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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Excellent article, thanks. This article is succinct enough to help explain practical mathematical chaos to the lay person.
KR says:
June 13, 2011 at 9:45 am
“The claim is made that weather is chaotic – yes, it is. But the averages are not. ”
Averaging is only dampening high frequencies in a well defined way – a lowpass filter operation- the power spectrum of chaos is not the (regular) power spectrum of noise but can have strong (and unpredictable) spikes. You don’t get rid of these spikes with a lame old general lowpass filter – you can only dampen them a little but they’ll still stick out. I wonder how low-passing should help you there.
“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.”
We need to be clear about what is being asserted. Someone observed that weather six months away always strikes him as unpredictable. That does not mean that it is unpredictable. More important, it also does not mean that the important features of the weather are being observed. Clearly, then, the assertion that some phenomenon is chaotic requires some evidence beyond the observations of several people that it strikes them as chaotic. Weather might seem unpredicatble. But climate science and meteorology are both in their infancy. What we call weather or climate today is not likely to be called weather or climate in ten years.
John Marshall says: June 13, 2011 at 8:31 am
“Another problem with climate models is that they rely on a theory, GHG effect, that does not exist. There are other explanations for Earth’s average surface temperature being ‘too high’ without need of a theory that violates the laws of thermodynamics.”
Please state exactly what part of the GHG effect you think violates what law of thermodynamics.
Smokey – You should have posted the next few very relevant lines from that piece: “The most we can expect to achieve is the prediction of the probability distribution of the systems future possible states by the generation of ensembles of model solutions. This reduces climate change to the discernment of significant differences in the statistics of such ensembles.” (http://www.ipcc.ch/ipccreports/tar/wg1/505.htm)
That’s the core of Monte Carlo statistical estimation, Smokey. Predicting the long term average climate, not detailed weather.
As to “no evidence whatever of global harm from increased CO2, and much evidence of global benefit.”, I’ll have to disagree based on every study I’ve seen.
Terry Oldberg says:
June 13, 2011 at 9:14 am
Evidently, Dr. Edwards is unaware of the three decade old work of Christensen, Eilbert, Lingren and Rans that made it possible to predict surface temperature and precipitation related variables in the western states of the U.S. as much as 3 years in advance. I provide an introduction to the methodology that made this advance possible and compare it to the methodology of modern climatology at http://judithcurry.com/2011/02/15/the-principles-of-reasoning-part-iii-logic-and-climatology/ . In brief, the idea was to construct an information theoretically optimal decoder of a “message” from the future that conveyed the outcomes of weather-related events.
While chaos precludes the success of an approach to long range weather forecasting that is based entirely upon the principles of modern physics, it does not preclude long range weather forecasting. The same might be be found to be true of long range climate forecasting if construction of a climate-forecasing decoder were to be attempted.
If that worked then it would be in use right now – the users of it would be as rich as Croesus!
Have you any idea what construction companies would give for that kind of information let alone farmers?
You probably should demonstrate it at the ocean front property you have in Kansas.
KR,
Either provide testable empirical evidence of global harm from CO2 per the scientific method, or admit that there is no such evidence. Keep in mind that “studies” are not evidence, and neither are computer models.
And if you want solid evidence of the benefits of increased CO2, just ask.
Well, now I know a little more about chaos. Thank you.
Nevertheless, the physics of the planet demands that angular momentum and energy be conserved, that radiation depend on temperature, that convection in the oceans be constrained by the viscosity of water and changes in density forced by temperature … so all these provide boundaries within which the chaos will be confined. I suppose that is why life has survived for all these aeons.
Ed Mertin says: June 13, 2011 at 8:30 am
“You have to go back to the 1930′s to find as many volcanoes honking as we’ve had since 2008.”
According to this link of major volcanoes, the 1930’s were hardly an exceptional decade for volcanoes.
http://online.wsj.com/article/SB10001424052748703465204575208412972387390.html
Can you provide statistics from your source (not just the intro page listing a few interesting volcanoes) that show how the 1930’s were any more severe than other decades?
Excellent article and thank you.
@KR
“Weather is inherently chaotic, but climate (long term averages) is not. The IPCC is quite aware of that, see …”
The above statement makes no sense whatsoever. If the climate can change from one extreme to another, Ice Age to Holocene and there is no defined time scale or defined cause then it must be chaotic?
Sorry if I am missing the point.
June 13, 2011 at 10:07 am
KR says:
“Arguing that we cannot predict the climate is simply a plea to do nothing, to continue with business as usual. You’ve spent a lot of effort on a very deceptive posting.”
That is exactly what I am arguing. Don’t touch that dial. Do not pass go and do not collect $200. Resist the urge to think that you can legislate climate when climate is more chaotic than the stock market and look how that worked out for the likes of Long Term Capital.
KR
Since the IPC pretty much stakes all on the value of models (few of which agree with each other, let alone nature) it would be hard to believe that they would utter a word which would in any way question the utility of such models.
In any event, as the author notes:
“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.”
Once you have a highly complex system, it can behave very much much like a chaotic system in all ways which matter. Current models have rudmientary simulations of things like cloud cover, and they do not and can not deal with biological feedback systems. In the olden days the carbon cycle was a thing we studied, don’t you know. Running a 16km3 grid simulation might be convenient computationally, but since most features with matter are much smaller than 16km3, you pretty much immediately lose the opportunity to predict anything.
You know, there is a lot more money at stake in financial models and none of those have been shown to be worth anything either. Only climate science presumes what all other real scientific disciplines already know: models are nice and fun, but nature is the teacher.
How did Kepler end up as part of the conversation?
Nice explanation. You should point out that the example given using the logistics formula is the simplest of many, and that the first term (4) varies and equates to being the “driver” of the system. Other values will result in different behavior, as I’m sure you know, and it’s interesting to increment this value over the series.
Excellent article Dr. Edwards.
A couple notes on things that impact the edges:
1) The recurring case of the climate modellers taking results from widely disparate models and combining them – not into a ‘single model ensemble’ but into a ‘all available models ensemble’ – comes from the methodology of the individual models. “Combining into an ensemble” is fundamentally what they’re doing on a per-model basis. But all it does functionally is completely prevent the invalidation of -any- model.
2) The one area that seems fundamental in the methodology is the hindcasting to demonstrate any skill whatsoever. And yet the central theme of ‘historical temperatures are flat!’ of Mann et al. is less and less viable over time.
Ian W says:
June 13, 2011 at 10:00 am
Its not so much a random walk as a Levy Flight as some of the random motions are far more than others.
Thank you for this insight, I just learned something new and interesting. Indeed the some changes have more effect than others. The main problem with currernt climatological research is that conclusions are drawn too fast. I think that the main problem is that they have focused too much on the relatively simple parts as CO2 absorption and emission and not at the fact that there are number of phenomena varying at very different time-scales. The main reason for the poor predictive power of the models is that they have lumped the effects of multiple phenomena and explained them by just one component of the system. It’s a simplistic mechanistic approach to a very complex system. Its just sad that major economic and political decisions are based on predictions based on a science that isn’t mature.
KR says: “Weather is inherently chaotic, but climate (long term averages) is not. The IPCC is quite aware of that…”
The IPCC was also aware that all the Himalayan glaciers are going to disappear by 2035.
In regards to long term averages and behaviors:
Dr. Edmonds, are you stating that the chaotic attractor of the weather does not have a mean and standard deviation? If so, that would make it unlike just about every chaotic system I’ve seen. The weather cycles around the attractor, but summer is predictably warmer and winter predictably cooler, as the average changes.
Stacy – Long term variations in climate come from changes in forcings (input/output changes in energy balance), such as insolation, orbit, etc.. For the ice ages the Milankovich cycles of orbital precession appear to be the major cause of climate change. And those changes are pretty well defined and timed. Right now, based on our position in the tapering of the interglacial portion of the Milankovich cycle, we should be seeing cooling temperatures. We’re seeing warming, because we’ve added another forcing – extra CO2, to a level currently 100 ppm greater than anything in the last 800K years.
I spent my nuclear engineering career as a modeler. Nuclear systems are simple systems compared to climate and I had a tough enough time with them to immediately be suspicious of climate models when AGW became the fad of the day. So I don’t disagree with the arguments and conclusion made here. But I think we should distinguish between chaos and complexity. Chaotic behaviour can arise from a few simple equations subject to minute changes in initial conditions. In contrast, complex systems are characterized by many equations with many parameters that are not precisely known. Even starting from the same initial conditions with computers of infinite word length, the variability of the parameters is enough to make the results unpredictable. Of course the initial conditions are also imprecisely known, computer word length is not infinite, discretization is limited and so on. Small wonder climate is not predictable. Negative feedback can provide bounds for models, including climate models and my guess is that is the case for us – else we would not have made it this far.
Anyway, my point is that climate is complex enough to not need chaos to ensure unpredictability. If we could restart the planet with exactly the same initial conditions at some point in the past, it would be the influence of small differences in parameters, caused by small external perturbations, that would ensure a different evolution. It may or may not be bounded depending on the path evolution. That is complexity, not chaos.
Semantics perhaps but when I think of chaos, I think of sensitivity to initial conditions and when I think of complexity I think of sensitivity to the details of the equations, parameters and boundary conditions. Of course complex systems can be chaotic and chaotic systems can be complex….
At any rate, it is negative feedback and overall energy considerations that provide climate bounds and provide some level of predictability, in spite of any chaotic or complex nature of the models.
Bill
Dr.Edwards, thank you for a fascinating article. This math challenged individual actually understood most of the concepts raised. Actually tried your excel experiment. Pretty neat. To K.R.: 1) If all our scientific capabilities were available during the LIA, would the current warmer period be “averaged out”? 2) Why are negative feedbacks “averaged out” but not positive ones?
Alan S. Blue
The interesting thing with ‘back casting’ is that any model which cannot ‘back cast’ the data used to craft and groom (‘train’) its algorithms clearly isn’t worth spit, yet they do show up in the climate science world. Hoards of PhDs in Economics have been granted for the development of models which have the sole merit of ‘modeling’ the past. They have no apparent utility in predicting the future (if they did, according ot economic theory, they would not be published!).
It is bizarre beyond belief that a model’s ability to predict the past is considered somehow an indicator of its ability to predict the futre. If it can’t predict the past it is a piece of garbage, but not necessarily any worse at predicting the future than a model which can.
Smokey said “And if you want solid evidence of the benefits of increased CO2, just ask.”
OK, I’m asking. I want t osee the kind of thing you onsider evidence. Then I, or KR, or anyone else, can provide evidence of the same kind. e.g.. if, you post a photo, we can post a photo, if you post a graph, we can post a graph. Does that seem fair?
Bill garland:
I am not arguing with you, however, 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. The easiest one to consider is the biological feedback associated with the carbon cycle. My prof would use population dynamics over and over again as an example of the limitations of modeling. Now, a modeler might be able to assume certain population response but the real response would ultimately depend on starting conditions of everything from potasium in the soil to species’ adaptability.
The way I think of it, since the earth’s climate is a dynamic system, and modeling the impact of CO2 would have to take into account *all* (not a few and not average) biological impacts, and because those are inherently chaotic, that makes the system itself likely chaotic.
So even if you did know all the starting conditions, etc., the biosphere would have a major say and you can’t model that.
Mingy,
Mostly agree. I was really referring to extending beyond the training data. But I do have issue with this one, mostly that it leaves out ‘in a Monte Carlo simulation’:
“It is bizarre beyond belief that a model’s ability to predict the past is considered somehow an indicator of its ability to predict the futre.”
In non-climate science, the ‘training data/test data’ split is applied pretty regularly. In non-Monte Carlo situations, the ‘ability to predict the past’ on the test data is generally a -very- good indicator of something’s ability to predict the future. Think: Models of balls rolling on inclines, pendulums, etc.
The issue in Monte Carlo simulations is that you can fall into the trap of ‘model shopping’. That is “Hmm, this one didn’t work at all well. I’ll raise this parameter a bit, lower that one, and try, try again!” Repeat.
If you’re doing that, (which people are), you’ve fundamentally incorporated the -test-data- into the training period – because you’ve become part of the model.
But in a system where any chaos is swamped by deterministic action, testing models on ‘historical data’ is -the- crucial step.
Dr, Edwards,
A very thought provoking article –thanks for posting!
I do have a few specific comments/critiques
1) “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. ”
I wouldn’t quite say that. Take a simple example of chaotic motion, the double pendulum. The motion is “driven” by forces, not by “chaos”. The chaotic motion is a RESULT of the sensitivity of the motion to the initial conditions.
Chaos itself does not “drive” anything.
2) “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. ”
Doesn’t this assume that you know nothing about the TRUE drivers of weather and are basing your predictions simple on the short-term chaotic behavior? Based on your numbers above, a prediction for the temperatures 1 year from now would be +/- millions of degrees, but I am confident I could predict the high temperature of your location 1 year from now within +/- 20 C.
3) “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. …
… the information that the modellers give us seems to leave out alternate solutions in favour of the peak value.”
Of course, it makes sense to select a “typical” result of the calculations to report as the expected result. For example, using your spreadsheet equations, If I wanted to know the “typical” result of the calculation for initial condition of 0.3 after 25 steps, I could try values of 0.29999990. – 0.30000010 in steps of 0.00000001 and find the average (or median or geometric mean or what ever other version of “typical” is appropriate).
Beyond this point, weathermen OFTEN choose to tell us the other possibilities — eg “tomorrow will be warm and sunny, with a possibility of scattered thunderstorms”. I suspect that the papers on climate modeling ALSO give more than the “typical” value — information like the standard deviation or the actual distribution of the results.of the runs. Do you have data to back up your perception of climate science as only presenting one peak value??
4) “Chaos, however, is implicit in weather, so there is no reason why it should average out. ”
I can think of two reasons. Chaos does not mean completely random. There are “attractors” in many systems that lead to somewhat predictable paths. Also, weather and climate are constrained by actual physics. Energy must be conserved; net energy flow must be from warm to cool, … . If a weather system blows a little more north than south, the rain will fall in different, unpredictable places, but the total rainfall is still constrained.
I’d love to hear you response on these comments. There is always so much to learn! 🙂
John B, glad you asked. Here is real world evidence that CO2 promotes plant growth, showing that added CO2 has increased agricultural productivity:
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More CO2 is benefitting the biosphere. And there is no evidence of global harm due to CO2. Thus, CO2 is harmless and beneficial. QED