Guest Essay by Kip Hansen
“…we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”
– IPCC TAR Chap 14, Exec Summary
Introduction:
The IPCC has long recognized that the Earth’s climate system is a coupled non-linear chaotic system. Unfortunately, few of those dealing in climate science – professional and citizen scientists alike – seem to grasp the full implications of this. It is not an easy topic – not a topic on which one can read a quick primer and then dive into real world applications. This essay is the second in a short series of essays to clarify the possible relationships between Climate and Chaos. This is not a highly technical discussion, but a basic introduction to the subject to shed some light on just what the IPCC might mean when it says “we are dealing with a coupled non-linear chaotic system” and how that could change our understanding of the climate and climate science. The first part of this series is here: Chaos and Climate – Part 1: Linearity. Today’s essay covers a single common feature of non-linear chaotic systems: Stability.
Definition:
For the purpose of this essay, I use the following definition of a non-linear system:
Non-linear system: A system in which alterations of an initial state need not produce proportional alterations in any subsequent states; one that is not linear.
This broadly general, non-technical, definition is taken from “The Essence of Chaos” written by Edward Lorenz, the father of chaos theory. From Lorenz’s introduction to that book: “Some thirty years previously [1960], while conducting an extensive experiment in the theory of weather forecasting, I had come across a phenomena that later came to be called ‘chaos’ – seemingly random and unpredictable behavior that nevertheless proceeds according to precise and often easily expressed rules”.
I note for those with a more technical bent that there are many other definitions of “non-linear” and “non-linear systems” – in mathematics, physics, and engineering. But, as I said, this is not a technical discussion, but a practical discussion. One will find that for application to the field of weather and climate, Lorenz’s definition is perfectly suitable. Although Lorenz made the following statement about a loose definition of “chaos”, it might be applied to his definition of “non-linear system” as well: “My somewhat colloquial definition may capture the essence of chaos [non-linear systems], but it would cause many mathematicians to shudder” [one might add: philosophers, statisticians and engineers].
Let’s note a few things about the definition before we get too far:
The first is that it speaks of altering an initial state, the state from which the system begins. In a dynamic system, the initial state can be “at the start of our experiment” or, more often, it is the state of a dynamic system at any given instant as the “initial state” for either the next instant or any subsequent length of time the observer or experimenter might want to consider; today’s weather as the initial state for the prediction of tomorrow’s weather, today’s weather for the calculation of the expected climate a hundred years from now, today’s market-close prices on the stock exchange for the starting prices tomorrow and/or the state of the economy next year, exactly where one starts the ball rolling down a hill and how hard one pushes it to get it started. All these can be seen as initial states.
Lorenz says “alterations of an initial state need not produce proportional alterations in any subsequent state”. It is important to note that he does not say that alterations do not, he does not say alterations can not, but rather, need not “produce proportional alterations in any subsequent state”. (Proportionality sets non-linear systems apart from linear systems in which alterations in the initial state necessarily produce proportional alterations in subsequent states.) This allows that small changes in initial states may produce small changes in subsequent states, they can, but they don’t have to. In other words, they need not….they might, they may, they could, and in fact often do, produce large changes in subsequent states.
How this simple definition plays out in the real world is the subject that came to be erroneously called Chaos Theory. Erroneously because it is not a theory at all, but a broad field of study that evolved, in a practical sense, from Lorenz’s discovery and his subsequent paper Deterministic Nonperiodic Flow, published in 1963 in the Journal of Atmospheric Sciences. [While the majority of this paper is highly technical and requires advanced maths skills, the link is to a .pdf and I highly recommend reading at least the first two paragraphs of the Conclusion section of this paper – which is easily understood by laymen such as I.]
In the following sections, I will lay out just one of the common features of the behaviors found in non-linear, dynamic systems. The fact that there are common features may seem counter-intuitive – one may object to the idea that non-linear systems that produce chaotic, unpredictable results could have common features. The fact that they do is what attracted my attention to ‘Chaos Theory’ in the first place. For those of you who have doubts – please take the time to find out for yourself by reading Dr. Lorenz’s book linked above, or either James Gleick’s CHAOS – Making a New Science or Ian Stewart’s Does God Play Dice?. Or at a minimum, take a quick read through the Wiki page on chaos theory which will give you enough information to benefit from this essay.
Stability — A Common Feature of Non-linear Chaotic Systems
Listing stability as the first of these common features might come as a surprise to many who are familiar with non-linear systems and chaos – but not to engineers. As we were told in the comments of Part 1 of this series, engineers use designs, out of necessity, which are based on non-linear equations all the time and find them perfectly stable. One of the more savvy engineers pointed out that engineers, as a class, are naturally well aware of the instabilities – the turbulences – that can develop in non-linear systems, and so use values for those systems that are well below the points which tend to devolve into turbulence or instability. Thus knowingly or not, they are taking advantage of this property of chaotic, non-linear systems: Stability.
In a comment to Part 1 of this series, Leo Smith wrote:
“In fact, as practicing engineers we go to enormous lengths to keep our systems linear, or if we can’t arrange that, at least keep them out of chaotic regions. One designs a car to get to journey’s end, not fly into a thousand pieces at the first corner.
…. the general case of a non linear dynamic system is that if it does exist in nature, its probably chaotic. Linear and non-chaotic non-linear systems are very much the minority in Nature, but of course, because engineers seek predictability, they are the rule in most engineering.”
This image, similar to the one used as the introductory image today, helps us to understand this point. I’m afraid you’ll have to trust me for the time being that this graph is common to many [all?] non-linear, chaotic systems in the real world – I admit that it doesn’t seem reasonable – but a great deal of research has been done on it over the last 50 years, and it is so. Versions of this diagram appear in all of the studied real world dynamical systems that I am aware of … I give just one example further on.
Figure 1: “Bifurcation diagram of the logistic map x → r x (1 – x). Each vertical slice shows the attractor for a specific value of r. The diagram displays period-doubling as r increases, eventually producing chaos.”
The line that extends to the left of the graph continues as a single line, sloping in a curve downward as r approaches 1 (see the graphic at the beginning of the essay).
When we graph this equation — x → r x (1 – x) — with a beginning “r” of 2.8, and an initial state value of 0.2, this is what we find:
Even though the starting value for x is 0.2, iterating the system causes the value to x to settle down to a value between 0.6 and 0.7 – more precisely 0.64285 — after 50 or so iterations. Jumping in at the 50th iteration, and forcing the value out of line, down to 0.077 (below) causes a brief disturbance, but the value of x returns to precisely 0.64285 in a short time:
Kicking the value out of line upward at year 100 has a similar result. Adjusting the “r”, the forcing value, down a bit at year 150 brings the stable attractor lower, yet the behavior remains stable, as always.
Refer to Figure 1, the bifurcation diagram, to see that the value 2.8 for r corresponds with a value of x of 0.64285. Had we used 2.4 for r, the stable value of x would have been 0.58333. All of the values from 1 approaching 3 produce a stable single value result.
This single value result is an “attractor” for the system. An easy way to think of a single attractor is to think of a funnel. Liquid poured anywhere inside the rim will be drawn to the bottom (by gravity) and exit in one, and only one location, the spout.
Alternately, consider the bowl. A marble placed anywhere inside the rim and released will roll to the bottom – it may roll around a bit, up the other side and then down again, but eventually comes to rest at the bottom of the bowl – that space, the bottom of the bowl, is the single attractor for that dynamic system.
When I was a kid, we had a nut bowl similar to the one pictured above, except that ours had a common rim that was 2 inches higher than the interior separators. We spent hours rolling marbles down the side from different points, like the ball in a roulette wheel, betting on which depression the marble would end up in. This nut bowl, with four separate bottoms but a common rim could be said to have four marble attractors. A roulette wheel could be said to have 37 attractors, 0 through 36 (or 38 in Las Vegas, where there is an additional 00 position).
We will take up the subject of attractors in a later part of this series but we should understand that the characteristic of stability in non-linear dynamics stems from the function of attractors. The bifurcation diagram gives the attractor for each value or “r” from 2.4 to 4.0. Some regions have a single value attractor, many are periodic with more than one – 2, 4, 8, 16, 32 and 3, 6, 12, 24 — stable attractors , and some regions are chaotic (we will have more on chaotic regions in a future installment of this series).
Where do we see such dynamic systems? The formula used here is the same as the basic formula for Population Dynamics, where x is the unit of the carrying capacity of an environment (in which 1 would represent 100%) and r is the growth factor. With low growth factors, populations tend to be stable and less than the carrying capacity of their immediate environment. This illustration for the fictional May Island Squirrel Population was included in Part 1. [ The Predator-Prey Equations, which reflect some populations, are also non-linear and are usually linearized in order to find approximate solutions.]
We see in this diagram the population of squirrels on May Island. With a growth rate below 3 – 2.7 in this example (green blue trace) – stabilizes at 0.6xxx, roughly 60% of the islands carrying capacity. Bumping the growth rate up to 3 (orange trace) causes the population to wobble, saw-toothing a little bit higher. The wobble increases as the growth rate increases until at a growth rate of 4 (green trace) the population is very unstable, chaotic, and suffers a possible extinction (or very low numbers) for years 14-18 or so. The purple line, provided for interest, represents what the average person would expect – a linear progression from a low population to a full carrying capacity population produced by a [incorrect] linear understanding of population dynamics.
In real world, complicated non-linear dynamic systems, such as the interplay between adult flour beetles, their pupae, and their larvae in a confined volume of flour – in which the adults happily cannibalize the pupae – we see this more complex version of [a small portion of] the bifurcation diagram which was then experimentally found to be valid.
The researchers focused on the chaotic regions except at the value “1”. We can see where we could expect stable single value attractor results in the region just above 0.1 and at all values above 0.45, probably some period of 3 (3, 6, 9…).
The characteristic we see in these examples is stability – even the period-two wobbles are stable around a central value.
In real life population studies, all these features are seen. Some species populations are more prone to developing growth rates that cause chaotic dynamics – such as deer population in rural NY State where I raised my children. With deer, two or three good years in a row result in a growth rate that spikes population to unsustainable levels, resulting in heart-breaking population crashes from winter starvation. As a result, the NY State Department of Environmental Conservation struggles to keep growth rates in check regionally through the issuance of additional deer hunting tags for females – chopping back growth rate directly.
Engineers can and do take advantage of the stability in non-linear systems by designing systems that fall within the stable portion of bifurcation diagram for the particular system – staying well away from the point at which wobble, turbulence, and chaos ensue. Not only are these non-linear systems stable – they embody stability as part of the dynamics – perturb them and they return “of their own accord” to their stable point.
In real world dynamic systems, there is always some element of randomness added into the system – breezes, vibrations, confounding elements of other systems, traffic in the street – always something that deflects the system from our perfect mathematical rendering above. The characteristic of a stable attractor dampens these effects – as long as the system stays away from the point of bifurcation, that period doubling which leads to Chaos.
Here’s what a non-linear chaotic system running in stable mode looks like in the real world: 
The graph above shows a ~ 5 % or so variation over the entire length — it has jiggles and an apparent trend. If this were a squirrel population somewhere, we’d suspect that things had generally improved a bit, perhaps increasing carrying capacity of the environment, a decline in predation, an increase in maturity of food providing trees or an incursion of a new food supply – say urban squirrel feeders. The point is that despite the multitude of things that could be affecting the overall system, it exhibits a high degree of stability, staying in a certain range.
It is a the same as the earlier blue graphs – Robert May’s population dynamics formula, a non-linear dynamic formula known to produce chaotic results when forced above a certain level (as in the green trace in the May Island Squirrel Population graph). This version, though, was created by slightly altering the forcing (the “r” in the formula) so that it increases and decreases minutely — by 1/1000th a year, up or down in various time periods – and the entire result being overlaid with a random addition varying from 2 to 6 percent.
Anyone recognize the graph? Ever seen this:
A rough, and widely used, version of land surface air temperatures over the last 140 years from the Met Office. Here’s what they look like overlaid:
Of course, this is a set-up. This proves nothing, nor is it intended to prove anything. The purpose is just to illustrate that in the stable zone of a chaotic system, with very slight changes to the “forcing” factors and a bit of the natural jitters and randomness found in all real world systems, it is easy to make a generalized non-linear chaotic system behave in the same manner as the part of the Earth’s climate system that produced surface air temperatures over the last 145 years.
Chaos, Stability and Climate:
“The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible.” – IPCC TAR Chap 14, Exec Summary
This much is not in doubt – “the [Earth’s] climate system is a coupled non-linear chaotic system” — nearly all sides in the Climate Wars recognize this simple-appearing fact. That is where agreement apparently ends.
Many have put forward the idea that the Earth’s Climate System is in a stable period-two state (see the bifurcation diagram above) – shifting on a very long time scale from Ice Ages to Interglacial Periods and back again. From this, we can get general agreement that the Earth is currently in Interglacial mode. Within each extreme, the climate appears surprisingly stable – nice solid well-constrained Ice Ages and nice solid well-constrained Interglacials. The sun seems to slightly perturb the system in each state, with some Interglacials or portions of them being a few degrees warmer or cooler and the same within Ice Ages.
In more recent times, kicking the climate system with a decade of frequent volcanism causes things to chill right down but after a few years, the system is back into its normal range. The Roman and Medieval Warm periods cool off and after a bit of a “Little Ice Age”, things warm back up. This warm period, cool period, warm period may be the result of a bit of wobble developing in the system or due to slight changes in the strength of the Sun, orbital changes, and other natural physical confounders – generally referred to as “natural variation”. It might be a sign that the system is “striving” for stability, “trying” to return itself to a single stable point. It is possible that the climate for the least ten thousand years is the stable value overlaid with a bit of physical noise.
The graph above (whether we accept it as accurate or not and ignoring the silly, unscientific additions of “future” values in red for 2050 and 2100) shows that for the last ten thousand years proxies of surface temperatures show a stability to within a range of 2°C, very well constrained. The left-hand panel shows the period-two behavior of Ice Ages and Interglacials. (Note: the time scale changes at the panel break. Earlier panels of the original image have been cropped out. There are questions as to whether the vertical alignment of the first, left-hand, panel is properly represented and/or supported by data.)
The incredible thing about the Earth’s climate is that it is so stable, over the last million years, given the huge geological and biological changes that have taken place, including the most recent post-glacial sea level rise, which resulted in a massive change to ocean volume, shape, and extent – the oceans being one of the two coupled non-linear dynamic systems that make up the whole of the climate system. Even with the Ice Ages, the climate has been stable enough for life to grow, change, and prosper.
Do we really know anything about why the geological-time temperature graph looks as it does? I’d have to say “No, not really.” At best we can describe it: Ice Ages and Interglacials and on a smaller scale, the most recent 10,000 years, warm periods and cooler periods; we may have some guesses as to causes of the changes, some guesses more likely to be correct than others.
Chaos Theory gives us another way to look at the question based on the fact that Earth Climate is a complicated complex non-linear dynamic system, made up of at least two closely-coupled non-linear dynamic systems: the oceans and the atmosphere. How that coupling affects the total system is what Climate Science is intended to study. How coupled chaotic systems behave in general, to my knowledge, is simply not known except in the studying of Earth climate as an example. In my opinion, the uncanny stability of the Earth’s surface temperature over the past 10,000 years is correctly represented as a single-value stable attractor of the coupled system.
Take Home Messages:
In this essay, I have tried to present the less-talked-about aspect of chaotic non-linear systems: their stability in certain regions, with a single-value attractor to which the system returns after being perturbed.
- Non-linear chaotic systems have regions that are not only stable but are high resistant to being de-stabilized – they return to their stable value, their single-value attractor, after being perturbed.
- The Earth’s land surface temperature record is extremely stable over the past 10,000 years. This stability may represent a single-value stable attractor for the system.
- The Earth’s Climate System is “a coupled non-linear chaotic system” – and while exactly what that coupling means one can or should expect from it is not yet well understood and remains unclear, we should look to Chaos Theory to provide the necessary insight we need to reach a better understanding.
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Author’s Comment Policy:
I love to discuss this topic and I will try to answer questions to clarify any points I have made above. Before asking more in-depth questions about Chaos Theory, please make sure you have read Part 1 of this series (I recommend reading through the comments as well – particularly my answers to questions and all comments by rbgatduke.) If you are less-than-up-to-speed on Chaos Theory in general, and want to know more, I recommend a quick read of the Wiki entry on Chaos and for those with deeper levels of interest, I gave an Intro to Chaos Theory Reading List.
I will not be defending the idea that the climate system is a coupled non-linear chaotic system – it is simply too well established and supported by the physical actuality. Those who wish to rail against this fact can have their say here, but I will not be replying. It would be interesting to read a well presented essay from those who hold such an opinion as to why they do so and I’m sure Anthony would post such an essay.
I would be interested in your guesses as to why I say in the last paragraph before the Take Home Messages: “made up of at least two closely-coupled non-linear dynamic systems”. Might there be more than two? If so, what might the additional systems be?
Further, this essay is not about the details of the Earth’s climate, CAGW, AGW, or related nonsense. I will not fight the Climate Wars in the comments – please reserve that for some other essay or take it over to the NY Times’ Dot Earth blog where a lively battle is nearly always taking place.
Thank you for reading here.
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[This essay was edited at 8:30 Eastern Time Nov 24 2015 to correct minor formatting issues and at 9:30 correcting the name of a trace color (h/t goldminor) – kh]
See what I mean:
Admins, feel free to delete my last two posts if you manage to edit the first one appropriately! 😉
Reply to SWB ==> Yes, that’s the way I think it should be done. Nothing wrong with a little humility — I could sure use some.
Reblogged this on gottadobetterthanthis and commented:
–
Simple, but involved. You’ll know more if you read. A bit of wisdom for the taking.
As the IPCC says, we can predict nothing of the future with regard to climate.
Hey Kip,
Did you ever wonder why the AR4 and AR5 notably ‘dropped’ the wording from the TAR ref. “…a coupled non-linear chaotic system… [which renders the prediction of long-term trends impossible]”?
Did you by any chance attempt to reach the Lead Author(s) from TAR and AR4 WG1 to determine their intent in using (respectively in NOT using) that phrase?
Reply to Kurt ==> Well, they can’t repeat everything they’ve ever said in every report. They have not backed off from the fact though.
I’m sure they are embarrassed by the reality — and don’t wish to keep bringing it up. They still stick to the point of “we don’t make predictions”…which are precluded by the chaotic nature of the climate.
Thanks, Kip.
The quote on the INHERENT unpredictability of earth’s future climate from TAR (2001) is a very powerful one. It would truly be enlightening to read an interview of WG1 lead authors from the past three reports on this very question (including why it was left out of AR4 and AR5).
The “we don’t make predictions” claim strikes me as daft. The ‘experts’ repeatedly claim that the upper and lower bounds of the global mean surface temperature trend are VERY robust; that long-term climate IS predictable, whereas short-term weather is not. Yet the DATA don’t seem to cooperate very well, n’est-ce pas?
BTW, I’ve pushed for opting out of the Verified Commenter’s status over at Revkin’s blog (NYT Dot Earth). Perhaps others may wish to follow suit. IMHO, this will improve the conversation.
Reply to Kurt ==> As you know, the IPCC always calls them “projections”. They are based on obviously chaotic results of climate models — see the original “bloom” graphs of the 1000 runs of the models that produce those neat little graphs with spreading triangles representing the “means” of those runs which they call “upper and lower bounds.”. The actual individual model runs produce projections that could be anything from Fire Ball Earth to Ice Ball Earth. Then they “average” the chaotic results….I don’t know how to characterize this nonsensical approach. Dr. Brown at Duke has written repeated, very amusing, rants on this topic.
As for Dot Earth….I inquired years ago into whether or not I could have an alternate sign-in not tied to my Verified Commenter status, so I could post comments that went to Andy Revkin for moderation, as I like to ask him questions. he doesn’t see the Verified comments normally. I was told it is one way or the other. It will be interesting to see what they come up with as the new system.
If a system has two stable attractors, (like the Earth and its oscillation between glacial periods), what is the nature of the cause for switching between them? Is the event that causes a switch between one and the other the same concept as a “tipping point” that is lurking within the system itself and waiting to be tipped? Or is it caused by a major change randomly coming from outside the system?
T-Braun, in the case of the earth you have a variability in the orbit which can lead to changes, however there are also random internal changes which could be responsible. E.g. the blocking of the connection between the Pacific and Atlantic oceans by uplift, change in atmospheric circulation due to the uplift of the Himalayas, etc.
Reply to T-Braun ==> Good question!
Generally speaking, a non-linear dynamic system, which is by its very nature prone to chaos, has built into it a time-factor. Ocean dynamics centered on the photosynthesis of plankton, for example, are timed by the Sun, the day length, the nigh-and-day cycle and by the seasons, a yearly cycle, and by various ocean circulation patterns with longer cycles. One would expect that photosynthesis of plankton system would be complex then, and it might display periodic behaviors on more than one scale.
It is the nature of chaotic dynamic systems to be periodic in this way — with the time periods – one or more — depending on individual systems.
Populations, for example, of terrestrial animals and plants, have a yearly cycle for obvious reasons related to the seasons and breeding cycles. When simple population systems (those not primarily driven by the predator-prey relationship, which as different dynamics, but is also chaotic) are “pushed” too hard — when their growth rate rises past 29…. or so, they become periodic, and the period would be based on the yearly breeding cycle. A squirrel plague one summer would drive current population down dramatically, and this would show up for the next few years as it does in the second population graph in the essay, with the blue trace, at year 50, with the population dragged way down, which then pops right back up, wobbles, and then settles down to the single-value attractor.
A Tipping Point, however, is defined (for Climatology) in the Wiki as follows:
“A climate tipping point is a somewhat ill-defined concept of a point when global climate changes from one stable state to another stable state, in a similar manner to a wine glass tipping over. After the tipping point has been passed, a transition to a new state occurs. The tipping event may be irreversible, comparable to wine spilling from the glass: standing up the glass will not put the wine back.”
I believe the term to simply be a Bogey-Man — invented loosely based on Chaos Theory to frighten little children and politicians. The idea is that Mankind will somehow do something that will precipitate a “disastrous climate” — usually Fire Ball Earth. There is no indication in the paleo-record that Fire Ball Earth is an option. To the contrary, the opposite is true. Any perturbation is likely to move the system slightly but, with the exception of the return of an Ice Age (a long a slow process, I think), the system seeks a stable, well-bounded range.
In the bifurcation diagram, you can clearly see that there are points, quite narrow points, at which the graph changes from a single-value attractor to a periodic-attractor, and then, in what is called a period-doubling cascade, rapidly transitions to a limited space-filling chaotic (deterministic but unpredicatble) region. In the diagram given, this occurs when the “r” reaches 3.6 or so.
Many feel that the climate is in a long-term period-two state — Ice Ages and Interglacials, as you say. If this is the case, there is not a “Tipping Point” but rather the system “has always been headed there” to the point of a shift of regime. This is almost the same as “We Don’t Know What Causes the Shift”. We know it happens, we know it happens on a fairly regular basis.
For our squirrels, a growth factor of 3.5 produces a wildly varying population, slamming on a yearly basis from 80% of the carrying capacity to 40% and back again — a doubling and halving . Nothing happens to “cause” it. Biologists come and rip their hair out trying to find out what is causing this terrible situation, slinging blame right and left. They somehow forget that population dynamics are non-linear…..
I hope this helps.
Thanks, Kip Hansen, for a very interesting essay.
You point to an interesting breakpoint in the history of the IPCC; the missing chaos that used to make long-term predictions impossible. TAR is dead, FAR killed it.
The true chaos here is that every year “adjustments” are made to past average temperature data since 1880, so that the gap between reality and the official numbers increases.
In time, I expect the 1930’s US “dust bowl” will be remembered in the history books as the 1930’s “snow bowl”.
Reply to Richard Greene ==> Children will ask: Was the Dust Bowl a famous football game? … like the Rose Bowl? the Orange Bowl?
Re: WUWT, Chaos & Climate Part 2, 11/23/15:
Chaos & Climate is about this lead quotation from IPCC:
“…we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.”
Part 2 corrects only the attribution. Part 1 said it was AR4 WG1. Now in Part 2 it is TAR Chap 14, Exec Summary. The significant thing that should have been corrected were IPCC’s conclusions about the climate system.
As I wrote on 3/15/15 @ur momisugly 10:19 am,
What the IPCC, like many others, has long recognized is false. Linearity and chaos apply to models, not to the real world. Whether models are linear often depends merely on the scale factor* applied. A system is linear if f(ax+by) = af(x)+bf(y). Equation do not exist in the real world to apply the definition. Models and equations are strictly manmade.
Chaos does not exist in the real world because the real world has no initial conditions to which it might be sensitive. Only models do. Climatologists and physicists alike often confuse the real world with their models.
The ensuing discussion there did nothing to change the facts, or the definitions of the terms chaos and linearity, nor, apparently, to remedy the confusion between models of the real world and the real world they model held even by people who should be able trained in some scientific field and who should be able to grasp the problem. This is a matter of epistemology, but more importantly, it is a matter of scientific literacy, a skill sorely lacking among voters.
On an obviously higher plane, Kip Hansen, for example, defended his essay on 3/15/2015 writing this:
Turbulence in fluid flows of all kinds, including the atmosphere. Heat transfer through and between materials. Everyday population dynamics. Passage of radiant energy through a translucent medium (the atmosphere). All nonlinear dynamical systems, and subject to all the behaviors of nonlinearity. @ur momisugly 11:25 am
and
There are so many real world examples of these chaotic behaviors in natural systems that I find your continuing assertions to the contrary difficult to understand.
A couple of examples might help Mr. Hansen in his quest for understanding. *An example of model dependence on scale factor, mentioned above, is radiation transfer. At the molecular level, it is nonlinear. But at the heat transfer level, it is linear, analogous to Ohm’s law. In fact, the entire climate system can be modeled linearly as heat transfer rather than radiation transfer, and with better – with success. Another example of model dependency is the flux of CO2 between the atmosphere and the surface ocean. According to Henry’s Law, uptake by the surface layer is linear in atmospheric CO2 concentration. Outgassing, however, is nonlinear, depending on the reciprocal of atmospheric CO2 concentration. IPCC doesn’t use Henry’s Law, and when it appeared in its experiments on the Revelle Factor, IPCC concealed its results. The real world flux is neither linear nor nonlinear; neither nonlinear nor chaotic. And this holds with the world flux deleted.
If Kip Hansen wants to prevail with his argument that chaos and nonlinearity exist in the real world, he needs to accomplish these three things:
1. Quote a reasonably acceptable definition of linearity (and its absence, nonlinearity),
2. Quote a reasonably acceptable definition of chaos, and
3. Choose any example of a real world process and show that it fits those definitions without resorting to any scientific model for the process.
As things now stand, each point is an independent, glaring omission in his continuing essay.
P.S.: The origin of IPCC’s claims of chaos and nonlinearity in real world climate is its excuse for its inability to model climate successfully, meaning not that it failed to be (1) peer-reviewed, (2) published in a certified journal, and (3) recognized in a certified consensus, but that its models are now proving invalid in making better-than-chance predictions, i.e., equilibrium climate sensitivity today measures at or below IPCC’s 5% confidence level, extrapolated.
Reply to Jeff Glassman ==> I quote from the Author’s Comment Policy:
Chaos is a description of a system or process that is incompletely or insufficiently characterized and unwieldy, thus preventing or degrading accurate predictions of its future states and paths. It is the implicit acknowledgement of people’s limited skill and knowledge that motivated establishment of a [limited] frame-based scientific philosophy and methods. A chaotic system can only be reasonably described by feature envelopes and estimated with stochastic methods within progressively limited frames of reference in semi-stable systems and processes.
Not correct. Chaotic systems are often quite simple, as the mathematical example given shows. What holds chaotic systems apart is, first, that they cannot be described with a simple time equation and, second, that they are extremely susceptible to “initial conditions”.
For example, given 4 or bodies in space, (I can’t remember if the 3 body problem has been solved, but I know that the 4-body cannot be) it is not even theoretically possible to derive an equation to predict one body’s path. The only way to predict trajectories is through numerical simulation, and even then you can only predict a certain distance into the future. The bit errors in your computation, and your limits of knowledge of the exact positions and velocities involved, will cause your model to eventually diverge from reality.
Left side of graph has intervals of 200,000 years, while the right side is 5000 years, so you are comparing apples and oranges in terms of periodicity and “stability.”
I have been thinking that Ren’s sudden stratospheric warmings (SSWs) may be a ‘butterfly’ in short to medium term seasonal weather. They seem to have the characteristics, If so, this leads to an observation that: Chaos, like magic, is just another name for things we do not yet know, and cannot predict. But if Piers Corbyn can accurately predict this solar effect, who can say how much we may advance? If we study the right things for a change, that is.
Reply to Barry ==> From the text below the graphic:
“The left-hand panel shows the period-two behavior of Ice Ages and Interglacials. (Note: the time scale changes at the panel break. Earlier panels of the original image have been cropped out. There are questions as to whether the vertical alignment of the first, left-hand, panel is properly represented and/or supported by data.)”
In other words, this is already explained.
Re-read that portion and see if you can see the point I am making. The graphic shows incredible stability over the last 10,000 years and over the longer term, 1 million years, shows the period-two period. We are in one of the Interglacials — which started about 20,000 years ago.
Kip, I hope this comment is not too late for you to see and respond. I believe it is important to examine the second part of what the IPCC said in the executive summary for AR4. The complete quote is here:
“In sum, a strategy must recognise what is possible. In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible. The most we can expect to achieve is the prediction of the probability distribution of the system’s 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. The generation of such model ensembles will require the dedication of greatly increased computer resources and the application of new methods of model diagnosis. Addressing adequately the statistical nature of climate is computationally intensive, but such statistical information is essential.”
The issue then focuses more precisely on the use of model ensembles to predict future climate states, AND is the IPCC doing this in a scientifically sound manner? Dr. Robert Brown (Duke University) has some thoughtful critiques of the IPCC methods. For example, the ensemble result from multiple models with different physics can’t be anything meaningful. My personal opinion is that even with the ‘perfect’ model we would still need to use non-parametric statistical analysis with each model realization (simulation) being equally likely.
Thoughts?
Reply to dougbadgero ==> Never too late — I usually leave my email address in a Post Script in comments to any essay I write — just so those reading later and having a question can bring it to my attention.
You are right — understanding the full context of a statement is very important. In fact — if not in word — the IPCC declares that it recognizes that the future state of the climate can not e predicted due to the very nature of climate as a couple non-linear chaotic dynamic system and then immediate preceed to explain how they think they can get around that and predict it anyway.
i am impressed that you have read Dr. Brown’s thoughts on this topic — some of them are quite amusing. I explain the problem this way:
” They (projections) are based on obviously chaotic results of climate models — see the original “bloom” graphs of the 1000 runs of the models that produce those neat little graphs with spreading triangles representing the “means” of those runs which they call “upper and lower bounds.”. The actual individual model runs produce projections that could be anything from Fire Ball Earth to Ice Ball Earth. Then they “average” the chaotic results….I don’t know how to characterize this nonsensical approach.”
Running a thousand or a million runs of a chaotic system (when in a known chaotic region) produces a million different results that are literally all over the map for the system. Averaging those chaotic results does not, can not, will not, can’t even be thought to possibly, produce a valid prediction of future states. The full set of runs does produce an idea of the possible breath of possible results, the space filled by the chaotic system, but the mean — by any method or measure — can not be thought to be more probable than any of the extreme values — by their very nature they are unpredictable.
If you haven’t already, read his comments to my chaos first essay..
This is how Dr Brown puts it in a later post:
“…. current climate models, for all of their computational complexity and enormous size and expense, are still no more than toys, countless orders of magnitude away from the integration scale where we might have some reasonable hope of success. They are being used with gay abandon to generate countless climate trajectories, none of which particularly resemble the climate, and then they are averaged in ways that are an absolute statistical obscenity as if the linearized average of a Feigenbaum tree of chaotic behavior is somehow a good predictor of the behavior of a chaotic system!
This isn’t just dumb, it is beyond dumb. It is literally betraying the roots of the entire discipline for manna.”
Thank you for the reply. I went back to your original essay and read rgb comments. I had seen many of his comments here but not on that thread. Very interesting, notably some of the physics the models obviously get wrong, e.g. Model variance versus observations.
Ahaaaag, “coupled non-linear chaotic system” is just gobbeldespeak for “it’s complicated”. As you say, every step is completely deterministic, but the only reason we can’t predict the result is that we are unworthy… so far.
Kip, Lonnie, IPCC et al: aren’t “predict” and “future” redundant? What else could you predict?
Reply to Brian H ==> Well, that is an interesting question, though I suspect you meant it rhetorically.
What types of things *can* be predicted?
Science is about investigating reality. Part of this effort is to form hypotheses — guesses — as what what the relationship between things, or the causes of things, might be or have been. To be successful, your hypothesis must have predictive power. Often, a hypothesis is tested against the past — if my hypothesis is correct, then we should find evidence that a very large asteroid struck the Earth about 65 million years ago. That is “predicting” the past.
One of the problems pointed out about the current crop of climate computer models is that they are not very good at predicting past climate (when run “in reverse”) thus doubt is raised about their ability to project future climates. [Note: this ignores that IPCC’s own stand that future climate states cannot be predicted.]
Predictions can be for the present as well (in the sense of hypotheses) — some intelligence agencies have predicted that the Syrian refugees contain an organized and planned sub-set of ISIS 5th Columnists. I believe this will be found to have been true.
So, in the loose sense used in Science for the testing of hypotheses, predict and future need not always be used together, nor does one require the other.
Thanks for asking, interesting idea.
g-sperm;
Maybe some of the crucial determinant data is below the level of even theoretically feasible detection!
Any thoughts on volcanic effects on W. Antarctic ice issues?
Reply to Dave Fair ==> See the point in the post script about the lithosphere/Earth’s-core being a possible third item in the “coupled non-linear chaotic system” that is Earth’s climate.
Reply to Dave Fair ==> That is a good example of how the solid part of the Earth, which is a ball of hot rock, some of which is liquid hot rock, can affect the climate — in the West Antarctic Peninsula, at least regionally. All the heat that “leaks” out into the oceans at hot spots, volcanoes, steam vents, etc must be doing something to the climate….it is the “other” source of energy/heat input into the climate system. The Sun, of course, is the one usually considered — often considered to be the “only” source.
Thank you, Captain (from an ex-drill Sgt.).
As pure speculation, by an ex-engineer, I wonder if ENSO, AMO, PDO, etc. are simply nature’s “one-finger-salute” to misuse of mathematics by climate modelers?
I wish you a pleasant Thanksgiving.
Dave
Reply to Dave Fair ==> Some of these circulations and oscillations were first “predicted” in experiments by Dave Fultz — the famous dishpan experiments. See here.
These experiments are the original inspiration for my thoughts about the heating of the oceans from the bottom and heating them in undersea volcanic zones — like a Bunsen burner under the dish pan.
Thanks, again.
Dave