Guest Essay by Kip Hansen
“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 WG1, Working Group I: The Scientific Basis
Introduction: (if you’ve read the previous installments, you may skip this intro)
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 fourth 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 three parts of this series are: Chaos and Climate – Part 1: Linearity ; Chaos & Climate – Part 2: Chaos = Stability ; Chaos & Climate – Part 3: Chaos & Models. Today’s essay concerns the idea of chaotic attractors, their relationship to climate concepts, and a short series wrap up.
Definitions: (if already understand the first sentence below, you may skip the rest of this section)
It is important to keep in mind that all uses of the word chaos (and its derivative chaotic) in this essay are intended to have meanings in the sense of Chaos Theory, “the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions”. In this essay the word chaos does not mean “complete confusion and disorder: a state in which behavior and events are not controlled by anything” Rather it refers to dynamical systems in which “Small differences in initial conditions …yield widely diverging outcomes …, rendering long-term prediction impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable.” Edward Lorenz referred to this as “seemingly random and unpredictable behavior that nevertheless proceeds according to precise and often easily expressed rules.” If you do not understand this important distinction, you will completely misunderstand the entire topic. If the above is not clear (which would be no surprise, this is not an easy concept), please read at least the wiki article on Chaos Theory. I give a basic reading list at the end of this essay.
Climate Attractors: An Attractive Idea
In the field known as Chaos Theory, the study of dynamical systems sensitive to initial conditions, there is a phenomenon known as an attractor. Here I give the definition of this concept from the venerable Wiki:
“…an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; … If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. …. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.”
In previous parts of this series, I have shared examples and images of various attractors. The household funnel is the simplest physical example. When held with the spout pointing down, any object entering the mouth of the funnel tends down and out the spout. Exact placement in the funnel mouth doesn’t matter, all points lead to the spout.
The funnel represents a type of attractor called a point attractor. Once the system enters the attractor, the value evolves towards this single point.
A cyclical attractor might have two or three values (ranges in some cases), cycling between them. We see this in certain values of the Bifurcation Diagram, expressed as the Period Doubling that leads to chaos.
From Part 2:
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.
In the above example, the attractor of the system is a single value, to which the numerical value tends to evolve even when perturbed. In other systems, the graphed values might appear to spiral in to a single point or travel in complicated paths that eventually and inevitably lead to a single point.
Following from the Bifurcation Diagram, one sees easily that at some values of “r” the system becomes cyclic, with periods of 2, 4, 8, 16 as “r” increases until chaos ensues, yet past that point one still finds points, values of “r”, where the period is 3 then 6, 12, 24. Each vertical slice through the diagram presents one with the attractor for that value of “r”, which could be represented by their own geometric graphic visualization.
Some dynamical systems do the opposite – no matter where you start them, one or more values races off to infinity.
And some attractors, when viewed as plotted graphics are fantastically varied and beautiful to look at:
© Creative Commons
Lorenz’s famous Butterfly Attractor (named for the two reasons 1. It looks a bit like a butterfly’s wings and 2. In honor of the Butterfly effect), is often used as a proxy for “the attractor” of Climate (with the initial cap).
See this animated here.
This error appears many times in the literature and in “popular science” explanations of both Climate and Chaos. The latest version making the rounds, recently posted to blog comments repeatedly, are two related videos (parts of a 9 chapter film) from Jos Leys, Étienne Ghys and Aurélien Alvarez at chaos-mbath.org. The films are lovely and very well made, well worth watching. However, though they specifically explain that the Lorenz attractor is not in any way a representation of the climate, “In 1963, Edward Lorenz (1917-2008), studied convection in the Earth’s atmosphere. As the Navier-Stokes equations that describe fluid dynamics are very difficult to solve, he simplified them drastically. The model he obtained probably has little to do with what really happens in the atmosphere.”, they go on to use it and the Lorenz Mill to make the suggestion that climate is predictable based on the finding that some of the features of the Lorenz Attractor and the Lorenz Mill are statistically probabilistic, hence predictable. In the second (Chapter 8) film, they specifically claim:
“Take three regions on the Lorenz attractor (they could represent conditions of hurricane, drought or snow). If we measure the proportions of the time that trajectories with different initial conditions spend within these regions, then we find that for all trajectories, these proportions converge to the same numbers, even if the order in which the trajectories encounter the three regions is incomprehensible. …. By refocusing on statistical issues, science can still make predictions!”
Readers who want the full blood-and-guts version of why this is nonsensical (other than in a trivial way) can read Tomas Milanovic’s Determinism and predictability over at Judith Curry’s excellent blog, Climate Etc. (Be sure to go through and read all the comments from Tomas Milanovic, David Young and Michael Kelly). Those with more pragmatic tastes (and a more common, lower, level of understanding of higher maths) can read my post (also at Dr. Curry’s) Lorenz validated.
Let me just make a couple of obvious points for those who don’t have the time to watch the two 13 minute films or read the two Climate Etc. posts.
- The Lorenz Attractor has [almost] nothing to do with climate or weather in the form used by Lorenz. “The Lorenz attractor arises in a simplified system of equations describing the two-dimensional flow of fluid with uniform depth and imposed temperature difference between the upper and lower surfaces.” — Richard McGehee
- One must use very specific parameters to get the Lorenz equations to produce the Lorenz Attractor – other parameters produce single point attractors,.
- Looking at arbitrarily selected “regions” of the Lorenz Attractor – and saying “they could represent conditions of hurricane, drought or snow” is disingenuous. The attractor has no snow, no rainfall or drought (as the equations are about fluid flow in two-dimensions under temperatures differences, it might describe some thing resembling a hurricane, if applied to a real physical system, such as the famous washtub experiments of atmospheric circulation). Regions of the Lorenz Attractor do not represent weather of any kind whatever.
- Probabilistic analysis of the Lorenz attractor is interesting to mathematicians – but not to weathermen or climate scientists
- The real world climate is chaotic, complex, bounded, multi-dimensional, and, if it has attractors, they will be themselves exist in multiple phase spaces – as Tomas Milanovic points out “the ability to compute phase space averages for particular attractor topologies changes nothing on the fact that the system is still chaotic and will react on perturbations in an unpredictable way over larger time scales.”
- We have absolutely (literally absolutely) no idea what the precise, or even an, attractor for the weather or climate system might look like, separate from the long-term historic climate record. We have no reason to believe it would be statistically smooth or even if it would be amenable to statistical analysis.
Given all that, the idea that the climate system might have the physical equivalent of a chaotic attractor, even if it is a strange attractor, is still quite appealing to many. If it did, and we could discover it, mathematically or physically, we might then attempt some kind of statistical analysis of it to have some idea of the probabilities of what climate might do in the future. But only probabilities, and “probabilities of what” is highly uncertain. Remember, the climate covers the whole planet, and while we are mostly interested in what takes place close to the surface, it happens at all levels – a huge complicated area in both space and time. The possibility of analysis that would reveal useful statistical probabilities for even general climate issues such as hard or mild northern hemisphere winters in anything but the near-present, certainly less than a decade, is unlikely.
Probabilities might be interesting mathematically. Every gambler knows the probabilities of his game – the chances – and knows that probabilities are not predictions or projections – a bet on lucky number 17 still has a one in 38 chance of winning a payout of 36x on every spin of the roulette wheel in Las Vegas – knowing the probabilities doesn’t give him any insight into what the spin will bring. The action of the ball in a roulette wheel is chaotic in the sense of sensitivity to initial conditions – the exact speed of the spin of the wheel, the force the croupier gives to the ball, the exact point of release of the ball and its exact relationship to the spinning wheel (which spins in the opposite direction to that of the ball) at that precise moment. The balls subsequent motion depends then on the exact conditions, speed and angle, when it leaves the track and strikes the first deflector – and while that motion will be entirely deterministic, it simply sets the initial conditions for the next contact of the ball with another deflector or separator. The path of the ball during this spinning and bouncing is chaotic. Rather quickly the ball runs out of energy and the ball is captured by one of the 38 numbered pockets in the wheel. In a fair wheel, with a large enough number of spins, the results are normally spread between all of the 38 possibilities, each coming up 1/38th of the time. The probabilities can be perfectly known, yet the outcome in any one spin cannot be predicted – we can however, predict the outcome of ten thousand spins – more-or-less 1 in 38 for each number. Such a probability prediction only allows the gambler not to make stupid mistakes – like thinking three reds in a row means the next spin must be black. Such a set of generalized probabilities would be useless for climate or weather. (I would, however, like to read an essay on the potential usefulness of climatic probabilities – what kind of probabilities some think might be discovered and how we might use them to our benefit.)
(You would be surprised by how many instructional videos there are on systems for beating the casinos at roulette – all of them showing remarkable results. Yet the makers of the films are not retired millionaire gamblers and one wonders why they don’t just tour casinos and make a mint with their own systems?)
Even if, by some quirk of fate, we were able to stumble upon the structure of the multi-phasic attractor of Earth’s climate in the present day, which could then somehow magically be analyzed for statistical probabilities in a useful spatial and temporal way, such as seasonally for a specific region over the next decade, they would still just be probabilities, with only one actuality allowed. After that, the minute alterations of the ever-changing initial conditions and determining parameters of the system would lead to unpredictable differences in the attractor or even a shift to a new attractors altogether. These issues make the possibility of long-term useful predictions of the climate impossible.
But can we make any useful predictions about the climate? Of course we can!
If there is a shift in the northern jet stream, we can predict things about near-term European seasonal weather. If an El Niño develops, we can predict certain general weather and climate conditions. If there is a persistent blocking high in one area, weather is predictably affected downstream. Where does our ability to make these predictions come from? From models? Only models of the past – looking at the historical climate, recognizing patterns and associations, checking them against the records, and using them to make reasonable guesses about what might be coming up in the near future.
An aside about Hurricane Forecasting using Models
We can make weather/climate predictions about the near-future in some cases – hurricane-path prediction models are “pretty good” out several days, certainly good enough to issue warnings and for localities to make preparations, with a current average track accuracy of a bit better than +/- 50 nautical miles at 24 hours out. The error increases with time – at 48 hours 75 miles, at 72 hours 100 miles, at 5 days it is 200 miles. These results are about one half of the track errors in 1989. This accuracy was enough to warn the barrier islands of Brevard County, Florida (Cape Canaveral, Cocoa Beach, Patrick Air Force Base) for the recent major Hurricane Matthew – the islands were evacuated based on 24 hour predictions of a direct hit.
The difference of ~50 miles is illustrated here – note the times of the two images – the path projected in the left image is three hours earlier than the right image — the difference in the path can best be seen in the blow-ups in the upper-left of each of the two images:
Live television broadcasters called this “the little 11th hour shift” that saved Cape Canaveral – the center of Matthew shifted east 20-30 miles, making the difference between the direct landfall of the eye of a major hurricane on the highly developed barrier islands and the effects of a near-miss pass 30 miles off-shore. You can watch this evolve in an animation in the National Hurricane Center’s archive of Hurricane Matthew.
How can we best predict future climates?
I maintain that the best chance of determining the probabilities of climate long-term future outcomes lies in the past, not in mathematical, numerical modeling attempts to predict or project the future. We know to varying degrees of accuracy, temporally and spatially, what the climate was in the past, it has had tens of thousands of years to go through its iterations, season to season, year to year, and has left evidence of its passing. The past shows us the actual boundaries, the physical constraints of the system as it really operates.
Some maintain that because we are changing the composition of the atmosphere by adding various GHGs, mostly CO2, that the present and future, on a centennial scale, are unique and therefore the past will not inform us. This is trivially true, the present is always unique (there is only one, after all). But similar atmospheric conditions have existed in the past. Has this exact set of circumstances existed in the past? No. If nearly these circumstances had existed, would this tell us what to expect? No again, climate is chaotic, and profoundly dependent on initial conditions.
This has nothing to do with the question of whether or not, or how much, increasing CO2 concentrations will add energy (by retention) to the climate system. That question is simply a matter of physics – if GHGs block outgoing radiation of energy, then the blocked energy will remain in the system until such time as a new equilibrium is reached. What the effects of that energy retention will be are what the various branches of science are investigating. Making early decisions and assumptions — no matter how reasonable they appear — would be an error – along the lines of those made in physics regarding the expansion of the universe.
So, why study the past to know the future? It is my view, shared by others, that the climate system is bounded – limited in its possibilities – and that these boundaries are “built-in” to the dynamical climate system. From the historical record, the climate system has an apparent or seeming overall attractor, one could say, outside of which it cannot go (barring something like a catastrophic meteor strike). Included in that attractor are the two long-term states known as Ice Ages and Interglacials, between which the climate switches, much like a two-lobed chaotic attractor. We have little understanding of what causes the shift, but we know it takes place and how long interglacials of the past have lasted. We also know that during the past interglacials, the average surface temperature of the earth has been remarkably stable – staying within a range of 2 or 3 degrees, producing a period during which Mankind has thrived (for better or for worse), with apparent Warm Periods and Little Ice Ages (cooler periods). There is no evidence other than the historic record for labeling this the or an attractor of the system — but it has the appearance of one.
This sounds a bit like I am saying that we can’t predict the far-future climate because of chaos therefore we must look to the [chaotic] past to predict the climate. Almost, but no prize. It is the patterns of the past, repeating themselves over and over, that inform us in the present about what might be happening next. Remember, chaotic systems have rigid structures, they are deterministic, and Chaos Theory tells us we can search for repeating patterns in the chaotic regimes as well.
Of course, this is exactly how weather forecasting was done prior to the advent of computers. The experience of the weatherman, well educated in the past patterns for his/her region, would look to the available data on regional temperatures, air pressures, cloud type and cover and wind directions, and give a pretty good guess at the coming day’s and week’s weather. The weatherman knew of bounds of weather for his locality for the calendar date, and with his knowledge of the weather patterns for his area, could feel confident of his general forecast.
At this point I would have written about the problematic essence of numerical climate models – Chaos and Sensitivity to Initial Conditions. I would have run some chaotic formulas, made tiny, tiny changes to a single initial condition and shown how those changes would make huge differences in outcome, then liken this to modern GCMs, general circulation models, the type of climate model which employs a mathematical model of the general circulation of a planetary atmosphere or ocean.
Serendipitously, a group at NCAR/UCAR did it for me and produced this image and caption (from a press release):
With the caption: “Winter temperature trends (in degrees Celsius) for North America between 1963 and 2012 for each of 30 members of the CESM Large Ensemble. The variations in warming and cooling in the 30 members illustrate the far-reaching effects of natural variability superimposed on human-induced climate change. The ensemble mean (EM; bottom, second image from right) averages out the natural variability, leaving only the warming trend attributed to human-caused climate change. The image at bottom right (OBS) shows actual observations from the same time period. By comparing the ensemble mean to the observations, the science team was able to parse how much of the warming over North America was due to natural variability and how much was due to human-caused climate change. Read the full study in the American Meteorological Society’s Journal of Climate. (© 2016 AMS.)”
The 30 North American winter projections were produced as part of the CESM-Large Ensemble project, running the same model 30 times with exactly the same parameters with the exception of a tiny difference in a single initial condition – “adjusting the global atmospheric temperature by less than one-trillionth of one degree”.
I will not repeat the essay here – but it contains what I would have written here. If you haven’t read it, you may do so now: Lorenz Validated.
Wrap-Up
Chaos Theory, and the underlying principles of the non-linearity of dynamical systems and ‘dependence on initial conditions’, inform us of the folly of attempting to depend on numerical climate models to project or predict future climate states in the long-term. The IPCC correctly states that “…the long-term prediction of future climate states is not possible.”
The hope that statistical analysis of climate model ensembles will produce pragmatically useful probabilities of long-term future climate features is, I’m afraid, doomed to disappointment.
Weather models today produce useful near-present, daily forecasts (and even weekly for large weather features) on local and regional levels and may produce useful short-term-future weather predictions. When coupled with informed experience from the past, weather/climate patterns, they may eventually provide regional next-season forecasts. The UK’s MET claimed this result recently, bragging of 62% accuracy in back-casting general winter conditions for the UK based on pattern matching with the NAO. Judith Curry’s Climate Forecast Applications Network (CFAN) is working on a project to make regional-scale climate projections. Success of these longer range projections depends in large part on the definition used for “useful forecasts”.
Hurricane path and intensity models have halved their error margins since 1990, achieving a useful average predicted-path accuracy of +/- 50 miles at 24 hours with an accuracy of +/- 200 miles at 5 days. Hurricane Matthew’s 11th hour shift may be an illustration of these models having nearly reached the limit of accuracy.
At the end of the day, a deep and thorough understanding of Chaos Theory, down at its blood-and-guts roots, is critical for climate science and should be included as part of the curriculum for all climate science students – and not just at the “Popular Science” level but at a foundational, fundamental level.
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Intro to Chaos Theory Reading List:
The Essence of Chaos — Edward Lorenz
Does God Play Dice ? — Ian Stewart
CHAOS: Making a New Science — James Gleick
Chaos and Fractals: New Frontiers of Science — Peitgen, Jurgens and Saupe
Additional reading suggestions at Good Reads (skip the Connie Willis novella)
Recent blog links:
At WUWT:
Chaos & Climate series: Parts 1, 2 and 3
A simple demonstration of chaos and unreliability of computer models
At Climate Etc.:
A simple demonstration of chaos and unreliability of computer models
Determinism and predictability
Chaos, ergodicity, and attractors
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Author’s Comment Policy:
Since I will still be declining to argue, in any way, about whether or not the Earth’s climate is a “coupled non-linear chaotic system”, I offer the above basic reading list for those who disagree and to anyone who wishes to learn more about, or delve deeper into, Chaos Theory and its implications.
Also, before commenting about how the climate “isn’t chaotic”, or such and such data set “isn’t chaotic”, please re-read the Definitions section at the beginning of this essay (second section from the top). That will save us all a lot of back and forth.
I hope that before reading this essay, which is Part 4, that you have first read, in order, Parts 1 , 2, and 3 . As the essay Lorenz Validated was originally intended as part of this essay, it is suggested reading.
I will try to answer your questions, supply pointers to more information, and chat with you about Chaos and Climate.
Thanks for reading.
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Outside of the scientific domain, there is no chaos, only perfect characterization and modeling. Let’s hope the scientific domain remains so perfectly known and predictable, despite observable and reproducible evidence to the contrary.
Bob they do not want to accept the fact that it is the sun that governs and determines the climate of the earth.
Salvatore this will change. C/AGW is already terminated – it’s just that very few know it yet.
If I believe anything, it is that the extended scientific community is vastly under-informed on this subject, and that this audience will respond to proper persuasion that includes solid theory and evidence.
The earth is so super sensitive to TSI that it’s short-term to long-term influence can be readily seen with the right information.
Even if I didn’t say another word, I am confident that due to the rapid solar cooling we are undergoing now, one by one doubters will come around, and no later than one year from now most of the skeptics will be on board, with 95% of the stragglers coming in after they see first hand the effect of the upcoming cycle minimum. The very last few will hold out until they see the TSI driven ENSOs that will occur at the onset of SC25 and after the peak of SC25, confirming the timing and pattern of previous solar cycle driven ENSOs.
By the end of the next solar cycle maximum it will be understood worldwide. The warmists will have no where to run, no where to hide. Technically it is already over for them, whether they know it or not, or whether they’ll ever believe it.
Weather and climate operate on extremely simple rules based on solar activity and insolation, not CO2, and it is most definitely not chaotic on a gross level.
I look forward to the day when we will be discussing the entire topic in much greater detail.
Exactly Bob.
By the end of the next solar cycle maximum it will be understood worldwide
That is not a given, considering that the next cycle will be no weaker [and probably a bit stronger] than the current cycle.
LS I appreciate your insight on this subject. However you are not fully up to speed on what I’m saying, due to no fault of yours. The climate response to whatever the sun throws at us in the next cycle can be understood in context of the response to previous cycles, and if SC25 is stronger, the solar climate signal will be that much clearer. I am confident that even you will be persuaded by my research.
As you know, there is nothing new under the sun…;)
Mmm, no, of course they don’t Salvatore. Do you accept the fact that the atmosphere has any affect?
Science itself has had a pretty chaotic past https://en.wikipedia.org/wiki/Science and the biggest attractor in modern times is the almighty $$$$. Dollars give you power = might is right ” those who are powerful can do what they wish unchallenged, even if their action is in fact unjustified.”
Kip Hansen, thanks for 4 parts of
‘The climate system is a coupled non-linear chaotic system, and’
– only missed
‘and that coupled non-linear chaotic system is self-regulating. ‘
Best regards – Hans
Kippen Hansen, let’s make it short: it’s not just the problem with computer models; it’s with the conditions of the real world.
Every new test run with the real existing world, starting March 17, 2016 at 10:08 am,
produces a completely different November 25, 2016 at 04:32 pm.
Cause that’s how the real existing world runs.
Johann Wundersamer ==> Yes, the real world weather/climate system is chaotic [as in Chaos Theory] … that’s a very important point and I hope that readers who have slogged all four parts of this series have come to realize that.
In the terms of this blog:
The null hypothesis of Laplace’s Demon is
– regardless the conditions on March 08, 2016
– there’s ALWAYS a completely different April 12, 2021.
Cheers
THE CLIMATE MODELS ARE USELESS – they are useless because they do not factor in the initial state of the climate correctly they ignore the strength of earth’s magnetic field which moderates solar activity which the models have no clue on how to account for, especially the secondary factors that effect the climate due to solar variations much less the solar variations themselves.
They are useless and I have more confidence in my climate outlook then any worthless climate model may predict.
I am sure every one agrees that if solar changes are extreme enough there would be a point where a solar/climate relationship would be obvious. The question is what does the solar change have to be in order to be extreme enough to show an obvious solar/climate relationship?
Again I have listed the solar parameters which I think satisfy this issue.
I have put forth those solar parameters /duration of time which I feel are needed to impact the climate and I think going forward the solar parameters I have put forth will come to be which will then manifest itself in the climate system by causing it to cool. I dare say I think it has started already.
How cool it is hard to say because there are climatic thresholds out there which if the terrestrial items driven by solar changes should reach could cause a much more dramatic climatic impact.
Terrestrial Items
atmospheric circulation patterns
volcanic activity
global cloud coverage
global snow coverage
global sea surface temperatures
global sea ice coverage
ENSO a factor within the overall global sea surface temperature changes.
Solar Parameters Needed and Sustained.
cosmic ray count 6500 or greater
solar wind speed 350 km/sec or less
euv light 100 units or less.
solar irradiance off by .15% or more
ap index 5 or lower
Interplanetary Magnetic Field 4.5 nt or lower
Solar Flux 90 or lower
Duration of time over 1 year following at least 10 years of sub solar activity in general which we have had going back to year 2005.
We should know within a year as prolonged minimum solar conditions become entrenched.
“manifest itself in the climate system by causing it to cool. I dare say I think it has started already.”
Actually. no Salvatore. Are there any graphs here https://wattsupwiththat.com/global-temperature/ that would support that position?
For what it is worth, I already use solar parameters in making multi year climate forecasts over my region in the Upper Rio Grande. The exercises demonstrate high accuracy. I have also engaged in additional work correlating and employing spectral signatures (time series spectra) relating to the Sun and my subject steams and rivers. You don’t have to wait a year to see this. My site contains numerous examples and of course I’m working towards publications, with a precursor that touches on this peripherally at:
https://www.academia.edu/26817206/A_DATA_BASED_TIME_SERIES_FOR_GLOBAL_OCEAN_PELAGIC_PH
One minor quibble. The increase in the amount of CO2 in the atmosphere has made the planet greener due to increased efficiency of photosynthesis… biology. Increased plant life has an impact on climate. So biology has an impact on climate…just like physics does.
And then there’s biology ==> Yes, true, and that photosynthesis captures and stores some of the energy retained by GHGs.
>“The climate system is a coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible.”
Let’s complete <a href="https://www.ipcc.ch/ipccreports/tar/wg1/501.htm"the thought, shall we, Kip?
I get it that you don’t understand that we only <a href="https://judithcurry.com/2016/10/05/lorenz-validated/#comment-815456"get one realization of actual events to work from, but your inability to “get it” is a poor excuse to continue misrepresenting what the IPCC has to say about the very real challenges involved in figuring out what a complex non-linear chaotic system *might* be expected to do in response to relatively abrupt changes in external forcing.
Typical.
I agree.
Hehehe!
Still sleeping on that rubber sheet and telling stories to scare the children, Brandon?
Still beating your wife with non sequiturs, catweazle666?
Kip,
I’ll repeat my complaint above that in this series, while you have talked a lot about chaos and attractors and drawn trajectory plots, I don’t believe you have ever plotted an attractor, or said anything quantitative about them. They are important, since they are what takes the randomness out of chaos. And they are the analogue of climate in chaotic weather.
Here is a plot from Wiki:
It is the “set of numerical values toward which a system tends to evolve” (your initial quote). And it has shape and topology. You have to determine it from trajectories, and this is a process analogous to averaging an ensemble. The equation for that system is:
with ρ=28, σ=10, β=8/3. Note again that the system is autonomous – time does not appear on te right hand side. That means that you can generate trajectories forever for the same attractors. For GCMs that isn’t true. But what is important is that while the trajectories change radically for small change in initial conditions, the shape of the attractor changes continuously with the parameters. This is analogous to the dependence of climate on forcing. Incidentally proving that was #14 of Steve Samle’s problems, solved in 2002(but numerically generally found to be true earlier). It is tracking the slow variation of that attractor (climate) with forcing that is the essential GCM climate problem. It has nothing to do with the initial value issues people are hung up on here.
I will write up something on this on my blog.
The plot didn’t quite work, though you can click to see the Wiki page. Anyway here it is, from Anders Sandberg, Oxford:
Nick ==> The best evidence against your point is given by Milanovic at Judy’s recently.
There is no doubt, however, that the climate operates inside of some sort of space that has the appearance of an attractor (the historical climate record) and that inside that space we find all the attributes of chaotic systems in general, both in physical space and time.
It is possible, because of this, that in time we might be able to recognize repeating patterns of “fractal-like” behavior inside that space, and work up some sort of probabilities in a very general way. That is light-years away from useful long-term climate prediction or projection by numeric climate models.
Nick ==> we might actually be able to agree on the last two paragraphs above….yes?
Here’s a plot of the surface gain on the Y axis (surface emissions / total solar forcing) vs. surface emissions along the bottom. Sure looks a lot like the behavior of an attractor, albeit it a trivial one with only one destination, which is a ratio of about 1.6 for the surface gain or 1.6 W/m^2 of surface emissions per W/m^2 of forcing.
http://www.palisad.com/co2/sens/se/gs.png
Each dot is 1 month of data for a 2.5 degree slice of latitude of the planet extracted from the ISCCP cloud data set covering about 3 decades of weather satellite data. The larger dots represent the average over the entire sample period for each slice.
To what can the two lobes be analogous? Ice ages? ENSO? Droughts? All?
How long does the climate take to span its phase space?
Certainly a ‘stable’ few thousand years could be oscillations about islands of stability.
Why are models initialized to closely match current conditions? Won’t the attractor reveal itself regardless of initial conditions?
Do modellers expect to determine the attractor and tease out sensitivity in only 100 years of t?
“To what can the two lobes be analogous?”
The two ears case is just for one set of parameter values. chosen presumably for appearance. I don’t think there is a climate analogy for this shape.
“How long does the climate take to span its phase space?”
As I said, climate isn’t autonomous, so this isn’t very meaningful. By the time of “spanning”, conditions have changed.
“Why are models initialized to closely match current conditions? Won’t the attractor reveal itself regardless of initial conditions?”
They aren’t, and yes. Models are usually started “wound back” – to maybe a century or more ago. The idea is that it is better to let the less well known early initial state settle down than to use recent data which may, through lack of resolution or inaccuracy, be far from the attractor.
“Do modellers expect to determine the attractor and tease out sensitivity in only 100 years of t?”
Good question. Again it comes back to non-autonomous relations. They are trying to observe a moving attractor. One compromise is to look for TCR (transient) measured over 70 years. But that may vary with time.
“I don’t think there is a climate analogy for this shape.”
This is the general shape for a solution space with pair of quasi stable states, where the system is stable in either given the same stimulus, but can be easily pushed one way or another by orthogonal factors. El Nino/La Nina is an example and there are many others. The composite shape corresponding to the actual Earth climate system response is the sum of a lot of smaller shapes with 2 or more lobes which when combined provide a solution space for the background ‘noise’ centered around a steady state dictated by COE requirements. The take away should be that all this chaos is nothing but weather and that weather is not the climate.
Ice ages and interglacials are not an example of quasi stable states with the same stimulus, as the stimulus is a function of orbital characteristics with asymmetry between hemispheres and given the characteristics as compared to other similar times, global scale glaciation is not sustainable and we should either be in an interglacial period or transitioning into one. The chaos is around state pairs that are much closer together.
On the ice age side of the climate, there is an extenuating circumstance that makes ice ages deeper, which is increased reflection from increased surface ice and snow, however; we are relatively close to minimum possible average ice already and this albedo effect can only enhance future cooling but lacks the dynamic range to have much effect on future warming.
Can’t a non-autonomous system be converted to autonomous one?
“To what can the two lobes be analogous?”
Ice ages.
http://www.biocab.org/Geological_Timescale.jpg
Looks like two big lobes and a fair bit of noise to me.
And not a sniff of a relationship between temperature and CO2 in sight.
Oh, and it seems inevitable it is going to warm up quite a bit sooner or later, whether we want it to or not.
I tend to agree – many lobes over many time scales.
“many lobes over many time scales.”
Ice ages and interglacials are not 2 stable solutions given the same stimulus and do not fit this pattern. Ice ages and interglacials are unambiguously related to changes in the Earth’s orbit and axis. This is not chaotic noise, but a causal response to a quantifiable change.
The solution space certainly has many lobes over many time scales, but the lobes are close together (i.e just on either side of balance) and the time scales are short since the climate systems time constant is only on the order of a year. If it was the decades to centuries claimed by the IPCC, we would not even notice seasonal change since the response would be too slow.
So, let’s dump 30Gt into the air and see what happens. Where’s my popcorn.
What’s the denominator?
“Can’t a non-autonomous system be converted to autonomous one?”
Not usually. Non-autonomous means the equations (coefficients) change with time. To find an autonomous set which admitted the same solutions would be extreme good fortune.
Nick ==> While I disagree with your point, I look forward to seeing your post on it.
“Coulomb’s law or Coulomb’s inverse-square law, is a law of physics that describes force interacting between static electrically charged particles. In its scalar form the law is:
F = k e q 1 q 2 r 2 {\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}} {\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}},
where ke is Coulomb’s constant (ke = 8.99×109 N m2 C−2), q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of interaction between the charges is attractive if the charges have opposite signs (i.e. F is negative) and repulsive if like-signed (i.e. F is positive).
The law was first published in 1784 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton’s inverse-square law of universal gravitation. Coulomb’s law can be used to derive Gauss’s law, and vice versa. The law has been tested extensively, and all observations have upheld the law’s principle.”
https://en.wikipedia.org/wiki/Coulomb%27s_law
Forcing something will produce a resistance and the result = Heating .
The harder the electron has to work to hold the molecule together the hotter it gets .
Kip
This is a great article on an important subject, but careful though is needed as to where chaos-nonlinearity actually move the climate debate.
To say “climate is chaotic so can’t be predicted” is an exaggeration and provides alarmists with a straw man to burn and a pretext to crow to one another that they have seen off again the threat of chaos to their orderly and simplistic doom architecture.
Among all the details of chaos theory, the most important message of chaos should not be lost. This is that chaotic-nonlinear dynamics, together with the vast ocean heat content and its sharp temperature gradients – especially vertical – that climate changes itself by internal chaotic dynamics. Talk of climate change as always requiring external forcing exposes profound ignorance of chaotic dynamics, or alternatively, denial of chaos.
It is not correct that extreme sensitivity to initial conditions is a sufficient condition for chaos. Non chaotic systems also display such extreme sensitivity. There are further conditions that are needed for chaotic-nonlinear dynamics to emerge. Some of these are listed below although I can’t say which of these are either necessary or sufficient:
– A dissipative system with open flow through of energy
– Negative feedback, also called friction or damping
– Positive feedback, also referred to as excitability or reactivity; interaction between positive and negative feedbacks can drive chaotic dynamics
– A negative Lyapunov exponent, often associated with dissipative damped systems, makes outcomes converge to an attractor.
– Degrees of freedom in a number of parameters that provide the dimensions of a phase space within which a negative Lyapunov exponent and chaotic attractors can emerge.
ptolemy2 ==> This quote: “To say “climate is chaotic so can’t be predicted” is a doppleganger of the real quote which is: “… therefore the long-term prediction of future climate states is not possible.” And this conclusion was not drawn from “sensitivity to initial conditions” alone but from the expanded study of dynamical systems in general.
Lorenz’s computer bug turned out to be “initial conditions” and passing his paper around got a lot of people excited and looking into different aspects of what later was named Chaos Theory.
All your points are valid of course, they are part of the field. Thank you for bringing them up.
Many thanks for these posts on Chaos. Chaos as used in this post appears to adopt a standard but typically unspoken assumption that one knows all of the variables at play very well, even as strange attractors emerge from the repeated numerical experiments. That’s easy to see for any who work with nonlinear dynamics and the analytical and numerical implementations thereof.
But what if all of the variables and/or mechanisms are not truly known? Then the concern is not really about chaos but rather about epistemic uncertainty. In other words, how do we really know what we don’t know?
One way to advance is to consider alternative conceptual models, and run exercises for those. Then it would prudent to compare the forecasts to the data.. and also compare that validation exercise to the prior conceptual models and their predictive offspring, and see which model does a better job. It doesn’t necessarily solve everything, but if a better model is found, perhaps the chaos argument becomes somewhat more moot.
This is the basis for my own successful excercises which I believe demonstrate an ability to forecast drought and pluvials in some regions, many years in advance. This is done without reliance upon numerical determinstic models such as the serially-reinitialized GCMs. The proof is here: http://www.abeqas.com/mwa-demonstrates-proven-drought-forecasting-a-possible-first-in-the-climate-industry/
I love chaotic topics and am sure they will never go away in key aspects of climate science. But in this case, given my reproducible experiences, they may not be the true obstacle.
Mike ==> A lot of attention is being turned to the “uncertainty” issue in Climate Science — Judith Curry has been discussing it for some time. And yes, uncertainty is what we know, what we don’t know, what we don’t know we don’t know, ….
In this essay today I point out that one of the things we don’t know is if the climate system has an attractor?, and if so, what does it look like? I do offer my best guess that the historic climate record reveals at least the limits of the attractor-like behavior of the climate system.
Perhaps it is much simpler than that.
Climate scientists and many others declare that since the TSI changes only fraction of percentage point that the sun can not be a principal driver of climate change.
Climate change as seen through the global temperatures periscope is result of a finely balanced system, which can be disproportionally thrown off from its natural tendency towards equilibrium even by the smallest of changes.
http://www.vukcevic.talktalk.net/CSb.gif
The biggest attractor re: climate change is Earth (Ground) Half of atmospheric heat is a process of the resistance build up between Earth and Sun.http://physicsworld.com/cws/article/news/2011/jul/19/radioactive-decay-accounts-for-half-of-earths-heat If you stand back and look at Earth as a complex molecule and like all molecules , it’s surrounded by a cloud of electrons . Earth surface is like a giant Van de Graaf generator . The spark that is produced between ground and atmosphere we call lightning, even if you don’t see a spark the exchange of energy still takes place. A low pressure system works in the up direction and can produce foul weather and a high works in the down direction good weather .
https://en.wikipedia.org/wiki/Van_de_Graaff_generator
There are knows, then there are known unknowns and then are unknown unknowns…
… and then there are unknown unknowns…
In the real world the climate change caravan moves on while the skeptic dogs bark.
In the town where I live the mayor forbade the use of plastic shopping bags. Protesters stop pipeline construction. The federal government will introduce a carbon tax.
I hope you all are having a good time. The left of course is driving the camels.
I was intrigued by the NCAR/UCAR images, but it seemed to me that comparing the ensemble mean (EM) to the observations cannot produce a valid measure of natural vs. man-made contributions. I assume what they’re saying (although I’m grossly over-simplifying) is basically, if you look at the observations, and “subtract” off the EM, you get humanity’s contribution (or, they somehow “parse out” the contribution).
But, the reality is the climate isn’t “an average” of all possible climates, so if the natural state were actually image 24, then we contributed much less (if any at all) to the warmth. Am I missing something here?
P.S. I have long understood that the climate is a“coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible,” but astounded that the IPCC seems to have forgotten that.
Barbara Hamrick ==> You have it exactly right — the ensemble mean of 30 chaotic outputs is only the mean of 30 chaotic outputs — nothing more — nothing less. I wrote an entire post on this at Climate Etc titled Lorenz Validated. You’ve pretty much nailed the central point. Thanks for reading and commenting here.
> Am I missing something here?
That we only have one realization of the actual system from which to work might be a good candidate, Barbara.
> P.S. I have long understood that the climate is a“coupled non-linear chaotic system, and therefore the long-term prediction of future climate states is not possible,” but astounded that the IPCC seems to have forgotten that.
They haven’t. Kip likes to omit the rest of the paragraph in that particular quotemine:
He then likes to “pretend” that he doesn’t understand how Stoopid Modulz Ensemblez can be useful to obtain that stated stastical goal, even as he gives the concept some lip-service. Here’s Kip’s end-game:
Quite convenient that searching an effectively infinite state space is required before being able to make useful policy decisions, innit.
Barbara Hamrick ==> You have it exactly right — the ensemble mean of 30 chaotic outputs is only the mean of 30 chaotic outputs — nothing more — nothing less. I wrote an entire post on this at Climate Etc titled Lorenz Validated. You’ve pretty much nailed the central point. Thanks for reading and commenting here.
Here’s an interesting article on Chaotic Circuits Can Mimic Brain Function, Aid Computing. The authors show
What is particularly interesting here is how, in a ring of oscillators running in a chaotic fashion,
In other words, very small signals through the intermediate oscillators synchronize much larger signals in separated units.
This could explain, for instance, the apparent observed synchronization between planetary alignment and solar activity. A “driving” action is not necessary, simply the kind of chaotic synchronization mentioned in the paper.
Kip Hansen:
“We have absolutely (literally absolutely) no idea what the precise, or even an, attractor for the weather or climate system might look like, separate from the long-term historic climate record.”
Here:
I’ve tried explain a physical basin of attraction. There’s a lot of water. Some of it is strongly attracted to Greenland but most of it on any give day is not. Sea ice could also be a basin of attraction as would be the sea water near it. Humidity level changes can be thought of as basins. The fact that water is so important to climate coincides with its ability to change form as with a bifurcation diagram as well as its information carrying ability and memory. Another example is a lake in Minnesota. In fall the evaporation rate is high until it comes to about a full stop when it ices over. The Winter basin of attraction is don’t evaporate. The Summer one is to.