Just to be clear ahead of time, chaos in weather is NOT the same as climate disruption listed below – Anthony
Guest submission by Dr. Andy Edmonds
This is not intended to be a scientific paper, but a discussion of the disruptive light Chaos Theory can cast on climate change, for non-specialist readers. This will have a focus on the critical assumptions that global warming supporters have made that involve chaos, and their shortcomings. While much of the global warming case in temperature records and other areas has been chipped away, they can and do, still point to their computer models as proof of their assertions. This has been hard to fight, as the warmists can choose their own ground, and move it as they see fit. This discussion looks at the constraints on those models, and shows that from first principles in both chaos theory and the theory of modelling they cannot place reliance on these models.
First of all, what is Chaos? I use the term here in its mathematical sense. Just as in recent years Scientists have discovered extra states of matter (not just solid, liquid, gas, but also plasma) so also science has discovered new states that systems can have.
Systems of forces, equations, photons, or financial trading, can exist effectively in two states: one that is amenable to mathematics, where the future states of the systems can be easily predicted, and another where seemingly random behaviour occurs.
This second state is what we will call chaos. It can happen occasionally in many systems.
For instance, if you are unfortunate enough to suffer a heart attack, the normally predictable firing of heart muscles goes into a chaotic state where the muscles fire seemingly randomly, from which only a shock will bring them back. If you’ve ever braked hard on a motorbike on an icy road you may have experienced a “tank slapper” a chaotic motion of the handlebars that almost always results in you falling off. There are circumstances at sea where wave patterns behave chaotically, resulting in unexplained huge waves.
Chaos theory is the study of Chaos, and a variety of analytical methods, measures and insights have been gathered together in the past 30 years.
Generally, chaos is an unusual occurrence, and where engineers have the tools they will attempt to “design it out”, i.e. to make it impossible.
There are, however, systems where chaos is not rare, but is the norm. One of these, you will have guessed, is the weather, but there are others, the financial markets for instance, and surprisingly nature. Investigations of the populations of predators and prey, for instance shows that these often behave chaotically over time. The author has been involved in work that shows that even single cellular organisms can display population chaos at high densities.
So, what does it mean to say that a system can behave seemingly randomly? Surely if a system starts to behave randomly the laws of cause and effect are broken?
A little over a hundred years ago scientists were confident that everything in the world would be amenable to analysis, that everything would be therefore predictable, given the tools and enough time. This cosy certainty was destroyed first by Heisenberg’s uncertainty principle, then by the work of Kurt Gödel, and finally by the work of Edward Lorenz, who first discovered Chaos, in, of course, weather simulations!
Chaotic systems are not entirely unpredictable, as something truly random would be. They exhibit diminishing predictability as they move forward in time, and this diminishment is caused by greater and greater computational requirements to calculate the next set of predictions. Computing requirements to make predictions of chaotic systems grow exponentially, and so in practice, with finite resources, prediction accuracy will drop off rapidly the further you try to predict into the future. Chaos doesn’t murder cause and effect; it just wounds it!
Now would be a good place for an example. Everyone owns a spread sheet program. The following is very easy to try for yourself.
The simplest man-made equation known that produces chaos is called the logistic map.
It’s simplest form is: Xn+1 = 4Xn(1-Xn)
Meaning that the next step of the sequence is equal to 4 times the previous step times 1 – the previous step. If we open a spread sheet we can create two columns of values:
Each column A and B is created by writing =A1*4* (1-A1) into cell A2, and then copying it down for as many cells as you like, the same for B2, writing in =B1*4* (1-B1). A1 and B1 contain the initial conditions. A1 contains just 0.3 and B1 contains a very slightly different number: 0.30000001
The graph to the right shows the two copies of the series. Initially they are perfectly in sync, then they start to divert at around step 22, while by step 28 they are starting to behave entirely differently.
This effect occurs for a wide range of initial conditions. It is fun to get out your spread sheet program and experiment. The bigger the difference between the initial conditions the faster the sequences diverge.
The difference between the initial conditions is minute, but the two series diverge for all that. This illustrates one of the key things about chaos. This is the acute sensitivity to initial conditions.
If we look at this the other way round, suppose that you only had the series, and let’s assume to make it easy, that you know the form of the equation but not the initial conditions. If you try to make predictions from your model, any minute inaccuracies in your guess of the initial conditions will result in your prediction and the result diverging dramatically. This divergence grows exponentially, and one way of measuring this is called the Lyapunov exponent. This measures in bits per time step how rapidly these values diverge, averaged over a large set of samples. A positive Lyapunov exponent is considered to be proof of chaos. It also gives us a bound on the quality of predictions we can get if we try to model a chaotic system.
These basic characteristics apply to all chaotic systems.
Here’s something else to stimulate thought. The values of our simple chaos generator in the spread sheet vary between 0 and 1. If we subtract 0.5 from each, so we have positive and negative going values, and accumulate them we get this graph, stretched now to a thousand points.
If, ignoring the scale, I told you this was the share price last year for some FTSE or NASDAQ stock, or yearly sea temperature you’d probably believe me. The point I’m trying to make is that chaos is entirely capable of driving a system itself and creating behaviour that looks like it’s driven by some external force. When a system drifts as in this example, it might be because of an external force, or just because of chaos.
So, how about the weather?
Edward Lorenz, (1917, 2008) was the father of the study of Chaos, and also a weather researcher. He created an early weather simulation using three coupled equations and was amazed to find that as he progressed the simulation in time the values in the simulation behaved unpredictably.
He then looked for evidence that real world weather behaved in this same unpredictable fashion, and found it, before working on discovering more about the nature of Chaos.
No climate researchers dispute his analysis that the weather is chaotic.
Edward Lorenz estimated that the global weather exhibited a Lyapunov exponent equivalent to one bit of information every 4 days. This is an average over time and the world’s surface. There are times and places where weather is much more chaotic, as anyone who lives in England can testify. What this means though, is that if you can predict tomorrows weather with an accuracy of 1 degree C, then your best prediction of the weather on average 5 days hence will be +/- 2 degrees, 9 days hence +/-4 degrees and 13 days hence +/- 8 degrees, so to all intents and purposes after 9-10 days your predictions will be useless. Of course, if you can predict tomorrow’s weather to +/- 0.1 degree, then the growth in errors is slowed, but since they grow exponentially, it won’t be many days till they become useless again.
Interestingly the performance of weather predictions made by organisations like the UK Met office drop off in exactly this fashion. This is proof of a positive Lyapunov exponent, and thus of the existence of chaos in weather, if any were still needed.
So that’s weather prediction, how about long term modelling?
Let’s look first at the scientific method. The principle ideas are that science develops by someone forming an hypothesis, testing this hypothesis by constructing an experiment, and modifying the hypothesis, proving or disproving it, by examining the results of the experiment.
A model, whether an equation or a computer model, is just a big hypothesis. Where you can’t modify the thing you are hypothesising over with an experiment, then you have to make predictions using your model and wait for the system to confirm or deny them.
A classic example is the development of our knowledge of the solar system. The first models had us at the centre, then the sun at the centre, then the discovery of elliptical orbits, and then enough observations to work out the exact nature of these orbits. Obviously, we could never hope to affect the movement of the planets, so experiments weren’t possible, but if our models were right, key things would happen at key times: eclipses, the transit of Venus, etc. Once models were sophisticated enough, errors between the model and reality could be used to predict new features. This is how the outer planets, Neptune and Pluto were discovered. If you want to know where the planets will be in ten years’ time to the second, there is software available online that will tell you exactly.
Climate scientists would love to be able to follow this way of working. The one problem is that, because the weather is chaotic, there is never any hope that they can match up their models and the real world.
They can never match up the model to shorter term events, like say six months away, because as we’ve seen, the weather six months away is completely and utterly unpredictable, except in very general terms.
This has terrible implications for their ability to model.
I want to throw another concept into this mix, drawn from my other speciality, the world of computer modelling through self-learning systems.
This is the field of artificial intelligence, where scientists attempt to create mostly computer programs that behave intelligently and are capable of learning. Like any area of study, this tends to throw up bits of general theory and one of these is to do with the nature of incremental learning.
Incremental learning is where a learning process tries to model something by starting out simple and adding complexity, testing the quality of the model as it goes.
Examples of this are neural networks, where the strength of connections between simulated brain cells are adapted as learning goes on or genetic programming, where bits of computer programs are modified and elaborated to improve the fit of the model.
From my example above of theories of the solar system, you can see that the scientific method itself is a form of incremental learning.
There is a graph that is universal in incremental learning. It shows the performance of an incremental learning algorithm, it doesn’t matter which, on two sets of data.
The idea is that these two sets of data must be drawn from the same source, but they are split randomly into two, the training set, used to train the model, and a test set used to test it every now and then. Usually the training set is bigger than the test set, but if there is plenty of data this doesn’t matter either. So as learning progresses the learning system uses the training data to modify itself, but not the test data, which is used to test the system, but is immediately forgotten by it.
As can be seen, the performance on the training set gets better and better as more complexity is added to the model, but the performance of the test set gets better, and then starts to get worse!
Just to make this clear, the test set is the only thing that matters. If we are to use the model to make predictions we are going to present new data to it, just like our test set data. The performance on the training set is irrelevant.
This is an example of a principle that has been talked about since William of Ockham first wrote “Entia non sunt multiplicanda praeter necessitatem “, known as Ockham’s razor and translatable as “entities should not be multiplied without necessity”, entities being in his case embellishments to a theory. The corollary of this is that the simplest theory that fits the facts is most likely to be correct.
There are proofs for the generality of this idea from Bayesian Statistics and Information Theory.
So, this means that our intrepid weather modellers are in trouble from both ends: if their theories are insufficiently complex to explain the weather their model will be worthless, if too complex then they will also be worthless. Who’d be a weather modeller?
Given that they can’t calibrate their models to the real world, how do weather modellers develop and evaluate their models?
As you would expect, weather models behave chaotically too. They exhibit the same sensitivity to initial conditions. The solution chosen for evaluation (developed by Lorenz) is to run thousands of examples each with slightly different initial conditions. These sets are called ensembles.
Each example explores a possible path for the weather, and by collecting the set, they generate a distribution of possible outcomes. For weather predictions they give you the biggest peak as their prediction. Interestingly, with this kind of model evaluation there is likely to be more than one answer, i.e. more than one peak, but they choose never to tell us the other possibilities. In statistics this methodology is called the Monte Carlo method.
For climate change they modify the model so as to simulate more CO2, more solar radiation or some other parameter of interest and then run another ensemble. Once again the results will be a series of distributions over time, not a single value, though the information that the modellers give us seems to leave out alternate solutions in favour of the peak value.
Models are generated by observing the earth, modelling land masses and air currents, tree cover, ice cover and so on. It’s a great intellectual achievement, but it’s still full of assumptions. As you’d expect the modellers are always looking to refine the model and add new pet features. In practice there is only one real model, as any changes in one are rapidly incorporated into the others.
The key areas of debate are the interactions of one feature with another. For instance the hypothesis that increased CO2 will result in run-away temperature rises is based on the idea that the melting of the permafrost in Siberia due to increased temperatures will release more CO2 and thus positive feedback will bake us all. Permafrost may well melt, or not, but the rate of melting and the CO2 released are not hard scientific facts but estimates. There are thousands of similar “best guesses’’ in the models.
As we’ve seen from looking at incremental learning systems too much complexity is as fatal as too little. No one has any idea where the current models lie on the graph above, because they can’t directly test the models.
However, dwarfing all this arguing about parameters is the fact that weather is chaotic.
We know of course that chaos is not the whole story. It’s warmer on average away from the equatorial regions during the summer than the winter. Monsoons and freezing of ice occur regularly every year, and so it’s tempting to see chaos as a bit like noise in other systems.
The argument used by climate change believers runs that we can treat chaos like noise, so chaos can be “averaged out”.
To digress a little, this idea of averaging out of errors/noise has a long history. If we take the example of measuring the height of Mount Everest before the days of GPS and Radar satellites, the method to calculate height was to start at Sea level with a theodolite and take measurements of local landmarks using their distance and their angle above the horizon to estimate their height. Then to move on to those sites and do the same thing with other landmarks, moving slowly inland. By the time surveyors got to the foothills of the Himalayas they were relying on many thousand previous measurements, all with measurement error included. In the event the surveyor’s estimate of the height of Everest was only a few hundred feet out!
This is because all those measurement errors tended to average out. If, however there had been a systemic error, like the theodolites all measuring 5 degrees up, then the errors would have been enormous. The key thing is that the errors were unrelated to the thing being measured.
There are lots of other examples of this in Electronics, Radio Astronomy and other fields.
You can understand climate modellers would hope for the same to be true of chaos. In fact, they claim this is true. Note however that the errors with the theodolites were nothing to do with the actual height of Everest, as noise in radio telescope amplifiers has nothing to do with the signals from distant stars. Chaos, however, is implicit in weather, so there is no reason why it should average out. It’s not part of the measurement; it’s part of the system being measured.
So can chaos be averaged out? If it can, then we would expect long term measurements of weather to exhibit no chaos. When a team of Italian researchers asked to use my Chaos analysis software last year to look at a time series of 500 years of averaged South Italian winter temperatures, the opportunity arose to test this. The picture below is this time series displayed in my Chaos Analysis program, ChaosKit.
The result? Buckets of chaos. The Lyapunov exponent was measured at 2.28 bits per year.
To put that in English, the predictability of the temperature quarters every year further ahead you try to predict, or the other way round, the errors more than quadruple.
What does this mean? Chaos doesn’t average out. Weather is still chaotic at this scale over hundreds of years.
If we were, as climate modellers try to do, to run a moving average over the data, to hide the inconvenient spikes, we might find a slight bump to the right, as well as many bumps to the left. Would we be justified in saying that this bump to the right was proof of global warming? Absolutely not: It would be impossible to say if the bump was the result of chaos, and the drifts we’ve see it can create or some fundamental change, like increasing CO2.
So, to summarize, climate researchers have constructed models based on their understanding of the climate, current theories and a series of assumptions. They cannot test their models over the short term, as they acknowledge, because of the chaotic nature of the weather.
They hoped, though, to be able to calibrate, confirm or fix up their models by looking at very long term data, but we now know that’s chaotic too. They don’t, and cannot know, whether their models are too simple, too complex, or just right, because even if they were perfect, if weather is chaotic at this scale, they cannot hope to match up their models to the real world, the slightest errors in initial conditions would create entirely different outcomes.
All they can honestly say is this: “we’ve created models that we’ve done our best to match up to the real world, but we cannot prove to be correct. We appreciate that small errors in our models would create dramatically different predictions, and we cannot say if we have errors or not. In our models the relationships that we have publicized seem to hold.”
It is my view that governmental policymakers should not act on the basis of these models. The likelihood seems to be that they have as much similarity to the real world as The Sims, or Half-life.
On a final note, there is another school of weather prediction that holds that long term weather is largely determined by variations in solar output. Nothing here either confirms or denies that hypothesis, as long term sunspot records have shown that solar activity is chaotic too.
Andy Edmonds
Short Bio
Dr Andrew Edmonds is an author of computer software and an academic. He designed various early artificial intelligence computer software packages and was arguably the author of the first commercial data mining system. He has been the CEO of an American public company and involved in several successful start-up businesses. His PhD thesis was concerned with time series prediction of chaotic series, and resulted in his product ChaosKit, the only standalone commercial product for analysing chaos in time series. He has published papers on Neural Networks, genetic programming of fuzzy logic systems, AI for financial trading, and contributed to papers in Biotech, Marketing and Climate.
Short summary: AA discussion of the disruptive light Chaos Theory can cast on climate change, for non-specialist readers. This will have a focus on the critical assumptions that global warming supporters have made that involve chaos, and their shortcomings. While much of the global warming case in temperature records and other areas has been chipped away, they can and do, still point to their computer models as proof of their assertions. This has been hard to fight, as the warmists can choose their own ground, and move it as they see fit. This discussion looks at the constraints on those models, and shows that from first principles in both chaos theory and the theory of modelling they cannot place reliance on these models.
On his Website: http://scientio.blogspot.com/2011/06/chaos-theoretic-argument-that.html
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1 dimension (time) isn’t enough.
Can’t ignore the spatial dimensions.
Spatiotemporal chaos differs FUNDAMENTALLY from temporal chaos. (See Milanovic’s writings at Curry’s blog Climate Etc.)
I’m willing to tentatively entertain the notion of INTERANNUAL SPATIOTEMPORAL chaos, but longer-term TEMPORAL chaos is ELIMINATED from contention by BOUNDARIES, INCLUDING SPATIAL ONES:
http://wattsupwiththat.com/2011/06/08/on-the-amopdo-dataset/#comment-678688
Earth Orientation Parameters (EOP) inform us about HARD boundaries on climate. With absolute certainty, we are NOT dealing simply with temporal chaos.
Thanks for the stimulating article.
Andy; you have just put an event which happened to me 64 years ago into a single word:
“If you’ve ever braked hard on a motorbike on an icy road you may have experienced a “tank slapper” a chaotic motion of the handlebars that almost always results in you falling off.”
It was a pushbike, not a motorbike, and it was on the main drag of a hot and dusty little wheat town, Nagambie, in Australia. I was seven, the bike was flying, then the handlebars went rogue…
“Chaos” huh? Thank you.
John B says:
June 13, 2011 at 5:52 pm
“Theory says that CO2 should cause warming, observations of many kinds show that it does. ”
Huh? You say “many”, could you name me , say, two observations that CO2 causes warming? With source if possible?
Thank you Dr. Edwards – that was an excellent introduction into the role of chaos in climatology. When I first started getting into looking at climatology about 3 years ago what surprised me the most was the total absence of chaos in the models. This was even more surprising in view of Lorenz’s discovery of chaos in climate. This alone convinced me that the climate models over a period of many decades are essentially petaflops worth of garbage.
My interest in chaos goes back 20 years when I first read James Gleick’s book Chaos and suddenly a huge number of anomalous electrophysiologic findings from my research career suddenly made sense. My interests have been primarily dabbling in chaos theory as it applies to physiology and medicine and, in physiologic systems, chaos = health. The normal heart rate time series is chaotic and multifractal, based on my amateur analysis, whereas the heart rate time series in heart failure is linear. I worry when I see a Holter monitor of a patient that has essentially straight lines of heart rate for most of the day.
The primary failing of climate models is that assumption that by averaging a large number of runs one will come up with a result that will approximate the true climate. We don’t want to know the average of a large number of theoretical models, what we’re interested is what is going to happen to the earth’s actual climate which is a unique time series. I see this confusion all of the time in patients who assume that if they eat the right foods, exercise and do all of the things that they’re told will keep them healthy that they won’t become ill. When they see me after they’ve had their MI or some serious illness one of the first things I hear from them is “I did everything right and still I got sick”. While medical interventions may demonstrate a population effect, they are for all practical purposes useless in determining whether a particular patient will suffer an adverse event. I suggest that the earth’s climate is more akin to an individual patient’s medical history rather than that of the population.
Another observation I’ve made is that people can’t understand randomness or chaos. Almost inevitably they have the belief system that everything is causal; I’ve given up trying to discuss acausality with patients. If something goes wrong there has to be an external reason for it and I hear all of the fashionable reasons of why people assume they have gotten sick. We don’t throw virgins into volcanoes or burn witches at the stake to deal with crop failures any more, we just blame “pollution” or demonize CO2. When it comes to time series analysis, the majority of physicians are uncomfortable with even non-linear relationships let alone the assumption of chaos in the time series.
When I was an electrophysiology researcher I noticed we stayed away from the chaotic in what is a highly non-linear system and attempted to deal with the non-linearity by using very small perturbations of the system in a linear realm. I’ve also noticed that engineers tend to stick to analytically tractable areas and avoid the chaotic. Awareness of chaotic properties of nature is not new and Hurst was the first to actually look at fractal nature of river flows in his measurements of the Nile river. His calculations on reservoir sizes for dams date from the 1940’s. Given that the earth’s climate is chaotic, the primary response to this should be to setup the infrastructure of civilization in such a manner that it is capable of withstanding the adverse climates that result from living in a chaotic environment. Unfortunately LENR power plants aren’t sufficiently developed yet so that we can each have our own decentralized home power production but, when LENR actually produce power then this will make for a more robust society. Such a system is much less vulnerable to CME’s than the current centralized electrical production system. Similarly, where one has extreme variability in river flows constructing dams to level out the fluctuations is useful.
Given that humans have survived on the earth this long means that we have some means of dealing with chaotic systems. What is needed is to make people far more aware of the role of chaos in climate so that there is an intellectual capacity to appreciate it rather than the intuitive capacity that seems to be the norm.
one of the most common chaotic systems people encounter is the dripping tap or spigot.
With a constant pressure or head of water and a constant spout size the flow is very predictable, to the point that the system has been used to make ‘water clocks’ where the rate of flow is used to meause time.
But each drip varies in size and timing around an average, each drip is chaotic and inherently unpredictable in size and timing.
Like many natural systems there is a driving energy, the head or pressure or water in this case, and a pathway for that energy to be expended, the spout. While the way in which the energy is dissipated may be chaotic, the rate at which it is expended is constant over many drips even though each drip is chaotic. Changing the energy input, the pressure or changing the spout size, the energy dissipation process, will change the drip behavior, it will still be chaotic but the average rate of flow will change to reflect the new conditions.
The implications for climate, a similar system constrained by its energy input and energy dissipation processes, are obvious.
Climate system is not a chaos, but on decadal or century scale unpredictable, which I think is a different matter. On such scale climate change is driven by natural causes with an unpredictable future time line. This can be clearly demonstrated in case of CET:
http://www.vukcevic.talktalk.net/CET-NAP.htm
Correlation between two is by no way exceptional, but it is indicative of high degree of a cause-consequence relationship.
Boris Gimbarzevsky says:
June 13, 2011 at 10:36 pm
Great comment. As a whole scientific research communities across biology, physics, engineering etc. pay lip service to nonlinear dynamics and chaos but stick to linear systems for the vast majority of their working models. Its something akin to the rabbit-in-car-headlights phenomenon, a freezing in terror at the apparent violation of a tidy (but illusory) linearity lying at the heart of assumptions about how the world – and the scientific method – works. However such numinous dread of chaos / nonlinearity is unneccesary – there are ordered principles and logical structure within nonlinear chaotic systems also – just of a different kind. Science remains too compartmentalised. The field of study of chaotic / nonlinear systems is well developed and such systems despite their “chaos” label display conformity to a number of rules and patterns and types of analysis that are well understood. Such insights need to be communicated to fields where they are needed, e.g. climate, physiology, biology etc. in a qualitative manner. FWIW my own attempt to do so was posted here on WUWT in January this year.
Mingy,
You wrote “while perhaps the physical system that is the earth may not be in isolation a chaotic system, I am pretty sure there is no doubt some of the feedbacks are….So even if you did know all the starting conditions, etc., the biosphere would have a major say and you can’t model that.”
Good point. I agree. Thanks.
Bill
Anthony,
thank you for the introduction. There is a nice appendix for your equation:
http://en.wikipedia.org/wiki/Logistic_map
KR says:
June 13, 2011 at 6:42 pm
“In the past, CO2 levels followed temperature changes as a feedback, amplifying them. Now we’re increasing CO2 on our own.”
Yes, the ice cores clearly show that CO2 levels followed temperature changes. But, as far as I know, the data shows no sign of any feedback at all. If increases in CO2 caused a corresponding increase in temperature then it should show up in the data, but it doesn’t.
This is what the empirical data says: when temperatures go up the CO2 goes up, and vice versa – and that changes in CO2 have essentially zero effect on the climate.
Forget the models and look at the data.
Chris
Chaos theory is a rich and powerful branch of mathematics, and it can not be summarized in any short popular article. Still I want to add some considerations to the text above to dismantle widespread misconceptions:
1) Chaotic systems can display different levels of chaoticity, from barely detectable to fully developed. There is a known universal rout to chaos by period duplication. At first we see quasi-periodic dynamics, and as parameter of chaoticity grows, more and more different periods emerge being powers of 2 of original period.
2) Statistics of chaos is quite different from that of noise, so looking for signatures of chaotic behavior in Fourier transform of time series is a standard procedure in this field. Unfortunately, it requires rather long time series, often unobtainable in actual measurements. But model outputs can be always tested this way for detecting chaotic behavior of the models. Actually this is how the first chaotic attractor (Lorentz attractor) was discovered.
3) Mathematical models which display chaotic behavior are not robust. That means that their reliability as true representation of real-world phenomena can not be proved by comparison to measurements, and their parameters can not be reliably identified. This severely restrict their usefulness to prove or disprove any hypotheses about real world. They are merely a basis for speculations and insights, but hardly anything else.
Chaos. There seems to be a purist argument here versus something theoretical? On one side the purist believes we can never know everything (Heisenberg etc), BUT, we certainly can determine *some* things. The others argue vehemently against chaos on principle, and they appear to believe it is theoretically possible to obtain all parameters and be deterministic, perhaps perfectly?
Isn’t it merely a question of exactly what can be determined? In my opinion, certainly not everything. It would require hubris to state we can obtain *all* existing information (clouds, wind, location of electrons too?). Someone said (cannot remember) that to store all the required information of a system in order to be perfectly deterministic it would exceed the mass of all the matter in the system (or something along those lines, someone help!).
I don’t understand why the two sides here, chaos vs determinism simply cannot agree that Chaos == Incomplete Information, and move on. It seems like semantics. I’ll stick my neck out and say: we’ll never know everything. But that does not mean we cannot try.
It went right over your head. How about this, just pick a day, a famous one, the NH Summer Solstice, usually June 21. Now pick a time, high noon. Now compare the conditions of that date/time in the same place for all the years you can find data for. We’ll see 100 ° F and 55 ° F and pouring rain and drought and if you go back far enough (1816 perhaps, in the NE), snow flurries. That is the real world Lazy Boy and it is chaotic, from our point of view. The sum total of countless forces (parameters/variables) interacting for a *minimum* of 364 days (think about it, years are our invention) preceding June 21, give a result that will never be perfectly determined in advance.
Now your model, due to lack of information, at best will only be a poor approximation of that gigantic system that created those various outcomes found at high noon on June 21. So the model can only suck. The question is, just how much can you reduce the suckiness of it as to not waste our time, and our money chasing the un-catchable. I say you cannot, but you are free to try, just use your own money, okay?
Am I the only one who barfs when math is written as maths? I must be getting old.
I find it humorous that KR brought up chaotic attractors without knowing what it meant. There’s a reason for attractors. It means physical mechanisms exist that keep the system close to the attractor state. What are these mechanisms called? Well, in climate they are called negative feedbacks.
Thanks KR for mentioning that the climate feedbacks must be negative for us to exist in an attractor state.
As for comments that CO2 increases are dangerous. Pure poppycock. The current low values are the dangerous situation. We even have empirical evidence that increases promote plant growth and make MOST plants more resistent to drought.
Dr Andy Edmonds
Even if we don’t know the analytic forms for the chaotic attractor(s) of weather, we still have the observational data to determine limits on them. If we didn’t, farmers could not make even a wild guess as to whether or not next year’s crop would even be possible in their area, or whether they should up and plant it 100 miles north or south. We know the rough outlines of how warm or cold next year will be within some limits of variation.
The major issue I have with your post is that you are taking an initial value problem, predicting weather, assigning its difficulties to a boundary condition problem, climate, and stating that therefore climate prediction and analysis is impossible. Which leads right into “We can’t know, so let’s not do anything about it…”
The boundary condition problem of climate is in terms of energy balances. Over a period of time, despite internal variation (fluid dynamics, ENSO, lead/lag responses, moving pressure zones), any imbalance, positive or negative, will correct itself through basic conservation of energy.
In terms of climate modeling, estimations can be made will full coupled General Circulation Models (http://en.wikipedia.org/wiki/Global_climate_model) running with a variety of initializations to perform a Monte Carlo sampling of the interaction space (and yes, while the one and two sigma bounds are often left off graphic representations of the results, they are available, contrary to your post).
Alternately, you can get essentially the same results using a zero dimensional climate model (same wiki page) that simply looks at the energy imbalances due to radiative physics, insolation, and GHG levels. A zero dimensional boundary condition model like this cannot tell you the geographic spread of temperatures, obviously, but it will tell you the average temperature based on those conditions.
Boundary condition problems are.not.chaotic. Their solutions cannot give you daily weather – that’s the wrong question. But they can be solved for long term values that the chaotic system will average to based on energy considerations.
The only remaining question is the time scale of weather, of chaotic variation, how long for the attractors to cycle. People have spent a great deal of time on this, and 30 years sampling appears to be long enough to cover observed variations. See http://tamino.wordpress.com/2011/03/02/8000-years-of-amo/ and http://tamino.wordpress.com/2011/02/26/mathturbation/ for some numeric analysis of this issue. A much shorter term period can be used to look at trends if you account for the larger known variations, such as the ENSO, and for forcing changes, such as total solar intensity, volcanic aerosols, and the like. But 30 years as a simple running average appears sufficient to encompass multiple +/- swings of weather variations.
In summary, your “We can’t know, so let’s not do anything about it…” conclusions (whether that was your intention or not, that’s how it will be used) are based upon a mischaracterization of the the problem.
John B says:
June 13, 2011 at 2:20 pm
1) Why do you believe that humans will be more affected by CO2 than other animals?
2) According to the geological record, CO2 rates often change quite fast.
KR:
There are no costs to enhanced CO2.
There are many benefits to enhanced CO2.
CO2 production should be subsidized, not taxed.
Since our CAGW believers are once again focusing on CO2, I will once again challenge them to explain why the cooling effects of GHGs like CO2 are never mentioned in any discussions. For some reason they always run away and avoid the topic.
John B says:
June 13, 2011 at 3:09 pm:
And what pray tell is this so called evidence that the IPCC sumarizes? Is it the loss of Himalayan glaciers? Oops, that has been disproven.
Was it the loss of the Kilamanjaro glaciers? Oops, that was disproven as well.
The only thing the IPCC has is conjecture and supposition backed by either unproven or disproven “facts”.
LazyTeenager says:
June 13, 2011 at 4:36 pm
No, he proved that there is no way to predict with any certainty how warm summer will be, or how cold winter will be.
Of course winter and summer involve changes in energy flow that are huge compared to what CO2 is capable of generating.
KR says:
June 13, 2011 at 5:20 pm
The claim that the cooling of the 60’s and 70’s was caused by [aerosol] cooling is trivially easy to disprove.
The places with the highest loads of aerosols saw the least cooling.
Aerosol’s are just another wild guess used by modelers to explain away the failings of their models.
In the past, CO2 levels followed temperature changes as a feedback, amplifying them.
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Prove it.
DirkH says:
June 13, 2011 at 10:15 pm
John B says:
June 13, 2011 at 5:52 pm
“Theory says that CO2 should cause warming, observations of many kinds show that it does. ”
Huh? You say “many”, could you name me , say, two observations that CO2 causes warming? With source if possible?
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Dirk, he’s trying to claim that correlation is proof positive of causation.
IE, we have measurements shonwing that CO2 has increases.
We also have very poor and problematic data shows that temperatures have probably increased during the same time.
Therefore, CO2 must be the cause.
Blade says:
June 14, 2011 at 4:21 am
Am I the only one who barfs when math is written as maths? I must be getting old.
If you ever come to the UK, bring plenty of barf bags.
KR,
The point is that the models you cite assign all residual warming to man-made CO2. However, chaos can produce the same warming without man-made CO2. Moreover, as climate science advances, we find other explanations for for the residual warming that the AGW community assigns to man-made CO2. As it now stands, the cost and coordination problems required to reduce the small amount of unexplained warming are so large as to render the entire AGW proposition moot.
Here is a question for you Andy.
Can your software determine if the amount of chaos in the temperatures or other climate variables such as wind speed is changing with time and if so what does it show?