More chaos than you can shake a stick at.
Guest post by Andi Cockroft
(Anyone familiar with the Moody Blues should recognise the title – from “Higher and Higher”)
As some will have learned by now, I do not possess the scientific skills of the regular WUWT contributors to engage in in-depth evidential-based posts. Rather I like to think that just like the great unwashed masses, I have an intellect and an enquiring mind, and want here to share my musings and seek feedback to better help me (and hopefully other readers) understand some of the more complex subject matter. For my shortcomings I apologise. For raising questions requiring answers I do not!
Way back in January 2011, Phil Salmon posted here on WUWT “Is the ENSO a nonlinear oscillator of the Belousov-Zhabotinsky reaction type?” – His alternate title “Standing on the shoulders of Giant Bob” Perhaps my alternate title should be the same. I have read and re-read Phil’s definitive article, and as Isaac Newton was believed to have complained of the three-body problem:-“his head never ached but with his study on the moon”. So in my own way, I want to raise issues associated with what I see as true chaos, and whilst following (albeit very slowly) Phil’s work, that was nonetheless focused towards ENSO and away from the general Climate Models that I want to investigate.
Why a butterfly? Most students of chaos theory will know the “butterfly effect”, whereby it is asserted that in a chaotic non-linear system, a butterfly beating its wings in say Brazil could inject such feedback as to disrupt the airflow sufficiently that many years later a tornado would form over Texas.
Similarly, travelling back in time and moving the butterfly a few centimetres would cause the tornado not to form, or form elsewhere.
Also note that the Quantum version of the Butterfly Effect (the Quantum Butterfly), is a different beast altogether – although some parallels are drawn.
Ascribed to Edward Lorenz, the US mathematician and meteorologist who sadly passed away a few years ago. Initially Lorenz referred to a Seagull flapping its wings forever changing the weather, but later in a 1972 speech entitled “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas”, the butterfly analogy was born.
It is Lorenz’s work on meteorological chaos that I want to look at specifically.
In or around 1961, vacuum-tube computers arrived at Lorenz’ disposal, and not surprisingly the first weather model was born as a set of a dozen or so differential equations involving such things as temperature, pressure, wind velocity etc.
During a re-run of this early model, Lorenz is believed to have restarted the program in the middle of its run by entering a variable to 3 decimal places – to his surprise the results were completely at odds with what was achieved earlier.
Restarting and re-entering the variable to its full 6 decimal places produced a repeat of the initial results – from this Lorenzo drew the inevitable conclusion that with his dozen or so equations, even a miniscule variation on input is capable of creating massive change in output.
But why such a radically different outcome for such a miniscule difference in input?
It transpires that the equations were non-linear, with a so-called “great dependence on initial conditions” – change the initial conditions even slightly and a large change in output is observed in a later state.
The conclusion that Lorenz drew, was that given that such small variations can create such massive variation in output, it was impossible to “model” a weather system.
This “sensitive dependence on initial conditions” was destined for higher things however.
Around this time, Lorenz published perhaps his most important paper “Deterministic Nonperiodic Flow”, and with it was born Chaos Theory, and the concept of the Lorenz Attractor.
(For those wanting to investigate the Lorenz Attractor further, I would recommend reading Phil’s original article here, or Wikipedia here )
I’m not sure if there is any relationship here to Peter, but James Gleick’s bestseller, ‘Chaos: Making a New Science’ built on Lorenz’ musings, became the mantra for many to follow in all walks of life:- finance, science and even time-travel effects in science-fiction. It is now bandied around in insurance, marketing and business boardrooms throughout the world.
Being quite a reserved individual, Lorenz was taken aback by the devotees to his speech. ‘I was just trying to determine why we didn’t have better luck with our weather forecasts, I never reached a point where I believed the butterfly was a scientific fact. At most, it’s a hypothesis. I never expected it to become so huge outside meteorology.”
So my question now is, given that we cannot even begin to measure things such as SST to anywhere near 3 decimal places, how can we expect low-accuracy and highly volatile data, entered into chaotic models of even more chaotic systems to produce anything of significance?
If Lorenz gave up when he discovered weather to be totally chaotic and unpredictable beyond a few days, what makes the Climate Modellers believe they can do better forecasting years or even decades ahead?
Andi
Kasuha says:
March 15, 2012 at 7:43 am
What models are used for is not to determine whether it will rain 100 years from now, but rather to determine the attractors around which the weather is oscillating and where will they move in the years to come.
That is not how the IPCC uses models. The current climate models are linear parametrized models super-imposed on weather forecasting (GCM) models. Thus, this article is correct in stating that current climate models cannot hope to predict the future climate.
Where is the average in this diagram?
http://en.wikipedia.org/wiki/File:Lorenz.png
Question to ponder: What were the initial conditions within the Singularity that lead to the Big Bang and the subsequent expansion of Spacetime? Because that’s where/when this needs to start. Good luck.
I went into atmospheric physics because of my interest in world development and the problem of hunger. It seemed to me that was the best thing I could do to help by contributing to or at least helping to deploy climate forecasts. I found out that was a vain hope, not least because of the stochastic complexity of the system. This was nearly 40 years ago. I spent some time in weather forecasting, and then an interest in air pollution led me to applied statistics, and by this time I had already decided that the major barriers to hunger reduction were political ones – the physical ones of energy production and agricultural and other techniques having been sufficiently reduced. And while I was engrossed in industrial statistics, the great climate crisis movement was getting underway big time. When at last I noticed it, only a few years ago, it was a bit of a Rip van Winkle moment for me. How could I not have noticed earlier!
It seems to hinge on CO2 having been declared by some to be a major driver of climate, a property which it has somehow failed to convincingly display in the past – a past which includes of course, far higher ambient concentrations of it. How has this happened? I suspect an unholy mix of unscientific thinking (more ‘geography’ than ‘physics’) and very effective political opportunism by such as the Club of Rome, mutually reinforcing in a very lucrative manner over the past 30 years or so. A key part of scientific method – the search for testable hypotheses and examining them by observation and experiment – seems to have been sidelined by emotive speculations, and graphic descriptions of climate doom, thanks to a ‘settled science’ giving such influence to a now much maligned molecule. The odious machinations of the IPCC have also played an important part in this sorry spectacle, with their specious urgency and alarming messages succeeding, it would seem, in suppressing critical thought in and around governments the world over.
Back in the late 1970s, it seemed to me that climate histories would have to suffice to give warning of possible conditions to come, and of course then there was superficial talk of a new glaciation just around the corner. My academic mentors did not take that at all seriously, and I do recall one lecturer being amused by the antics of a young Stephen Schneider who did. To my shame, I used to unsettle people in casual conversations by relaying the dramatic threat – not of ice sheets creeping down slowly from the north, but merely of the winter snow not going away over spring and summer. The ice was to grow up around us in due course, but in the meantime a covering of snow was more than enough to give us agricultural and other difficulties. I like to think I usually put them right about how speculative it all was, and that it was not in the least a real worry to me.
Now we have far more powerful computers, and we have had the breakthrough of a theory accounting for some of the covariance between sunspot cycles and weather records – the cosmic ray hypothesis by which these particles affect the rate of production of condensation nuclei relevant to cloud formation. A theory which seems to have been curiously disregarded by many, perhaps because it is not a suitable one for adding to the useful guilt of those pesky humans who are so detested by at least some of the people so keen on CAGW.
It seems to me still absurd to think of running grand climate models of the whole system by cycling through the simulated years and hoping for practical guidance by way of forecasts – the basic problem described by Lorenz remains. But perhaps there will be scope for elucidation of subsets of the system, say the regional impact of large mountains or extensive surface changes. Coupled with improved forecasts of magnetic field variations, more insights into the great ocean-related oscillations and other specific effects (such at those mountains), we might yet get our money’s worth out of those computers by their contributing more to the simple extrapolations of cycles and other trends. But I suspect the fixation on CO2 that has led to so much funding and so much fear will need to be dealt with first, coupled with a deliberate and sustained effort to make sure politicians in particular acquire a realistic expectation of what such models might do.
Because nature isn’t chaotic unless you insist on confusing it with mathematical models. In real life, “chaotic” merely means “really complicated”. Just because it’s hard doesn’t mean no one should try.
Not everything is caused by a butterfly flapping its wings. Some things are predictable from beginning to end – others have no known origin or termination point. If modelers were more honest about what they can’t predict we wouldn’t have reached this point.
“So my question now is, given that we cannot even begin to measure things such as SST to anywhere near 3 decimal places, how can we expect low-accuracy and highly volatile data, entered into chaotic models of even more chaotic systems to produce anything of significance?
—–
Small nit. We can indeed measure SST to three decimal places. The error is not in the measurement but in the presumption that such measurements no matter how aggregated can yield even so much a single digit representations of climate conditions.
The old saying goes that an economist knows the price of everything and the value of nothing.
Climate alarmists know the temperature of everything and nothing of the climate.
Surging and receding …
Surging and receding …
The sound of the waves rolling in and rolling back out has echoed across the world for hundreds of millions of years, a long reach toward eternity.
Not once in that span has it ceased rocking and crossing this blue world, sometimes gently, sometimes powerfully; stormy as the morning, calm as the deep of night.
Surging and receding …
Surging and receding …
The sea rolls in and rolls back out. One hundred billion shimmering stars rise between the wave crests, only to sink back into the vastness of the waves with the first dim light of dawn.
On a night of exceptional darkness, a faint shooting start cuts across the void, trailing a long tail of light, then falls behind the nacreous line of the horizon, its glow becoming an unfading scar-a memory in the space between the stars.
Gradually, the constellations change their shapes; white stars take the place of blue stars, red stars take the place of orange, each making way for the next as they slide past each other to weave new shapes in the sky.
Surging and receding …
Surging and receding …
Time that knows no haste flows over the waves as they roll in and roll back out, through the night and into day and into night again.
***
The vast flow of time leaves traces of its passage across everything without exception. It moves within everything that is, ……………………
From the Prologue of
Ten Billion Dats & One Hundred Billion Nights
by Ryu Mitsuse
I believe the basic idea of the butterfly theory is incorrect.
To make my point, let me replace it with a “domino theory.”
Let’s say that you dump a box of 10,000 dominoes on your kitchen floor. Now balance one of them on its end. Then knock it down. Does this have an effect on a domino on the other side of the room? I don’t think so.
Now set up each of the dominos on their ends in some beautiful pattern that winds around the kitchen floor. Then knock one down. Does this affect a domino on the other side of the room? Much more likely, I think.
The climate of the planet is much more akin to the first domino experiment than to the second one. The climate, like the first domino experiment, is in an overall quasi-equilibrium. It is like a marble at the bottom of a bowl, not a marble balanced on the point of a needle.
Another point: Once the second domino experiment has been completed, the remaining pile of knocked-down dominoes is basically the starting condition for the first domino experiment. That is, a system may start out in an unstable situation (even an unstable equilibrium) but will tend to move to a stable one.
It is very difficult to get all the dominoes between the butterfly’s wings in Brazil and the air circulating in Texas lined up in such a way that the wing motion will trigger a tornado. This is because there are nearly an infinite number of dominoes between the two events.
On the other hand, a model can reduce the nearly infinite number of dominoes to just a handful of dominoes. Then there is a probability that the modeled dominoes will line up and a small effect at one end of the model will have a big effect at the other end.
In my opinion, it is this misunderstanding that causes many environmentalists to start with science and end up with Gaia. They believe the world is inherently unstable. Hence, any small change can have a profound effect – so all changes should be suspect and avoided. But how does the world exist in such an unstable state? Well, there must be a higher power (Gaia) that is keeping the dominoes properly aligned.
Andi: It is true that the weather/climate/atmospheric system of Earth exhibits nonlinear chaotic behaviors and that attempts to model-to-predict weather are severely hampered by sensitivity to initial conditions–a fact that comes more into play the longer the model runs, the further into the future (or past) one attempts to look. As I’m sure you know, weather forecasting is limited to about a week to ten days at best, after which it is a crap shoot.
But….like many nonlinear chaotic systems (NCS), there are known or assumed bounds and known or assumed ‘attractors’. For the Earth Climate System, northern hemisphere ice ages are considered by some to be one stable attractor with a fairly long temporal existence before the system shifts to a interglacial warm period–another considered attractor for the system.
As for bounds, it is generally accepted (but not proven in any scientific way) that Iceball Earth is not within the bounds of climatic variation and nor is Earth-as-Venus.
There are illustrations in James Gleick’s book of these concepts. For instance, on my laptop, I have Basic programs I wrote 20 years ago when I was toying with Chaos Theory. One of these draws a triangle. Depending on initial conditions, reiterating the formula through thousands of cycles draws a filled-in triangle (all points on the triangle and inside the triangle) OR points only on the outside lines of the triangle OR points only on the outside lines of the triangle and a particular ‘x’ shape inside the triangle. But ONLY these three choices….not any others. So this system has three possible states and definite bounds.
What do we know about the climate system and its possible attractor-states or its bounds? I’d say not that much — except for the direct observations of weather and climate in the historical period and the indirect–derived–observations about paleo-climate conditions.
Weather is local. It can be sunny one side of the street and pouring down on the other side.
Take the global temperature anomoly and reconstruct all the data that went into producing it.
@ur momisugly tommoriarty says:
March 15, 2012 at 10:06 am
I believe the basic idea of the butterfly theory is incorrect.
================================================
Not necessarily incorrect. But likely insufficient and simplistic. As is your domino theory. 🙂
I will add for the few commenters who read ‘nonlinear chaotic system’ (NCS) as ‘that weather is completely chaotic in the long term’.
The term Chaos for behaviors such as ‘extreme sensitivity to initial conditions’ is an unfortunate artifact of popular science. It does not mean that the resultant system itself is chaotic — in fact, nonlinear chaotic systems can be devilishly ordered but not predictable. Other systems show unpredictability/randomity within bounds over a wide range and then, in the middle of that, throw up a small patch that is finely ordered.
Because the movement of the planets is generally NOT a NCS, we can send a rover across a huge distance and time span to land on the surface of Mars. But because weather is, we can not place a bucket at a certain spot and catch a predicable bucket of rain water on a certain day one month from now.
Politics is a non-linear chaotic system with strange attractors /sarc
fredb says:
March 15, 2012 at 7:35 am
Weather is not climate. To conflate the initial condition dependency problem of weather forecasting with the boundary condition problem of climate simulation is fundamentally erroneous.
Turn that around an think about it. If weather “is not climate,” yet we derive climate “data” from weather records, and assume that climate “determines” weather, then it follows that the initial conditions to which weather is sensitive are embedded in the climate system – if there is such a thing. That in turn means that the chaos that appears in “weather” must come from the climate system. If you instead consider “climate” as a long-term integral that derives from weather, then “climate” patterns and cycles are the product of oscillations typical of a system like Lorenz’s “butterfly.” That pseudo-cyclic pattern is scalable from daily, through annual to geological time scales from glacial epochs to much longer term patterns like the “hot house” – “ice house” pattern.
What may be fundamentally erroneous is assuming that climate is a “real” aspect of nature rather than an a reified (in the minds of climatologists) concept derived from an average experience of weather over time. Weather is real, but climate may be wishful thinking.
“During a re-run of this early model, Lorenz is believed to have restarted the program in the middle of its run by entering a variable to 3 decimal places – to his surprise the results were completely at odds with what was achieved earlier.
Restarting and re-entering the variable to its full 6 decimal places produced a repeat of the initial results – from this Lorenzo drew the inevitable conclusion that with his dozen or so equations, even a miniscule variation on input is capable of creating massive change in output.”
One would hope that he also tried it with the 3-digits and three trailing zeros, so as to see if it wasn’t an artifact of the number of digits input.
Steve Garcia
Three cycles of lunar declination tides from Christmas 2009 to march 8 2010 starting at 10 degrees North of the equator back to the same point.
[youtube http://www.youtube.com/watch?v=Ml5UljLqlIQ&w=480&h=360%5D
The real chaos driver of the global circulation is the lunar declinational tides in the atmosphere, most of the energy of the declinational tidal effects is converted to meridional flow surges that manifest as Mobile Polar Highs, Rossby waves, or jet streams (call them what you want) but they are predictable from past patterns and make long range forecasting possible, with out their consideration numerical models hit the wall just past 7 – 10 days, as the tide turns every 13.6 days.
Start time and some of the jumps in the movie are due to problems with the GOES data base missing some of the picture needed, however the synchronizing is based on the same lunar declination angle on all three, per each frame with in a degree or so. The hope was to be able to show that there are repeating patterns in the global circulation because of the lunar declinational tidal effects acting on the atmosphere.
I live in New Zealand and forecast weather for cruising yachts. Weather as ‘Chaos’ causes us to smile as we have to endure the input of initial conditions when we evaluate the weather models we use daily (GFS,ECMWF, UKMet, Access, etc). A good forecaster will always look at the actual conditions and compare them to the model day 1 forecast. If they don’t agree we lose confidence in that model run. From a weather forecasting point of view Chaos to us is simply that the atmosphere is not linear and the main reason a model loses the plot is an error in the initial conditions. (not to mention that our understanding of weather and the modeling thereof is incomplete). Most of us use ensemble models now. Take the GFS, a robust and fairly good skill score model, tweak the initial conditions 30 or more times just ever so slightly and look at , for example, the overlay of SLP. If the isobaric lines all stack up nicely as the model forecasts forward in time we have confidence in the model run, if it looks like a plate of spagetti the confidence level falls off. In the SW Pacific we think models are good for 3 days, ok to 5 days and anything afterwards is an idea.
@Bruce Stewart 7:40 am:
“How is it conceivable that climate could be forecast years ahead?”
Oh, I am certain that it will be.
Look at so much that we have done with computers in each of the last 5-year periods since 1977. Not once in any of those would we have known what was coming in the next 5-year period. Certainly not in the 2nd one ahead.
How to do climate ahead? First we need to nail down the individual factors until they are repeatable. This will be done. But not by the dodos currently ‘running’ climatology.
There are a lot of those factors, so it will be some time before that is accomplished. But it will happen.
Secondly, someone will develop deterministic-Monte-Carlo math at a level we don’t know now. A math that handles truly complex problems. A new type of computer may even need to be developed to handle the complexity – it may not be just more HP or speed that is needed. That will be the day.
As a general rule, modernity sees itself as an apex. In reality it is a point along a continuum. Seen as an apex, there is nothing but void all around. When seen as a continuum, one sees that the present works with the past and the future. The ties to the future can be seen, but not from our present bottom-up scientific mindset, from which the apex-thinking derives. It can only be seen from the continuum mindset, if any.
That is what I see. It is amusing to see the floundering at present. But it won’t always be that way.
Rupert Sheldrake has a peek at all this, and so does Freeman Dyson have a glimmer. Sheldrake is a bit of a flake. No one has ever accuse Dyson of that!
But the math – that will come from someone like Mr Butterfly himself, Kerry Mullis, and his PCR — out of left field or riding in on a surfboard. I can’t wait to see it happen. Except it might be 125 years from now. But I don’t think so.
Steve Garcia
The short answer to the question is, they don’t.
Thats why they uses ensembles and take some mean vaue of all the results, even if they differ substantially.
In this way they get only the forcings, and all the computer models are just a smokescreen put on to hide this simple fact, which would not look so good when asking for more money and computers.
Because they have discovered an input parameter that completely dwarfs all other possible input parameters: CO2!
They are not very good at finding out if this input parameter is correctly used, but that would destroy all their certainty, so they ignore that.
There is another factor to make the climate models even more suspect. Climate models have positive feedbacks. That is, a relatively small change in inputs (e.g. greenhouse gases), result in a huge change in outputs (global surface temperatures and the stability of the weather) due to being amplified by other factors (e.g. water vapour). Mainstream economics models (based on similarly complex systems) assuming negative feedbacks (equilibrating systems) can still blow apart even with accurate data inputs. They need stringent “assumptions” about parameters (often a bit of common sense or standard economic assumptions) to keep in touch with the real world, especially the forecasting models.
Climate models have even more dogmatic assumptions, with a disdain for testing the accuracy of those assumptions, and an extreme haziness in reconciling the models with real world data. Look at the Skeptical Science website to see what I mean. Yet the reconciliation needs to be accurate. Why? Temperatures rose by around 0.7 Celsius in the 20th century, of which the anthropogenic factor was, at most, 0.4 C. The IPCC models reckon around 1.5C to 5.6C of anthropogenic warming this century, or at least 3.5 times and maybe more than 20 times the 20th century. So, even with nice linear, non-chaotic systems, the amplification factor is huge. Add in some chaos theory, and you end up with models scenarios little better than astrological charts.
Re : “Weather is not climate. To conflate the initial condition dependency problem of weather forecasting with the boundary condition problem of climate simulation is fundamentally erroneous.”
One could say that one butterfly’s wing flaps may ultimately produce an effect that increases the amount of energy radiated from the earth for a brief time and hence that butterfly was involved in a cooling event. Obviously different butterflys may be involved in warming events.
The effect of CO2 can be likened to a butterfly’s wing flaps too, but will it cause more cooling events, more warming events or be neutral to those events? AGW believers are strongly in the camp of neutrality and that the warming effect of CO2 is unaffected by the inevitable changes in day to day weather. That may be a valid view for the CO2 effect itself, but is it valid for its feedbacks too?
Interesting post! The thing about chaotic systems is that they are predictable in a statistical sense, but only as long as the parameters in the system are constant. Many chaotic systems are not only sensitively dependent on initial conditions, but also sensitively dependent on the parameters. The well known logistic map x(n+1)=r x(n)(1-x(n)) is chaotic for r=4 and has a very specific bath tub shaped statistical density (worked out by Ulam and Von Neumann) but as you reduce r the statistical distribution of trajectories changes completely. This is (one more reason) why climate modelling is so daft….you would need to know the governing equations and their parameters (which are also changing dynamically) as well as the initial conditions to infinite precision. The qualitative approach to climate prediction, looking at sun spots, ocean oscillations etc seems to me to be a far more fruitful approach than supercomputer number crunching approach. My two cents.
Curiousgeorge says:
March 15, 2012 at 10:36 am
The general description for the butterfly effect is not what deterministic chaos is about. Deterministic chaos in non-linear dynamical systems is internally generated (intrinsic to the system), and not caused by random stochastic fluctuations caused by a butterfly. It is bound to the energy flow through the far from equilibrium system. Think of the formation of Benard cells, the temperature at which the cells appear is the bifurcation point.
Another great book about the subject is The Arrow of Time by Peter Coveney. Yes, that pesky Second Law and chaos seem to go hand in hand (irreversibility).