever that might be, but only what we have learned to see. My concept of red is entirely my own. Whatever we study will always be ordered and we will always find constants if we keep looking. It's what the brain is wired for. That's why all those researchers, Crikey, found their own patterns. We cannot NOT find patterns. It is something we are stuck with. Any "theory" is a suggestion of some type of realised order. So Chaos Theory is itself an oxymoron.

Coming back to ENSO, it doesn't matter what words are used, like 'order within chaos', 'cycle', etc, eventually the pattern will become clear. There has been mention of 4.6. Well, about 4.5yrs is the longterm average of the whole ENSO cycle according to my reckoning, and that is also the interval of each lunar declination quadrant. But it could be 4.6, I'll have to check!

Agreed KEN K , Fascinating.and mind boggling to contemplate these things.
Hopefully ENSO is a major/predominant oscillation and is easier to predetermine
and a mathematical pattern can be found..

Doesn't surprise me johnno that 30 day SOI has gone positive
I observed an anomalous protrusion of low MSLP on the global MSLP come down over the top end and over parts of OZ a few weeks ago but this protrusion has since receded.
THe mean pentad mslp ( 15yr) is the top map and the anomaly map below
http://www.flickr.com/photos/crikeyawf/7555427214/in/set-72157630385336684/lightbox/

actually still some low anomaly , looking tonight,the low over Papua NG is anomonously low atm..

http://www.bom.gov.au/australia/charts/v...it=Refresh+View

The current run of soi this season looks uncanningly like the 2009 pattern atm
However l doubt the SOI trend will mimick 2009 exactly .
that would be unchaotic pun..LOL

In 2009 the SOI went neg', pos', neg' ,pos' and strengthened positive from as late as october.
Compare 2009 pattern and 2012 pattern to data for May to may



I think l saw a forecast map for SST's anoms' for the first week of August on a another thread on WZ tonight and if l remember l saw the forecast is for much of the equatorial waters to warm?

Yes - that is a scenario that I am very aware of. I think I mentined this a couple of times recently, but it was a major WWB / Kelvin Wave in mid / late Sept that was without a doubt the genesis of that late forming Nino. The atmospheric indicators up to that point were showing weak warm.

I also suspect that because the atmospheric indicators SOI / GLAAM / GWO were not fully on board that we had that Nino classified as a "modoki" Nino... But that's another discussion.

"...but it was a major WWB / Kelvin Wave in mid / late Sept that was without a doubt the genesis of that late forming Nino. The atmospheric indicators up to that point were showing weak warm."(quote Arnost)
Funny, if that was the case, why did my models have a late forming Nino already forecast some distance beforehand!

Based on my own analysis of trends associated with the 20 degree isotherm along the Pacific equatorial basin over the last 10 years, I think that we're actually nearing the peak of the development of this 'El Nino' and fairly neutral conditions will develop through spring and into summer, with a return to La Nina conditions during 2013.

All I'm saying is that even though the indicators at the moment similarly to 2009 point to warm neutral, this can change very quickly and we could have a sting Nino yet... But my bet is that it'll cool from here still.

OK, Arnost, I won't disagree too much with those forecast comments.

Originally Posted By: _Johnno_
Perth heading for its driest July on record (27.8mm as it stands) & Hobart has only had 12mm which indicates the lack of decent frontal activity this month

But on the flip side

http://www.weatherzone.com.au/news/melbourne-soaking-in-wettest-start-to-winter-in-16-years/22154

Nino 3.4 Index at 0.75C last week.

Last 13 weekly numbers from OiSST V2.

-0.0603813
0.0831514
0.0351037
0.0880478
0.289335
0.248033
0.428576
0.578563
0.733169
0.654816
0.547698
0.66258
0.751418

There has been some research done on fractals using data sets from the SOI, Nino 3.4, the DMI and NAO

http://www.math.human.nagoya-u.ac.jp/preprint/2011-1.pdf

Wavelet-based multifractal analysis of global environmental Oscillations
Fumio Maruyama, Kenji Kai and Hiroshi Morimoto
Graduate School of Environmental Studies, Nagoya University, Nagoya, Japan

Somewhat over my head. but may be interesting for any mathematicians

I was able to understand that climate shifts are associated with particular fractal pattern changes.. Multifractality to monofractality. If l have read this research correctly?
and strong enso events l believe

quote
Before the 1976/77 regime shift, the Nino3.4 and DMI had high coherency, and the multifractality was observed. Change from
multifractal to monofractal was observed at the 1976/77 regime shift for Nino3.4 and DMI and was observed at the 1988/89 regime shift for
NAO. Hence we infer that a regime shift occured when the fluctuation was large and the multifractality was strong. When the strong
multifractality was observed, the climatic state changed and the regime shift occured.
---------------

3.4 holding steady and reading +0.6 again last week. GFS is predicting trades to drop right off over the Pacific in the coming week to be possibly replaced by a burst of westerlies, particularly in the far east. Not sure if we'll see warming as significant as we saw a couple of months ago but still something to keep an eye on I think.

Is anyone relly certain - nina - neutral - nino? It's certainly not set in concrete yet but the National Climate Centre appears to be betting on a Nino - but with some resvervations.

http://www.theage.com.au/environment/wea...0804-23mnb.html

There is certainly a very active ITCZ in the northern hemisphere at the moment bringing some extreme rainfall to the Philippines - wouldn't mind putting a wager on another wet summer across the north of Australia as it moves south from November.

it depends on what sort of set up the Northern Hemisphere has this winter, if the set up is similar to last winter up there combined with the El Nino, then hello drought, Kingaroy had a dewpoint of -13 degrees today, which I have never it that low before.