Mike Jonas
I have put a bit more work into Chaos Theory (aka the Butterfly Effect), and whether it can apply in the real world. It seems that just about every time someone tries to demonstrate Chaos Theory, they do it with a model. Trouble is, their findings then always turn out to have come from the model itself. As with the turtles that prop up our planet, the climate modelling world sometimes feels like it is propped up by circular logic all the way down.
The strictest version of Chaos Theory cannot apply to the real world, because it refers to variations in initial conditions, and the real world only has one trajectory. In other words, there is only one version of Earth’s climate at any one point in time, so it can’t have a variation in initial conditions. Unfortunately, the theory has morphed into something which many in climate science think applies to Earth’s climate, and when they run climate models they get confirmation. Well, they think it looks like confirmation.
First, let’s be clear about what we are looking at. Chaos Theory says that Earth’s weather and climate are very sensitive to local conditions: a tiny variation grows exponentially into a large difference. We know that weather and climate show natural variations on many physical scales and many time scales – there is turbulence in both the atmosphere and the ocean. We know that turbulence can be very difficult to predict, and we know that differential equations such as Navier-Stokes can be useful for understanding it. We don’t know that a tiny variation will grow exponentially. My suspicion is that the exponential growth described by Chaos Theory is an artefact of the models, not a natural phenomenon, and that it is being confused with natural variation. Further, that if we ditched Chaos Theory we might end up with a better understanding of our world.
So I did an extensive search of the literature, using Grok of course because it is amongst other things a powerful search engine. Amongst all the attempts to demonstrate Chaos Theory using models, there were some that tried to do it using atmospheric analogues: they look for pairs of very similar situations in historical records to see whether they then diverge rapidly as per Chaos Theory. The concept is that the difference between the two situations is a proxy for Chaos Theory’s variation in initial conditions. Unsurprisingly, they found divergence (otherwise weather forecasting would be easy), but equally unsurprisingly the situations were never close enough to be a proper test – Chaos Theory is based on infinitesimal differences.
And then Grok served up a bombshell. Some of its AI mates have got into climate modelling, and when some of their model runs showed the rapid divergence expected from Chaos Theory their handlers did a very interesting test: they repeated the exact same model runs on a more accurate computer. The divergence was eliminated or severely reduced. The divergence, in their words, “is caused by numerical noise, which is an artifact of the computation rather than a real atmospheric process“. If chaos can be created by using a less accurate computer, imagine how much chaos can be created by the crude iterations of a GCM. (GCMs are General Circulation Models, which have been the mainstream climate models for many years).
I had already written most of a paper covering the other tests, and obviously I needed to add this in. I couldn’t claim that all chaos in models was numerical noise, even though it could be (and probably is?). Although I suspected that GCMs’ iterative errors would be orders of magnitude larger, I couldn’t address that in any detail without a lot of work. So I put it mainly into the “Discussion” section, on the basis that it did not have to be argued and referenced as assiduously there as in the “Analysis” section, and that one day I might get around to doing that detailed work. The paper is Chaos Theory remains void for the real climate and is now published, and here is the abstract:
Weather and climate model results, and studies related to Chaos Theory, are examined for evidence that Chaos Theory applies in the real world rather than only to models. No such evidence is found, and in some cases rapid growth in model divergence as expected from Chaos Theory has been found to be an artefact of the models. Results from models coded with mathematical formulae that exhibit rapid growth in divergence cannot be used to assess the applicability of Chaos Theory to the real world, because that would necessarily involve circular logic: the model results are only exhibiting an emergent property of the formulae as used in the models. Tests with atmospheric analogues have been unable to assess the applicability of Chaos Theory to the real world, because they could not emulate the infinitesimal perturbations at the core of Chaos Theory. Some AI models have shown that their rapid growth in divergence, as expected from Chaos Theory, is caused only or primarily by numerical noise, and is therefore an artefact of the computation rather than a real atmospheric process. General Circulation Models use processes with inaccuracies similar to numerical noise, which could have a similar effect. Other AI models do not exhibit rapid growth in divergence. The model findings apply only to the models, so they cannot be used to assess Chaos Theory’s relevance to the real world. In the real world, Chaos Theory remains void (scientifically inapplicable).
Even if every model run in history is shown to have been the source of its own chaos, that still would not prove that Chaos Theory does not apply in the real world. Even if Chaos Theory does apply in the real world, it seems impossible to demonstrate it for the reason given above, hence the “remains void” in the title. What I suspect will happen (I would like to be wrong) is that Chaos Theory will be changed to something that actually can be demonstrated in the real climate, and then it will be represented as having always been correct.
I would really like to see a change in some of the thinking in climate science, so I added a paragraph arguing that at least some of the weather and climate variability that is regarded as chaos may ultimately be resolvable by better observations and better understanding, exactly as happens in other complex fields. In other fields of science, the normal attitude to unknowns is that the relevant factors are not yet understood, not that they are deterministic chaos. It seems reasonable to take a similar approach in the field of weather and climate.
Then I would like to see GCMs not being used for climate modelling. What a massive waste of time and money they have been.
Don’t forget…”The Butterfly Effect” refers to the shape of the graph…
If you use a large enough crayon, all the letters blur together.
It’s time for your next lesson.
https://www.twinkl.com.au/blog/an-artistic-adventure-unleashing-the-benefits-of-finger-painting-for-children
Always?
Don’t forget. Your ego is larger than the universe.
The Lorenze graph looks that way because there are two chaotic mechanisms in his model — warm air trying to rise and cold air trying to rise. They interfere with each other. They are the low and high pressure systems that create much of the weather.
I know a lot about chaos theory—my one peer reviewed paper gave both a history of productivity (four successive ‘sources’, the then most recent being ‘quality’ and its sequelae) plus a real life sequelae example in a heavy truck assembly that we were able to model.
The two ‘chaotic mechanisms’ in Lorenz seminal paper are both mathematically known as ‘strange attractors’ in N-1 Poincare space. The problem with chaos theory in climate is that N-1 Poincare space is still an unknown very large number, so an unknown but very large number of potential strange attractors—arguably usually cancelling.
There is only a single strange attractor in the Lorenz model. And it is a 3 three dimensional object that exists in the full space rather than the 2 dimensional (N-1) Poincare space.
Sounds right Izaak. It has to be 3D as trajectories can never intersect. I think the Lorenz attractor has two “eyes” because the system tends to spend a lot of time in either high or low pressure then jumps to the other, back and forth. An aperiodic oscillator like all chaos (and weather).
But you two know a lot more about the math than I do. My focus is on the epistemic impact on science and policy of widespread intrinsic unpredictability. As one chaos buff puts it: “After 400 years it is about time we got something new.”
Why not? A characteristic of the strange attractor is that it is, well, strange. Although the paths are constantly changing, is there a rule which states that a 3d point can never be used again by any path?
What would happen when you run out of points? Alternatively, when the system proceeds to zero (as it does for an infinite number of inputs), it sits there saying the point is 0,0,0 over and over.
Chaos is chaos. Not intuitive at all, and asking AI will often just regurgitate incorrect but widely held beliefs.
Weather is unpredictable, however you look at it.
The rule is that the system’s derivatives are completely determined by its position in phase space. So if a system returns to the same point in phase space then its next point has to be the same as when it got there last time since everything is deterministic.
And you can never run out of points. Between any two points there is an uncountable infinity of points. And if the system does proceed to zero it never actually gets there, rather it just gets infinitely close to it without every reaching it. Not only is the system deteministic it has to be capable of being run backwards in time.
A nontechnical explanation:
Rhttps://www.cfact.org/2023/02/10/the-math-of-chaos-why-weather-and-climate-are-unpredictable/
Sorry it is so long.
Link garbled. Try this:
https://www.cfact.org/2023/02/10/the-math-of-chaos-why-weather-and-climate-are-unpredictable/
You are right. Viewed from one viewpoint, the 2d projection of the widely used representation of the 3 axis Lorenz attractor appears roughly butterfly-shaped. Of course, this is mental reinforcement of the title of Lorenz’ address “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas”.
Change your viewpoint, or the 3 precise inputs, and voila! A completely different, never repeating trajectory may appear. Or the equations may proceed to zero. Or generate repeating stable patterns – knots, for example.
Most people (including many physicists) have little to know understanding of chaos – or acceptance of the uncertainty principle.
The must be a bottom tortoise.
The smallest computer capable of describing the state of the earth at any one time is the universe. And the state at each jiffy is the new initial condition for the next result.
I have recently discovered that my lifetime intuition is shared by others and that I belong in the group calling themselves ultra-finitists. Infinite/Infinitesimal is the bedrock of differential and integral calculus and is to be expected to be flawed under many conditions.
My question, does human free will alter the calculation?
Phillip Chalmers wrote: The smallest computer capable of describing the state of the earth at any one time is the universe. That is correct. Even if we had a capable computer, we cannot measure and input enough data into the computer.
To know, really know, even the smallest thing, is beyond us
Reminded me of this.
“Gunga Din says:
May 14, 2012 at 1:21 pm
joeldshore says:
May 13, 2012 at 6:10 pm
Gunga Din: The point is that there is a very specific reason involving the type of mathematical problem it is as to why weather forecasts diverge from reality. And, the same does not apply to predicting the future climate in response to changes in forcings. It does not mean such predictions are easy or not without significant uncertainties, but the uncertainties are of a different and less severe type than you face in the weather case.
As for me, I would rather hedge my bets on the idea that most of the scientists are right than make a bet that most of the scientists are wrong and a very few scientists plus lots of the ideologues at Heartland and other think-tanks are right…But, then, that is because I trust the scientific process more than I trust right-wing ideological extremism to provide the best scientific information.
=========================================================
What will the price of tea in China be each year for the next 100 years? If Chinese farmers plant less tea, will the replacement crop use more or less CO2? What values would represent those variables? Does salt water sequester or release more or less CO2 than freshwater? If the icecaps melt and increase the volume of saltwater, what effect will that have year by year on CO2? If nations build more dams for drinking water and hydropower, how will that impact CO2? What about the loss of dry land? What values do you give to those variables? If a tree falls in the woods allowing more growth on the forest floor, do the ground plants have a greater or lesser impact on CO2? How many trees will fall in the next 100 years? Values, please. Will the UK continue to pour milk down the drain? How much milk do other countries pour down the drain? What if they pour it on the ground instead? Does it make a difference if we’re talking cow milk or goat milk? Does putting scraps of cheese down the garbage disposal have a greater or lesser impact than putting in the trash or composting it? Will Iran try to nuke Israel? Pakistan India? India Pakistan? North Korea South Korea? In the next 100 years what other nations might obtain nukes and launch? Your formula will need values. How many volcanoes will erupt? How large will those eruptions be? How many new ones will develop and erupt? Undersea vents? What effect will they all have year by year? We need numbers for all these things. Will the predicted “extreme weather” events kill many people? What impact will the erasure of those carbon footprints have year by year? Of course there’s this little thing called the Sun and its variability. Year by year numbers, please. If a butterfly flaps its wings in China, will forcings cause a tornado in Kansas? Of course, the formula all these numbers are plugged into will have to accurately reflect each ones impact on all of the other values and numbers mentioned so far plus lots, lots more. That amounts to lots and lots and lots of circular references. (And of course the single most important question, will Gilligan get off the island before the next Super Moon? Sorry. 😎
There have been many short range and long range climate predictions made over the years. Some of them are 10, 20 and 30 years down range now from when the trigger was pulled. How many have been on target? How many are way off target?
Bet your own money on them if want, not mine or my kids or their kids or their kids etc.”
This is really what it all boils down to.
“The map is not the territory”.
My concept of the butterfly effect rests within the inability to predict how a binary “choice” turns out. An iterated function blowing up, or not (Mandelbrot set). A single molecule of water condensing, or not. There’s always a boundary, but you really can’t specify it. The tiniest change in initial conditions can cross the boundary. That’s chaos, or at least sensitivity to initial conditions.
Somehow, I feel like I’m describing quantum mechanics, too 😉
Chaos Theory is low dimensional . Assuming a single butterfly .
But there are billions . So the result is the average of billions of catastrophes .
Not to say tipping points don’t exist . Crystallization , like ice , is an example .
Rock slides are another .
Well, I have this take on Chaos Theory and its “butterfly effect”: there is the “Hand of God” effect that can eliminate any random perturbations from propagating chaotically over unlimited time.
By “Hand of God”, I’m thinking of things like the Chicxulub impactor that was not “envisioned” by Mother Nature and reset evolutionary pathways that were up to then progressing via chaos theory, yielding dinosaurs as the top-tier life on Earth. I don’t believe Chaos Theory, as is currently envisioned and debated, admits to the fact that at any given time processes underway can be subjected to a step-change due to an unexpected, external event upsetting/resetting the system being considered.
Some other “Hand of God” possibilities:
— a supermassive solar flare, say X100 or higher, directly impacting Earth,
— worldwide nuclear/thermonuclear war,
— a “nearby” star going supernova and having one of its astrophysical jets of intense radiation sweep over Earth,
— a random black hole—or more unlikely, a hypothetical cosmic string— being on a trajectory intersecting Earth or the Sun.
Given that mankind has only been technically “advanced” in physics and cosmology for less than 400 years, and given that mankind does not currently understand what comprises about 95% of the universe (other than the ability to call it “dark matter” and “dark energy”), there could be other pitfalls to life on Earth that we humans can’t even contemplate.
Modern cartography of our universe might still find use for affixing the phrase “thar be monsters there”.
“a tiny variation grows exponentially into a large difference”
I never had much confidence in the butterfly effect. While some small event may grow, all the NOT small events may grow too and much more so- so the idea that some small event can over ride the bigger events, makes no sense to this NON scientist.
Well said !
And on the political instead of climate ….
https://theconservativetreehouse.com/blog/2026/09/13/russian-federation-president-vladimir-putin-outlines-how-eu-leadership-create-crisis-then-manage-it-terribly-energy-example/
Or maybe not – how would anyone know?
The way I see it, JZ, is that any event can grow, and any event can fizzle out. Larger events simply have more chance of growing.
So I was watching this You Tube Titled:
“Something About Wyoming’s Devils Tower No Longer Makes Sense”
When around 6:30 this sentence went by:
It’s the newest theory backed by real modeling and it still hasn’t settled the argument.
Yeah, real modeling as opposed to fake modeling.
Does someone want to destroy the definition of {real, reality, realism, realistic} in preparation for the next political regime?
First we have real real, then we have real unreal, then we have unreal real, but then there is unreal unreal which can be real tough to define… HT to Rumsfeld
What doesn’t make sense about Devils Tower? Where did all the material that eroded away from the lava core go?
The same place all the dirt that was in the prairie dog holes went
Alarmists have a fetish for stasis. Whenever something “changes” (usually from a “baseline” that is meaningless as it is generally NOT a “norm”) it must be “bad.”
Oh and don’t forget, it’s all the “fault” of humanity, and we must “do as they say” to “save” us from whatever imagined “crisis” that they insist will otherwise ensue.
Wyoming’s Devil’s-Tower-of-Doom
I checked it Saturday night.
It’s still there, and nothing about it ‘no longer makes sense’
“We know that weather and climate show natural variations on many physical scales and many time scales – there is turbulence in both the atmosphere and the ocean.”
“My suspicion is that the exponential growth described by Chaos Theory is an artefact of the models, not a natural phenomenon, and that it is being confused with natural variation.”
I have yet to see where climate science *really* studies natural variation in anything. It’s always “averaged” away by never associating the average value of the natural variation with a variance calculated from the base natural variation.
Then the resulting averages are averaged as if that can actually tell you anything about the base. And even the variances of the resulting averages are left to lie in limbo!
Anomalies calculated from averages don’t help anything. They take on the variance of the averages which have no relationship to the variance of the base natural variation — and even the variance of the averages is left to lie in limbo by substituting instead a metric for how precisely they calculated the average instead of carrying to actual variances of the average values forward!
And don’t even get me started on trying to characterize climate using temperature as the metric at the local, the regional, or even the global level. Chaos theory *does* depend on initial conditions that can actually be used to characterize the system being studied. Temperature simply doesn’t meet that test.
Are you saying its… averages all the way down?
Yep. Somehow it gets forgotten that statistical descriptors of a distribution only tell you about the shape of the distribution. The average is *NOT* a measurement nor is it actual data. An average of averages only tells you about the *shape* of the distribution of the average values. It tells you *nothing* about the physical realities of the base data. What’s worse is that the average isn’t a sufficient descriptor to actually tell the shape of the distribution. You also need to know the standard deviation at the very least.
Climate science doesn’t even recognize that the global temperatures form a multimodal distribution where the average value is *really* meaningless. All it gives you is the center of gravity of the distribution. It tells you nothing about the actual shape of the data distribution. And anomalies don’t help. Anomalies are calculated from average values that have already hidden any multi-modal effects! And since the variance of even the anomalies are different for cold temperatures than for warm temperatures, you *still* wind up with some sort of crazy average.
If I were King of Climate Science, I would force the use of the 5-number statistical descriptor. Although the GUM doesn’t really lay it out, the inter-quartile interval always contains 50% of the values, even for non-Gaussian distributions. It makes comparing the accuracy, i.e. the measurement uncertainty, of distributions simple. If you want a wider interval just define a coverage factor standard.
Climate science does what it does because it is EASY! But the easy way is very seldom the best way, or even an adequate way. Climate science and Teyve from Fiddler on the Roof would get along fine! “TRADITION”. Climate has been studied using temperature for hundreds of years and what was good enough for our ancestors is good enough for us!
My problem with averages and anomalies in climate science is the true value of the earth’s temperature is unknown. We calculated one, but it may not be correct.
When I was an engineer/plant manager of a company that did metal work we knew what ground truth was because the design said what the dimension was to be. (6 inches +/- .03 example). You can do SPC with that info.
I like to summarize it as follows: An average is nothing more than a midpoint of extremes.
And as you say, it tells you nothing about the range or characteristics of those extremes.
“I have yet to see where climate science *really* studies natural variation in anything.”
Do you understand natural variation? It’s hard to see how anyone who defends the Monckton “pauses” does. Otherwise, they’d understand how a long term warming trend forced by GHGs can have short term natural variability from ENSO superimposed on it, producing those apparent “pauses.”
“Chaos theory *does* depend on initial conditions that can actually be used to characterize the system being studied. Temperature simply doesn’t meet that test.”
Uh… temperature is one of the fields used to characterize the initial atmospheric state in weather models that demonstrably have predictive skill, and weather prediction itself is an initial-condition problem in a chaotic system.
Temperature alone obviously can’t specify the complete state of the atmosphere; you also need pressure, humidity, winds, etc. But that doesn’t somehow mean temperature isn’t an important part of the initial state.
Stupid question but what is temperature a measure of?
You are just copying a reason that consensus climate scientists are relying in order to use a simple trend to predict what is going to occur. Most of what occurs on this planet is cyclical. The sun comes up and the sun goes down. The earth tilts in a cyclic fashion. The earth heats up and the earth cools down. IT IS MULTIMODAL, that is, there are different cycles of various periods of different things that are constantly aligning and realigning.
Once, long ago, I tried to make an analog square wave generator from 10 different oscillators. Fourier did the original math that defined what frequencies and amplitudes would be needed. It never worked. This was in the days of discreet components where temperature drift was de rigor. All kinds of waveforms showed up and every once in a while, a square wave would appear. Exactly what would a trend of an average amplitude have provided.
Long story short. A simple trend of one component in a turbulent atmosphere will tell you absolutely nothing. Especially when that component is temperature, an intensive property.
Actually, weather models work because temperatures are autocorrelated in the short term. Where do you think the adage “forecast tomorrow to be the same as today” came from? Yes, fronts being monitored can change that, but simply putting in a temperature for today and hoping for a good prediction 10 days away is only going to work based on luck alone.
And when the actual “averages” have large uncertainties, do you really think a correct answer will result?
There is no “long term warming trend forced by GHGs”. We know this because the strength of the greenhouse effect has not changed. See “greenhouse efficiency insights” figure 4.
Do *you* understand natural variation? What *is* a long term warming trend? Decades? Centuries? Millennia?
The boundary conditions on the earth’s biosphere are 1. a frozen ball, and 2. a molten rock. Obviously the earth started as a molten rock. Also obviously neither of these boundary conditions have been reached again. That means that the earth’s biosphere has “VARIED” over time between the boundary conditions but has never actually reached one of them. Wavelet analysis of paleo data has shown cyclical frequencies as long as 20,000 years for glacial/inter-glacial periods.
If GHG’s cause a long-term warming TREND, then it should be obvious to anyone that when GHG’s were more prevalent in the atmosphere over the millennia that the earth should have been pushed back into the molten rock it started as – with little hope of ever exiting such a phase. Yet I can’t find any research that says the earth ever ascended back into the molten rock phase it started as.
Think about it for just one minute. It’s obvious that the earth has seen cyclical natural variation of at least thousands of years in period over its past. And here is climate science, looking at a 30year-long to 100year-long time period and asserting a warming trend that is going to see extinction of life on the planet because of a “tipping point” that has never been reached in the past.
In fact, it’s not even apparent that you understand *what* the ENSO cycles represent. It *isn’t* cyclical heating and cooling. It’s physical movement of the ocean surface by cyclical *trade winds”. The exposing of warmer water is a *result* and not a “cause”. It’s not from “extra heat being stored in the deep ocean suddenly appearing at the surface”. It’s from the trade winds exposing more area of warm water. It’s a physical and cyclical phenomenon. It’s from warm water piling up on the east side (El Nino) and then from warm water being covered up by the ocean sloshing back toward the west side (La Nina).
The Monckton “pauses” really have nothing to do with the actual cyclical phases in the biosphere. They have to do with the falsifying of the climate science claim that CO2 is *the* temperature control knob for the biosphere.
“Uh… temperature is one of the fields used to characterize the initial atmospheric state in weather models that demonstrably have predictive skill, and weather prediction itself is an initial-condition problem in a chaotic system.”
Nice try at changing the subject at hand. But it’s a BIG FAIL. Weather models are *NOT* climate models. Local, current temperatures have a large impact on weather. They have almost *NO* impact on climate if any impact at all. If temperatures did determine climate then Phoenix and Miami would have similar climates. The US Central Plains and central Africa would *not* have similar climates since they have vastly different temperatures.
“But that doesn’t somehow mean temperature isn’t an important part of the initial state.”
Temperature is *NOT* an important part of the initial state. Geography, terrain, humidity, and precipitation *are*. The temperatures in San Diego are different than the temperatures in Ramona, CA because one is a coastal plain and the other an inland plateau (geography and terrain) even though their physical separation is small. Their temperatures are a *result* of the geography, terrain, humidity, and precipitation. Temperature is *NOT* a cause of the geography, terrain, humidity, and precipitation. Temperature does *not* define the climate state of these two locations. Temperature is defined *by* those other factors – which are largely ignored in climate science. Similar pairs are all over the globe. Denver, CO and Burlington, CO. Topeka, KS and Wichita, KS. Worcester, MA and Boston, MA. And on and on and on …… ad infinitum.
Climate science likes to use the garbage meme that temperatures are correlated over distance and therefore homogenization and infilling of missing areas is justified – while ignoring the actual truth that the correlations are typically what is called “spurious”. They are each actually correlated to the confounding variable of earth’s orbital mechanics diurnally and seasonally, not because they are physically close.
This was written: The paper is Chaos Theory remains void for the real climate and is now published, and here is the abstract:
I write: Water is abundant, the conditions that water changes states is fixed, Thunderstorms cool the tropics more when the tropics are warmer, Ice cools the polar regions more when there is more tropical currents carrying more energy into the polar regions using more evaporation and snowfall and sequestering of ice and ice cooling the oceans when pushed into turbulent salt water currents. Climate has always warmed after being colder, climate has always cooled after being warmer, climate is different in different parts of the earth, but where there is water in changing states, climate in all the different parts of the earth is self correcting. Ten thousand years ago, the sun was closer to the earth when the northern hemisphere was in summer, now the sun is closer to the earth when the southern hemisphere is closer to the sun in summer. That provides a difference of warming in summer of more than 30 watts per meter squared, yet the northern hemisphere cooled some and the southern hemisphere did not change much. An order of magnitude larger change than CO2 warming caused little change, that is powerful self correction. Northern Hemisphere glaciers and ice sheets have depleted over the ten thousand years because less ice is needed to self correct for less solar energy in. Give this some Critical Thought.
The appearance of chaos is the result of not knowing enough, it does not matter the accuracy of any computer when not enough is known to create a proper model.
OK, I will.
No, the ice is water which has been cooled below its freezing point.
No, cooling results when energy is being lost, not gained. The world is roughly spherical, and every particle on its surface is attracted to its center of gravity, remaining where it is unless subjected to an unbalanced force.
Neither air, nor water, nor earth, nor fire are suddenly consumed with the desire to move toward the poles! Do you find yourself irresistibly drawn towards the North or South Pole when the sun shines? I assume not.
The Earth’s surface has cooled to its present temperature from a molten state, and continues to do so. The movements of the atmosphere, aquasphere, and even the continents and the Earth’s interior appear to be chaotic, and not usefully predictable any better than a smart 12 year old could do.
If you want to criticise me without providing facts to support your criticism, please do it behind my back and not to my face – because I’m sensitive and easily hurt. Only joking.
Climate science has a magical crystal ball that *can* know enough. It is hidden in a secure, secret location known only to a few.
Excellent paper, well argued.
You show the Chaos argument against climate models is not sufficient, even probably false.
In my view, it is not necessary either. I have head posted why here several times before in graphically illustrated detail, but will briefly summarize why again here within this comment for reader convenience—using Navier-Stokes ‘actual physics’ as the specific example.
Climate modelers claim their models are ‘based on physics’. That is not true, and never could be. As regional weather models like ECMWF show, to ‘accurately’ model a thunderstorm convection cell using Navier-Stokes physics requires a grid on the order of 2-4km (in the ECMWF example, so called ‘fine’ and ‘coarse’ resolutions). That is possible for a bounded regional weather model with known boundary conditions ‘zooming in’ fine on future selected features of coarse interest, to a few (3-5) days out. That is literally impossible for a global climate model running out to 2100, whose finest CMIP6 grid (at the equator) is 100km—and the CMIP6 average grid is ~150km.
The inescapable reason for the ‘finest’ (in reality very very coarse, impossible for applying Navier-Stokes) newest climate model grids is (the proven in 1928) CFL theorem for numeric solutions to PDEs (partial differential equations). Navier-Stokes has five PDEs. One for conservation of mass, one for conservation of energy, and three for conservation of momentum in all three physical dimensions. The CFL theorem says (per NCAR) that halving grid resolution roughly increases computational effort by 10x (CFL theoretical is exactly 8x, plus actual additional supercomputer computational overhead). A global Navier-Stokes ‘actual physics solution’ convection cell would be ~7 ORDERS OF MAGNITUDE computationally intractable for just one 3 day period (assuming typical CMIP6 30 minute time steps), let alone for 75 years. And to realistically scale the CFL problem further, the average CMIP6 single model run took about two months of continuous 24/7 supercomputer effort (actual average at all the various CMIP6 model grid scales was 58 days).
So climate models have to be parameterized. Those parameters are tuned to best hindcast 30 years— a formal CMIP requirement. CMIP pretends this works well, with the resulting model hindcasts in good anomaly trend agreement. But that just uses 30 year temperature hindcast anomalies to hide the hindcast tuned temperature truth. In temperature terms the tuned parameter hindcasts vary between models by almost +/-3C—proof climate models are crap.
The situation is actually much worse concerning forecasts. Parameter tuning inescapably drags in the attribution problem—how much of the parameter was due to anthropogenic forcings, and how much was due to natural variation (which should be excluded from forecasts)? IPCC cannot pretend (altho they try) that natural variation does not exist. Their own AR4 WG1 SPM Figure 4 (addressing attribution) says it does. The published SPM figure compared the temperature rise of ~1920-1945 to that of ~1975-2000. The two periods are visually and statistically indistinguishable. The AR4 SPM fig 4 asserted that the latter period was mostly anthropogenic forcings, while conceding the former period mostly could not have been. Natural variation did not magically stop in 1975 as illogically assumed. QED.
Models allow the calculation of pi to many decimal places.
In the manner of “Trust, but Verify” the tricky part is to verify that the pi calculation is correct, or even how correct. As the number of digits increases, there are analogs with the number of turtles holding up Earth in the synthetic description. Does each new turtle have less certainty, so that in the extreme it cannot be recognised as a turtle?
I once bought a book about mathematics of uncertainty. I stopped reading at page 3. The author reminded me of a graduate mathematician we employed, who would reach for a pencil and draw a triple integral sign when asked any question.
To anchor the mind by occasional study of reality, recall that a great deal of the guesses about temperatures re global warming and past climates depend on daily observations of Tmax and Tmin made in many countries using in early years thermometers in screens, with millions of these now digitised and regarded as useful because they are raw and unadjusted, displayed just as original observers wrote them down. They were so good that nobody thought a check of their authenticity was needed.
Well, until we did a forensic statistical and numeric study of our Australian data and found extensive evidence of human manipulation.
We used “hard” Science, which is a relief from the poor standard of “Climate” Science that has plagued us since it began. Very little of the pop idea of climate change passes hard Science scrutiny. Geoff S
Try:
https://www.geoffstuff.com/V14_fullBOM.pdf
Great work Geoff. Many of us have expected this kind of problem. Here is one point that defines what climate scientists call bias detection.
Thru some mechanism, a “break point” is seen, and all temperatures prior to that have been adjusted, mostly downward, to “correct” so-called bias.
Bias can only be detected through calibration which can seldom be done. Different devices can provide different readings even when calibrated just because they are different devices with different modeling in their design. If bias is suspected, the data should be declared unfit for purpose, not modified to make it agree with some SUPPOSED systematic error.
Let’s be very clear that you obviously misunderstand chaos theory <g> – or maybe you have a different understanding of what chaos is. Edward Lorenz gave a simple definition of chaos when he said “Chaos: When the present determines the future, but the approximate present does not approximately determine the future.”
In a chaotic system, the precise initial conditions (eg., now) may be known, but future conditions cannot be usefully calculated. Put it another way, your forecast may be right or wrong – which is not much use. Talking about “probability distributions” is merely a sciency way of saying “I don’t know what the future holds”.
In any case, even if the atmosphere is supposedly fully deterministic in a physical sense, the uncertainty principle at the foundation of quantum mechanics says that the position and momentum of a photon cannot be simultaneously determined. The more you establish the one, the more indeterminate the other becomes. This is fully supported by the most rigorous experiments in the history of mankind. Now, there is no quantifiable minimum change to initial conditions (eg., from “now”)in a chaotic system which may lead to completely unforeseen outcomes. A smaller change can always be found!
Some time after Lorenz delivered his presentation “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas.”,he stated that he was posing a real question, and one which has never been successfully answered
Such is the nature of chaos. Richard Feynman had a simple view, not involving chaos theory –
Sorry to be so wordy, but “chaos” seems to be widely misunderstood and misused.
However, you’re right about “climate modelling” being a complete and utter waste of time, money, and effort! More power to your elbow.
“Talking about “probability distributions” is merely a sciency way of saying “I don’t know what the future holds”.”
Sometimes the long shot wins. Chaos Theory? Probability doesn’t pin the tail on the donkey of reality unless it equals 1.
I once stumped a physicist with the explanation of the uncertainty principle:
“Well, if you’re measuring momentum, that is by definition a measurement over time. Which blurs the position. If you identify the position, you cannot calculate instantaneous momentum, since there’s no such thing.”
He said: “Damn, you’re right. Never thought about it that way.”
The butterfly effect is epistemic. The world only has one trajectory but we cannot tell which one it is because infinitesimal differences between possible trajectories quickly lead to big differences making the real world intrinsically unpredictable. This is math not physics.
A model is a set of equations and assumptions we hope describes the real world to some useful degree. If a model is chaotic under realistic conditions then that is evidence the world is too under those condition. Saying the nonlinear dynamics is in the model but not the world is like saying physics is in the equations but not the world. This makes no sense.
Chaos is a mathematically certain outcome of nonlinear dynamic systems.
Nonlinear = feedbacks.
Dynamic = not instantaneous feedbacks.
So climate must be in a technical sense mathematically dynamic with at least 1 strange attractor per Poincare dimension. But in a very high but unknown dimension N-1 Poincare space—therefore having an unknown but very high number of strange attractors—the question is whether that really matters?
Not all nonlinear dynamical systems are chaotic. Chaos for example is impossible in 2 dimensions so you need at least a three dimensional system for chaos. And then there are plenty of nonlinear systems that are not chaotic. The Lorenz system for example is only chaotic for particular parameter values. If you choose the parameter values then the result might be that all trajectories converge to a single fixed point or to a limit cycle.
And dynamic does not mean “not instantaneous feedbacks”. Again the Lorenz system has instantaneous feedbacks in that the derivatives only depend on the values at that instant in time. Dynamic just means changing in time.
Well, the logistic map can exhibit chaotic behaviour, and is two dimensional. Maybe you have seen graphics of the Mandelbrot set. The set of points where the logistic map bifurcates is the same as the boundary of the Mandelbrot set. Two dimensional.
No matter really, as most people don’t seem to have a clue about chaos in the “scientific” sense, and tend to think that chaos is just randomness, and a chaotic system will “revert to the mean”, “average out”, or similar self serving nonsense.
You can ignore chaos if you like, and it makes no difference. As Feynman pointed out, the final result of the uncertainty principle at the quantum means that the problem of turbulent flow in the physical world is insoluble, and future states cannot be usefully predicted any better than a smart 12 year old can do.
I’d welcome being proven wrong, but my assumption is that I won’t.
The logistic map and the Mandelbrot set do not count as being chaotic in the mathematical sense. Chaos occurs in dynamical systems of differential equations and you can only see it in 3 or more dimensions. The behaviour of maps is similar but since it is discrete you need a very different set of tools to analyse it. The Mandelbrot set is not a dynamical system at all since a point in the complex plane is either in it or not and there is no time evolution at all. And there is no relationship between the Mandelbrot set and the logistic map. The Mandelbrot set exists in the complex plane while the logistic map is one dimensional and depends on a single real parameter.
Finally most chaotic systems do “average out” since the presence of a strange attactor means that the time evolution is restricted to a tiny volume of phase space and all trajectories end up on the strange attractor (it is just that neighbouring points end up at completely different points on it). For the Lorenz systems the long term time average all all initial trajectoris is the same since the system oscillates about the two unstable fixed points in phase space.
Chaos for example is impossible in 2 dimensions so you need at least a three dimensional system for chaos.
Really? I thought the pendulum with another pendulum attached to the bob (2-dimensional) was chaotic and non-deterministic.
The coupled pendulum problem is 4 dimensional if you talk to a mathematician. There are four degrees of freedom in the problem — the position and velocities of each bob. And so you need four coupled first order differential equations to describe the system.
And non-linear term(s).
Izaak Walton simply does not know what he is talking about, but is trying to appear intelligent.
I wouldn’t be at all surprised if he believes that Gavin Schmidt is a climate scientist, or that the faker, fraud, scofflaw and deadbeat, Michael Mann won a Nobel Prize!
I quote from the article: “The divergence, in their words, “is caused by numerical noise, which is an artifact of the computation rather than a real atmospheric process“.”. There is therefore a clear distinction between model and real world, so if a model is chaotic then it does not necessarily follow that the world is too. Note that the model may even be using equations that are trusted in the real world, as in the examples cited. ie, the physics is in the equations and in the world, and the equations are in the model, but the physics is not in the model because the model interprets the equations incorrectly.
In nonlinear dynamics the divergence is not caused by noise. But then I have no idea what “noise” means here. A perfectly accurate equation will diverge given infinitesimal differences in initial conditions. In the real world we cannot know which of those possible conditions we have. I see no noise in this unless noise means the lack of knowledge.
Wouldn’t it be partially “computational” noise? Where the computation itself has physical limitations, e.g. the limit on the computer floating point representation. Thus the result can be dependent on the order of the computations done. The result might even be dependent on how quickly stored files can be accessed using parallel access, on one run the order in which the parallel access is used, the order of computation might depend on lag time in the storage devices where the data is stored.
note to self: Much of the literature seems to focus on round-off and truncation of computational results.. I can’t really find where actual computer operation issues that can affect issues of parallel computing are discussed anywhere.
Mike,
You have put your finger on the real problem. A model cannot be used as evidence that the real atmosphere is chaotic if the rapid divergence is an emergent property of the formulae, the numerics, or the tuning. That is circular. The same circle sits one level up in the GCMs. They treat top-of-atmosphere radiative imbalance as the independent driver, treat surface temperature as the diagnostic, and then constrain the parameters so that the diagnostic matches the history they later claim to have explained. Turtles all the way down.
There is a way out that does not require a more accurate computer running the same top-down problem. It requires a change of independent variable.
The Dew-Point Anchor Hypothesis (DPAH) starts from a quantity fixed by a physical law and visible in the sky: the lifting condensation level of the dominant condensing volatile. On Earth that volatile is water. At the LCL the actual vapour pressure equals the saturation vapour pressure at the dew-point temperature:
e = e_s(T_d)
That equality is Clausius–Clapeyron. It is not a fitted coefficient. Cloud base is its observable expression. Once that phase-equilibrium surface is taken as the anchor, the tropospheric column can be integrated downward under hydrostatic balance and the appropriate adiabat. Surface temperature and surface pressure then become dependent variables. They are no longer free knobs that must be tuned until the model reproduces the thermometer record.
That is inverse modelling rather than forward radiative bookkeeping. The energy source still matters for the total flux and its latitude pattern, but it does not get to choose the thermodynamic skeleton of the column. A short thought experiment makes the point. A “Dark Earth” with the same total heat flux and the same latitudinal distribution, supplied from below by geothermal heat rather than from above by sunlight, would still have essentially the same LCL, the same lapse-rate structure, and the same surface climate. The direction of the energy supply is secondary. The phase-equilibrium anchor is not.
The same logic travels. On Venus the anchor is the sulfuric-acid cloud deck; integrating downward from that observable level produces a surface temperature near the Venera values without first prescribing surface T.
On Earth, Markovian state-space runs with an explicit dew-point dimension settle on a stable tropical ascent attractor near 299 K, with a realistic subtropical descent branch a few kelvin warmer and drier. Andy May and I tested the tropical column against IGRA2 radiosondes: temperature and dew-point depression follow the anchored moist structure to about 250 hPa with very high fidelity. Above that level the problem changes character — supercooled water, homogeneous freezing near –40 °C, cirrus, virga — which is why the frost point is a complementary upper anchor, not another tunable cloud parameter.
This is the opposite of “chaos all the way down.” Phase change is a hard constraint. It organises the column. What looks like irreducible sensitivity in a GCM is often the model being asked to invent a structure the atmosphere already possesses, because the model was given the wrong independent variable.
That is also why your closing plea matters. In other fields, unknowns are treated as physics not yet understood, not as deterministic chaos. Water’s phase changes are understood physics. They should be the boundary condition, not a residual after the radiative calculation has been forced to fit.
If the circularity you describe is real — and I think it is — the remedy is not another ensemble of GCMs. It is to stop asking the model to generate the boundary condition that the atmosphere already displays every afternoon as cloud base.
The foundational note is The Independent Variable in Geoscience Modelling: Why the Dew-Point Anchor Hypothesis Matters (Zenodo, April 2026):
Philip Mulholland
Mulholland Geoscience,
Edinburgh
This pretty much defines my idea that one must understand what occurs in the oceans/land surface as far as heat and radiation is concerned. It matters not what heats them; they are the surfaces that interface with the atmosphere and not insolation.
Any engineer who has studied PID (proportional, integral, derivative) control systems understands damping effects. Initial conditions are then irrelevant as the control system then forces the process to the set point. Too bad greentard climate scientists apparently don’t understand this. The control system then reacts to external stimuli or a changing set point to equilibrate the system. God created a wonderful climate control system which is beyond the mind of Man to understand. https://en.wikipedia.org/wiki/PID_controller
Effects of various numerical aspects on calculations of chaotic response:
Shijun Liao’s clean numerical simulation (CNS), here are selected papers, including work with coauthors:
Liao, S. (2009). On the reliability of computed chaotic solutions of non-linear differential equations. Tellus A: Dynamic Meteorology and Oceanography, 61(4), 550–564. DOI: 10.1111/j.1600-0870.2009.00402.x.
Liao, S. (2013). On the numerical simulation of propagation of micro-level inherent uncertainty for chaotic dynamic systems. Chaos, Solitons & Fractals, 47, 1–12. Author’s publication listing.
Liao, S., & Wang, P. (2014). On the mathematically reliable long-term simulation of chaotic solutions of Lorenz equation in the interval [0, 10000]. Science China Physics, Mechanics & Astronomy, 57(2), 330–335. DOI: 10.1007/s11433-013-5375-z.
Liao, S. (2017). On the clean numerical simulation (CNS) of chaotic dynamic systems. Journal of Hydrodynamics, 29(5), 729–747. DOI: 10.1016/S1001-6058(16)60785-0.
Li, X., & Liao, S. (2018). Clean numerical simulation: A new strategy to obtain reliable solutions of chaotic dynamic systems. Applied Mathematics and Mechanics (English Edition), 39(11), 1529–1546. DOI: 10.1007/s10483-018-2383-6.
Hu, T., & Liao, S. (2020). On the risks of using double precision in numerical simulations of spatio-temporal chaos. Journal of Computational Physics, 418, 109629. Author’s publication listing.
Qin, S., & Liao, S. (2022). Large-scale influence of numerical noises as artificial stochastic disturbances on a sustained turbulence. Journal of Fluid Mechanics, 948, A7. Author’s manuscript.
Qin, S., & Liao, S. (2023). A self-adaptive algorithm of the clean numerical simulation (CNS) for chaos. Advances in Applied Mathematics and Mechanics, 15, 1191–1215. DOI: 10.4208/aamm.OA-2022-0340.
For a general citation explaining the CNS method, the 2017 and 2018 papers are the most directly focused on it.
I was taught to approach chaos theory/butterfly effect as a philosophical mind expanding exercise, much like the solar system is an atom in the philosophical mind expanding exercise in infinity.
If chaos theory was real in the context of earth’s energy systems, we would not be here discussing the topic.
“…may ultimately be resolvable by better observations and better understanding, exactly as happens in other complex…”
There are many “better observations” available but are they ever included in someones model? For example, 1) Happer and Wijngaarden have shown very clearly that increasing CO2 concentrations in the atmosphere has a diminishing effect as the concentration increases and a further increase to double the current values cannot increase surface temperature by more than a degree or so. 2) Satellite cloud cover percentages as reported by NOAA have shown that overall in recent decades, cloud cover has declined by several percent which admits to the surface more sunlight which should increase temperature. 3) Geologic evidence points clearly to many times in the earth’s ancient history when CO2 levels have been in the thousands of ppm but the oceans didn’t boil as the UN seems to believe and temperatures remained at moderate levels promoting robust growth of plants and animals and in some eras, the formation of vast deposits of coal, oil, and natural gas. I expect there are many other similar observations. Do models incorporate this kind of information in some way?
No. They don’t. Climate science today is so full of garbage memes and assumptions that it has no resemblance to reality.
Your point that reality frequently does not match models is well taken, Jonas.
The choice of modeling language may be a hindrance.
Perhaps you could use something more natural-language so that you can more easily validate the model, though I’ve heard rumblings about TrueScript.