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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Smokey says:
June 13, 2011 at 2:14 pm
10,000 ppm CO2 directly diplaces 10,000 ppm O2.
I guarantee you that the drop from 21% O2 to 20% O2 is not noticeable.
You might notice it at 20,000 ppm CO2 (19% O2) if you are working physically hard (been there, observed that).
We’ll slap run out of fossil fuels long before 10,000 ppm is reached.
No danger. None.
Climate Modeling has itself generated a lot of chaos and angst.
The problem is that the real world diverged from the predictions, but the chaos of climate modeling continued well into the absurd.
How to guarantee damage to a scientist’s spleen; tell him there are some things he simply cannot know!
A kindergarten teacher was observing her classroom of children while they drew. She would occasionally walk around to see each child’s artwork. As she came to one little girl who was working diligently, she asked what the drawing was.
The girl replied, “I’m drawing God.”
The teacher paused and said, “But no one knows what God looks like.”
Without missing a beat, or looking up from her drawing the girl replied, “They will in a minute.”
Can anyone guarantee that if we drop CO2 levels back to 1850 levels….
….temperatures will not continue to rise?
Nope……and that lag crap don’t cut it
and if no one can do that, they are all talking out of their hats
So Andy Edmonds has just proved that winter, summer, spring and autumn are figments of our imaginations.
Because if the climate is entirely chaotic we should only ever see random variations and physical system inputs such as solar insolation can have no visible effect.
Seriously I think Andy has a bad case of model mania. The climate is not just about the maths of chaos. It is also about the physical processes involved and they put significant constraints on the amount of chaos and what part of the system is chaotic and what part is not chaotic.
Here is a little something from our friends at The Resilient Earth.
“Seven Climate Models, Seven Different Answers”
“Why Climate Models Lie”
and a little something from our other friends. ;O)
Nevermind, let’s make trillion Dollar decisions based on all or some of the above. CRAP!
I was debating the topic concerning extreme weather events. I challenged the consesus opinion on Skeptical Science and was provided a link to a presentation by Stu Ostro who is a meteorologist. He is making the claim that the weather patterns are indeed getting more extreme. In his powerpoint presentation by shows numerous charts of upper level activity and claims that they are most unusual and are proof global warming is shifting climate into very dangerous territory. I watch local weather but they do not go into upper level troughs and ridges or what normal or abnormal pressures are for this region.
I am wondering if anyone on this sight can either verify the powerpoint presentation or explain why the upper level disturbances are not that unique. Thanks.
Stu Ostro presentation proving global warming is shifting weather patterns in dangerous ways.
KR,
Your scary hokey stick video can be easily deconstructed with a simple graph: click Notice that temperature is independent of rising CO2. If CO2 had any more than a minuscule effect on temperature, then temperature would closely track the rise in CO2. It doesn’t. That’s because CO2 has little to no effect on the climate. If there is any effect, it is too small to measure.
CO2 is a function of changing temperature, not a cause [except in the most minuscule sense]. By using a normal zero-axis CO2 chart, the scariness goes away: click Keep in mind that CO2 is a very minor trace gas. Quadrupling CO2 would still make it a very minor trace gas. Here is a graph of atmospheric CO2 with a proper y-axis: click See the CO2? Didn’t think so.
Here is a graph with even better temperature correlation: click It makes as much sense as your silly video.
John B:
You claim there is “evidence” of CO2 changing the climate. That is not true. But feel free to post anything you’ve got, and we will find that it is not measurable, testable evidence per the scientific method, but rather, conjecture and/or always-inaccurate computer models. If there was any real “evidence” of CO2 changing the climate, we would hear it trumpeted 24/7/365. So post what you’ve got, and we’ll deconstruct it here.
Smokey – As I expected, you’re moving the goalposts. CO2 is increasing faster now than in the 1940’s or in the 1800’s, completely contradictory to your earlier statements, so you change the subject. Serious weak sauce there…
Here are the various forcings over the last few hundred years:
http://data.giss.nasa.gov/modelforce/
Temperature decline from 1940-1970 or so was due to a lot of aerosols – the Clean Air act and similar legislation cleaned that up, leading us right back to the CO2 driven temperature rise. Climate is driven by the total of all forcings – nobody claims that it’s a single factor. To state otherwise is a strawman argument (http://en.wikipedia.org/wiki/Straw_man), such as you have presented before.
As to your “Post Office charges drive climate change”, I would point you at: http://www.venganza.org/images/spreadword/pchart1.jpg
Correlation does not equal causation. On the other hand, we know the physics of CO2 and IR – that’s a physical cause that correlates to climate change. The only trumpeting we see is people (like you) loudly denying the evidence in front of you.
Stay on topic, Smokey. You said “CO2 may well have increased more rapidly in the past.” KR’s video shows that was not the case. No mention of temperatures. You are moving the goalposts, as ever. Had you referred to temperatures, I am sure he would have provided different counter-evidence.
Your postal charges graph would be amusing, if you didn’t seriously think it made a point. For the benefit of other readers, who might not be quite so stubborn, here is why it is silly:
Back in the day when the smoking/cancer link was still disputed, people used to show the link between cancer rates and, say, the number of TV aerials. The attempt was to show “correlation does not mean causation”. Yes, that is true, it does not. But there was also a causal link, which was soon demonstrated to be true, between cancer and cigarettes. Same thing with CO2 and warming. Not only is there a correlation, there is also a link – the greenhouse effect. The correlation is not linear beause there are other effects, such as solar cycles, volcanoes, etc., but do some hard math, look at long enough periods and the correlation is clear. Supported, as I said, by the link of the greenhouse effect. Theory says that CO2 should cause warming, observations of many kinds show that it does.
Smokey, you just so desperately want it not to be true, that no amount of evidence will sway you. Why is that?
Me? As I have said before, and KR and others have also said, if temperatures don’t go up in the next 10 years or so, something is seriously amiss with AGW. I will be swayed by the evidence, if and when it appears.
He doesn’t seem to know that, no matter what a computer may preduct about planetary positions in the future, look far enough ahead and there is no doubt at all that they are chaotic. We can’t even solve the equations of the Moon’s motion exactly, despite centuries of effort. We have only a good approximation which is useful for navigating spacecraft and predicting eclipses.
KR the alarmist is getting desperate:
“As I expected, you’re moving the goalposts.”
Not really, KR. That’s why you didn’t quote me verbatim.
And please, dispense with your links to models. They’re models, see? Conjectures. They are not evidence. But I did enjoy the pirate chart, which has been posted here off and on for the past four years. Like the postal chart, it makes a clever mockery of CAGW, like this and this.
And when you say I am “denying the evidence,” my response is: what evidence?! You haven’t provided any evidence. For the umpteenth time, evidence means empirical [real world], testable, measurable evidence subject to falsification per the scientific method. All you’re doing is pasting model-based conjectures. None of it is evidence.
On the other hand, Beck’s peer reviewed paper is based on empirical evidence showing CO2 spikes in the early 1800’s and the 1940’s, and it has never been falsified. The alarmist contingent is desperate to try and falsify it, but they have always failed. Their criticism amounts to: “That can’t be right!” But it is right.
Beck et. al is rigorously documented, with over 90,000 separate CO2 measurements, accurate to within ±3%, with the CO2 readings meticulously recorded by Nobel laureates and many other internationally esteemed scientists who took copious notes and made drawings of their test apparatus [which has been duplicated, and which proves their measurements were within ±3%].
The CO2 readings were taken by numerous scientists on the windward side of ships during mid-ocean crossings on the Arctic Ocean, the Antarctic Ocean, the Sea of Okhotsk, the South Seas, and the Atlantic and Pacific Oceans, where there was no chance of contamination by urban factories, only fresh sea breezes. Readings were also taken on rural mountain tops and the desolate Ayrshire coast of Scotland. Those scientists knew exactly what they were doing, and they did it right. But the alarmist crowd just can not tolerate the findings, because the rise in CO2 in the 1800’s and 1940’s was more rapid than the current rise.
More empirical evidence is found in the Northern and Southern Hemisphere ice cores. It shows conclusively that rises in CO2 follow rises in temperature by 800 ±200 years. Effect cannot precede cause, therefore it is reasonable to conclude that much of the current rise in CO2 was caused by the MWP.
Still waiting for any testable, measurable evidence showing that X amount of CO2 results in Y amount of temperature change. That’s because there is no such evidence. There is only model-based GIGO, conjecture, and unproven hypotheses. None of it is testable and measurable.
In the past, CO2 levels followed temperature changes as a feedback, amplifying them. Now we’re increasing CO2 on our own.
Do natural forest fires in the past disprove arson in the present? Hmmmm.
Now you’re referring to Beck? Published in Energy and Environment? Which ignores the last 50 years of carbon cycle research? Read http://www.realclimate.org/index.php/archives/2007/05/beck-to-the-future/ for a bit of perspective on that. If you want to convince people (like me) who actually read primary references, look at data, look at multiple analyses – you’re going to have to do better. Perhaps by posting some facts.
You appear to be suffering from confirmation bias (http://en.wikipedia.org/wiki/Confirmation_bias) – nothing we can say or do will dissuade you from your confirmed opinions. But perhaps, just perhaps, other, less blindered folks will learn something from this exchange…
In your little spreadsheet example of the diverging series, you may also need to consider the fundamental errors in floating point operations in modern computers. It is easy to show that basic mathematical “laws” do not apply and most people are totally unaware of that fact. It is true that using modern fixed size mantissa and exponent floating point representations that (A-(B-C) does not always equal ((A-B)-C), and this can also be easily shown in Excel.
Best reference for the technical discussion is Donald Knuth’s “The Art of Computer Programming” Vol 2.
As far as I know, all the “models” rely on the underlying floating point hardware and I have not seen one that tries to track or estimate accumulated errors or to use true number representations (eg arbitrary precision rational arithmetic). I believe that in models iterating millions of times over millions of elements this fundamental source of error make the results almost random, hence the need to marshal the hoardes of models and model runs in an attempt to “average” away this chaotic behaviour.
As I have pointed out many times, if it weren’t for psychological projection, the alarmist contingent wouldn’t have much to say. Case in point:
KR ignores the numerous verifiable facts I have posted here, improbably saying “you’re going to have to do better. Perhaps by posting some facts.” To make matters even worse, KR simply cuts ‘n’ pasts realclimate propaganda [and he should be aware that until RC allows uncensored comments by scientific skeptics, realclimate its links are not worth clicking on. KR needs to try and make his own arguments, instead of using the crutch of a propaganda blog like realclimate, home of Michael Mann the climate charlatan.
KR is just frustrated because he has no empirical evidence showing global harm from CO2. None. That’s because there is no such evidence. The whole CAGW conjecture is based on psuedo-science and promoted by religious true believers.
I have a completely open mind, and I’ve stated on a number of occasions that I will begin to change my mind if anyone can produce measurable, testable evidence, per the scientific method, showing global harm due specifically to CO2. That is not confirmation bias, that is the scientific method in action – something avoided by the alarmist crowd like Dracula avoids the dawn.
Oh, come on now. Surely the GCMs are chaotic enough to match the climate’s chaos to a high degree of precision! /sarc
Smokey – Did you read my post at June 13, 2011 at 11:55 am? It doesn’t seem so. That contains 60+ peer reviewed papers regarding benefits and costs of CO2 driven climate change. As I recall, cost papers outnumber benefit papers by more than 2x.
I don’t want to get into a insult-trading exchange here; I believe my posts stand on their own merits. Others may judge as they may. But that this point Smokey and I are at the “I hit you last” stage (remember that from childhood?), which is just not productive.
—
Back to the topic of this thread – weather (chaotic initial value problem) is not climate (boundary energy problem), and inability to predict weather does not invalidate long term climate averages. Weather is constrained by the average and standard deviation of the chaotic attractor, and if that mean changes due to forcing changes weather will (as an average) change accordingly. Claiming a boundary problem is insoluble based on an enclosed initial value problem is a distinct mislabeling of the situation.
Smokey, just answer me this one question: Why do you trust Beck’s paper, in preference to all the mainstream research that shows that CO2 has risen steadily but at an increasing rate?
Forget plant food for a moment, stick to that question. I am trying to get an insight into how you think.
Gah. Late night typing betrays me.
“Weather is constrained by the average and standard deviation of the chaotic attractor, and if those averages change due to forcing changes, weather will (as an average) change accordingly.” is what I meant to write.
KR,
You’re actually referring me to the disreputable Skeptical Pseudo-Science blog, run by a cartoonist?? Please.
When any of these censoring alarmist blogs list WUWT on their sidebars [like WUWT does for them], I’ll start clicking on their pseudo-science. But not before.
Try making your own resoned arguments like I do, without using propaganda blogs as a crutch. Cutting and pasting something from a Scientology blog is no substitute for a discussion or argument. Especially since those censoring blogs are not worth clicking on. So I don’t. I will read what you post here. But I draw the line at climate charlatans.
John B,
Let me turn the question around, and ask you why you casually dismiss the 90,000 CO2 measurements taken by well known scientists, incuding Nobel laureates [when the Nobel Prize really meant something]?
Is it because you have already arrived at your conclusion, and you don’t want inconvenient facts to get in the way?
KR says:
June 13, 2011 at 7:34 pm
Smokey – Did you read my post at June 13, 2011 at 11:55 am? It doesn’t seem so. That contains 60+ peer reviewed papers regarding benefits and costs of CO2 driven climate change. As I recall, cost papers outnumber benefit papers by more than 2x.
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So why don’t you take any one of those sh!t papers and show conclusively (or partially even), in your own words, the evidence that anthropogenic CO2 has caused any of those effects. You have 60+ to choose from. Should be a breeze right ? Although, if you do, you will be the first person in history to accomplish it.
John B
Why don’t you look at scenario A, B and C of Hansen’s models and tell us where CO2 linked temperatures are now in relation to the projections of the models?
And John B what’s your evidence? IPCC? Don’t make us laugh. Their statements are not science and are not backed by any empirical evidence. They are based on these models.
Why do you think Hansen and Trenberth are desperately searching for the ” missing heat ” in the troposphere and the oceans. That heat is indeed ” missing ” because it never existed in the first place.
Listen, model output is not evidence. Empiricallly measured data is evidence. And if data and models don’t agree, then the models are wrong, not the data. So the projections of these models are worth zilch.
Smokey, I asked first! But anyway…
I am skeptical of Beck’s paper because, among other things and in no particular order:
1. It contradicts the ice core data
2. It suggests wild swings of CO2 that accepted theory says can’t happen
3. If concentrations had been that high, there should be residual C13, which there isn’t
4. The chemical measurements on which the paper is based are known to be problematic
5. It is only one paper, and no one else has published work that supports it or can reproduce its results
Now, you tell me why you discount everything else that contradicts Beck?
John B says:
“1. It contradicts the ice core data”
No, it doesn’t, because the ice core data ends more than a century ago.
“2. It suggests wild swings of CO2 that accepted theory says can’t happen”
There is no “accepted theory.” There is only conjecture at this point.
“3. If concentrations had been that high, there should be residual C13, which there isn’t”
You probably get that misinformation from Skeptical Pseudo-Science. Try reading the WUWT archives, you will get the straight skinny here.
“4. The chemical measurements on which the paper is based are known to be problematic”
Really? “Problematic”? How so, exactly? The test apparatus has been replicated from the original drawings, and shown to be accurate to within ±3%. Looks like you’re just winging it with your ‘problematic’ comment.
“5. It is only one paper, and no one else has published work that supports it or can reproduce its results”
As Albert Einstein said, it doesn’t require a hundred scientists signing a letter to falsify Relativity, it only requires one fact. CAGW has been repeatedly debunked. Only CAGW true believers still demonize “carbon”. Wise up, and stop being a true believer. CAGW is pseudo-science. It is more credible than Scientology at this point.
Hi KR,
Just to jump in on someone else’s argument…
“Weather is constrained by the average and standard deviation of the chaotic attractor, and if those averages change due to forcing changes, weather will (as an average) change accordingly.”
This is just a variant of the It’ll average out argument. Even worse it’s a chaos is amenable to stats argument.
What attractor are we talking about here? Weather seems to have several acting at different scales. I used a software tool that was developed and tested on a variety of time series to look at yearly temperature data and found chaos. This simple result doesn’t begin to tell us the bounds of whatever attractor is operating at this scale.
Nor does it tell us that your simple implied equation is true: fundamentals + chaos = recorded values.
What if it’s fundamentals * chaos = recorded values? You’re making assumptions you can’t justify.
This is the point of the article, climate models are full of assumptions, made for convenience, and let’s assume with good intent, which cannot be tested in the real world.