Question on whether climate is chaotic or not

[Coldcall]

Hi Guys,

Okay I have a question i was wondering if anyone can enlighten me on this discrepancy.

I asked Gavin Schmidt on RC whether he thought the climate was a chaotic system. He said he did not know (seriously).

What i fail to understand is how can anyone be confident about the results of a computer model for which the underlying nature of the fundamental science is unknown?

Their argument is more or less that because climate changes over longer periods they don't need to treat it like a chaotic system (with all the inherent unpredictability that comes with a chaotic system).

But then on the other hand, they claim that a moderate increase in Co2 will cause this "tipping point" to occur causing run-away global warming.

Put that all together and we see a monstrous logical contradiction because they claim in equal measure that a) system is not chaotic and sensitive to initial conditions b) Co2 (which is an initial condition in the model) will push climate into new run-away warming configuration within decades.

Thats makes no sense at all. They are denying the chaotic nature of climate while using charcteristics of chaotic systems to scare the hellp out of us re the Co2 (initial condition).

I'm all ears for anyone who can explain this unambiguous contradiction.

 

[Coldcall]

I studied the 'runaway' tipping point issue based on paleo climate but if I explain it, my threads get locked -even if I use peer reviewed studies- because it is against that so called CRU type 'mainstream' and hence it is so called deniers 'crackpot'. So the rules have to change first.

That's crazy. As far as i can tell no-one in the agw community will explain the obvious contradiction.

In fact I've looked up the RC archives and various chaos experts have questioned Gavin on this issue and his answers are at best misleading.

So this issue is not about this or that graph but actually goes to the heart of the foundational science involved.

 

[Andre]

well for starters, if you look at the long term ice core "temperatures", like fore instance here in EPICA dome C and NGRIP there is a distinct autocorrelation.

http://www.ncdc.noaa.gov/paleo/pubs/jouzel2007/fig2.jpg

So if the temperature interpretation is correct then the climate is bi-stable, as an oversteered positive feedback system (flip flop) hence in that case climate is not chaotic.

However this is under the assumption that ice core 'water' isotope ratios (dD and d18O) is equivalent to temperature and when zooming in on macro level on multiple other proxies, the excrements start impacting the rotating wind generator. Hence that should not be challenged.

 

[Coldcall]

well for starters, if you look at the long term ice core "temperatures", like fore instance here in EPICA dome C and NGRIP there is a distinct autocorrelation.

http://www.ncdc.noaa.gov/paleo/pubs/jouzel2007/fig2.jpg

So if the temperature interpretation is correct then the climate is bi-stable, as an oversteered positive feedback system (flip flop) hence in that case climate is not chaotic.

However this is under the assumption that ice core 'water' isotope ratios (dD and d18O) is equivalent to temperature and when zooming in on macro level on multiple other proxies, the excrements start impacting the rotating wind generator. Hence that should not be challenged.

Hi Andre,

Okay but i don't get how that answers my question re climate and chaos, and the fact that there appears a need for agw to argue that climate is not chaotic (hence predictable), but then they claim that a little more Co2 (initial condition) will cause tipping point leading to run-away gw.

 

[Andre]

Because CO2 corrolate with that temperature graph, inducing the second* fallacy (correlation is causation). However it is also perceived that the CO2 lags the isotopes a few hundred years, this could be explained if the CO2 acts as a strong positive feedback, pushing the temperature to either of the system limits.

http://www.awi.de/typo3temp/pics/91b26f7eef.jpg

However there is a lot more to feedback and this interpretation could be challenged, if it was legal to do so here.

Note that the sealevel graph is derived directly from the isotope ratios and hence is not an independent corrolating factor.



* the first was in the previous post, affirming the consequent, if the temperature is high the isotopes are heavy, the isotopes are heavy, hence it was warm)

 

[D H]

Okay but i don't get how that answers my question re climate and chaos, and the fact that there appears a need for agw to argue that climate is not chaotic (hence predictable), ...

Whoa! You appear to have a (somewhat common) misperception of what chaotic means. Chaotic systems are not inherently unpredictable. The solar system is chaotic. That does not mean we cannot predict the locations of the planets over the course of a year or even millennia. The weather is chaotic. Weather forecasts are pretty accurate over the span of a week or so.

 

[Hepth]

No, he is just a scientist. You asked for a definite response to a system that obviously isn't 100% known, and its a pointless question anyway. Of course we don't know if it is chaotic or not. What do you mean by chaotic? If we have a period of relative predictability in an otherwise chaotic system, is it still "chaotic" in your sense? In our scientific sense it is, but if we can model the current state, and predictions tend to be nearly right (not necessarily in this case, but in general), and the predictability holds for say a hundred years or so before some unknowns change it drastically, then what should his response have been?
That's a very loaded question. Its like asking a scientist "Are you 100% sure you're right? no? Then how can you assert that its right at all!?"

 

[Coldcall]

Andre,

I think i get what you are getting at above, and i agree it needs way more invetsigation before anything can be called settled.

My point is focused on the physics on which the climate models are based. My issue is that gavin schmidt at RC says he doesn't know if climate is chaotic :-) I am 99% sure it is chaotic
because it has all the hallmarks of a bonafide chaotic system.

What i find odd is WHY Gavin and other agw scientists seem so keen on suggesting the climate is not chaotic. They don't say its not, but as they won't answer the question, that is the impression they want to make.

The other issue is that i find it laughable that they claim not to be able to define the sort of physics operating in a climate system. If they can't define the physics underlying their model then what good is their model?

 

[Coldcall]

Whoa! You appear to have a (somewhat common) misperception of what chaotic means. Chaotic systems are not inherently unpredictable. The solar system is chaotic. That does not mean we cannot predict the locations of the planets over the course of a year or even millennia. The weather is chaotic. Weather forecasts are pretty accurate over the span of a week or so.

pretty accurate is not the sort of accurate we need for the type of certain predictions being spouted from agw computer models.

I think you don't understand the nuance between a system one can predict with certainty and one which one cannot predict with certainty.

Chaotic systems are not predictable with any level of certainty at which one can rule out surprise behaviour.

You've also missed the central point in your rather sloppy attempt to disrupt the main focus of my question. The point being that gavin won't commit to an answer on this question at all, so until he commits himself to stating the basis of the underlying science of agw models, then there can be no confidence in the predictions of those models.

I suggest you read up on the n-body problem because it is unsolvable (from any practical perspective) and it is far simpler non-linear system than the climate.

But let me ask you : is climate a chaotic system?

 

[Coldcall]

Hepth,

"No, he is just a scientist. You asked for a definite response to a system that obviously isn't 100% known, and its a pointless question anyway"

Its not 100% known? Then if they don't fully understand the underlying physics of a climate system then they can say nothing for certain about the predictions of those models based on this unknown system.

Its like if i were to make up a bunch of bs and say: "our solar system does not obey the laws of relativity as does the rest of the universe, so the same rules which normally apply should not be applied to my solar system model". Now most people would rightly laugh at that.

Thats exactly the same as is being said by Gavin about climate. he is trying to imply it works on some law of physics of whcih we have no history or description, hence it cannot be criticised on fundamental scientific grounds.

"That's a very loaded question. Its like asking a scientist "Are you 100% sure you're right? no? Then how can you assert that its right at all!?"

Its a simple question asking a scientists to explain the underlying physics of his model. There is nothing loaded about it other than the bs answer claiming he does not know.

You can't have it both ways. Either he admits that climate is a chaotic system and then he has real problems because the certainty they claim to predict goes out the window, or they formulate a whole new science for the climate.

 

[vanesch]

Hi Guys,

Okay I have a question i was wondering if anyone can enlighten me on this discrepancy.

I asked Gavin Schmidt on RC whether he thought the climate was a chaotic system. He said he did not know (seriously).

What i fail to understand is how can anyone be confident about the results of a computer model for which the underlying nature of the fundamental science is unknown?

Their argument is more or less that because climate changes over longer periods they don't need to treat it like a chaotic system (with all the inherent unpredictability that comes with a chaotic system).

But then on the other hand, they claim that a moderate increase in Co2 will cause this "tipping point" to occur causing run-away global warming.

Put that all together and we see a monstrous logical contradiction because they claim in equal measure that a) system is not chaotic and sensitive to initial conditions b) Co2 (which is an initial condition in the model) will push climate into new run-away warming configuration within decades.

Thats makes no sense at all. They are denying the chaotic nature of climate while using charcteristics of chaotic systems to scare the hellp out of us re the Co2 (initial condition).

I'm all ears for anyone who can explain this unambiguous contradiction.

I'm no specialist, but I do see a lot of misconceptions here.

We know that the weather is chaotic, which means that close initial conditions can/will evolve in widely different systems on a certain, finite time scale. So that means that predictability is possible within that time scale, and hopeless beyond. That's why we have weather forecasts on the level of a few days, but we will never have day-by-day weather forecasts for 6 months in a row.

Now, climate is average weather over 30 years or so. In other words, climate is the statistical description of weather. Now, chaotic systems can have completely well-defined statistical descriptions. This statistical description can itself have a (slow) dynamics. This is what one is after in climate models: the slow dynamics of the statistical description of weather.

The question of whether this dynamics of the statistical system is chaotic itself is entirely different from weather the original system is chaotic. It could be that this dynamics is relatively "simple". It also depends what kind of dynamics one includes in "climate". Is El Nino part of the "climate dynamics" or is this still part of the "weather dynamics" ? Is there a long enough time scale beyond which the average weather is determined in a rather simple way ?

Also, it depends on what one considers to be "boundary conditions" and what are to be "internal variables". For instance, all "outer space" influences, like solar irradiation, cosmic rays,... are to be considered as boundary conditions. Not that we can predict them, and not that they may not alter randomly, but they are most definitely not part of the climate dynamics itself. They are external inputs. Probably one should say the same for geological events, such as volcanic eruptions or the like.
This doesn't mean that one knows how to predict them, but they are not part of the climate itself, they just "steer" it.

However, people building climate models should at least know whether their MODELS are chaotic or not - at least over time scales where one is interested in them (a few centuries/millennia). That shouldn't be too difficult to find out !

BTW, no sensible scientist would tell you that there will be a run-away climate. And in fact, a run-away climate would not be chaotic! We would know exactly where it would go.

Also, "chaotic" doesn't mean "it will sometimes do surprising things you didn't expect". Chaotic means that small changes in initial conditions will give you widely different outcomes after a certain time of evolution.

 

[Andre]

is climate a chaotic system?

Is that the main -important- question or is the main question if carbon dioxide is the main forcing function for global temperature?

 

[Coldcall]

Is that the main -important- question or is the main question if carbon dioxide is the main forcing function for global temperature?

Andre,

I agree with you that there are various weaknesses in the agw theory. I don't know enough about certain areas to comment, and i try to stick with a topic i am comfortable on.

You are right and determining once and for all the link between Co2 and temperature is part of coming to a conclusion.

But i rather hammer away at the fundamental nature of the physics underlying their models because i believe there is a major weakness in this question about defining climate as chaotic or not.

My point is not that they are necessarily completely wrong, as agw could be right to some degree. My point is about the level of certainty they project concerning their models and that we are facing catastrophe.

In fact agw could be partly correct and still not mean any catastrophes, so there are all sorts of shades involved from a scale of right---------wrong.

 

[turbo]

You can't have it both ways. Either he admits that climate is a chaotic system and then he has real problems because the certainty they claim to predict goes out the window, or they formulate a whole new science for the climate.

That's a perfect "gotcha" question because demanding a yes or no answer assumes a dichotomy in a complex situation. It is quite possible that climate is chaotic on small scales, yet more predictable on larger scales or over time, or when observations are averaged, etc, etc. That's what the models are for.

 

[Andre]

Nevertheless, predictions go nowhere when when it is based on flawed interpretations of proxies of the climate of the past.

 

[Andre]

Andre,

I agree with you that there are various weaknesses in the agw theory. I don't know enough about certain areas to comment, and i try to stick with a topic i am comfortable on.

Exactly, and that's also the big problem. Everybody does. The general picture is lacking if you can only think for your own expertise and have to rely on others like CRU personel for the rest.

 

[Hepth]

What I'm trying to say is asking "Do you think XX is chaotic?" Is a VERY poorly worded question. You can be very strong in your understanding of climate modeling, but nothign can ever be perfect, and no one ever claims it is.

Its like if i were to make up a bunch of bs and say: "our solar system does not obey the laws of relativity as does the rest of the universe, so the same rules which normally apply should not be applied to my solar system model". Now most people would rightly laugh at that.

No, its like saying "our solar system's planetary data does not seem to be obeying the laws of Newton, but more closely fits this other model we have. We may be right, wrong, or a little of each. The system may actually be chaotic. There could be a billion things wrong. We understand the majority of the physics behind it, and adding this new method makes it that much more accurate. So if this new method can replicate previous data, then it MAY be able to predict new data."

Its not 100% known? Then if they don't fully understand the underlying physics of a climate system then they can say nothing for certain about the predictions of those models based on this unknown system.

THAT is such a poor idea of what science truly is. NO ONE is saying ANYTHING about PREDICTIONS for "certain". They are "certain" only about previous data. There are no certainties for the future. To demand that there are before accepting a working model is ludicrous. That is not what science is about, its about modeling. I hope you're not too stubborn to realize the difference. (btw, I am not pushing either political stance. I'm just a scientist and arguing about the question being poor.)

 

[Coldcall]

Vanesch,

"We know that the weather is chaotic, which means that close initial conditions can/will evolve in widely different systems on a certain, finite time scale. So that means that predictability is possible within that time scale, and hopeless beyond. That's why we have weather forecasts on the level of a few days, but we will never have day-by-day weather forecasts for 6 months in a row..."

Agreed.

"However, people building climate models should at least know whether their MODELS are chaotic or not - at least over time scales where one is interested in them (a few centuries/millennia). That shouldn't be too difficult to find out!"

Agreed and this is exactly what i am demanding from Gavin or toher agw scientists: a commitment to state categorically whether he believes his models are chaotic or not. He/they will not! You will see that in their literature they ALWAYS resist giving a straight answer to this question. But ironically they have no problem telling us run-away global warming is a certainty or near certainty. Now if they say otherwise in private, its bloody time for them to communicate that to the media who appear to be under the impression its all settled (which to most ordinary folks means CERTAIN).

So i hope you can agree with me, that there is something fishy going on when these guys are so intent to skip the whole question of whether the climate is a chaotic system or not.

And i agree with most of your post and understand the nuances of chaotic systems and their properties.

But the other contradiction and is relevant to your explanation above is that while agw theorists argue that because the changes take place over a long time period (as opposed to the weather) they can question the chaotic nature of the "system", BUT in the same breath they claim that a moderate amount of extra Co2 will have a tipping point effect, hence catastrophe. If the initial condition or call it variable Co2 can have such a dramatic effect on temperatures in a relatively small space of time, then that in itself contradicts the idea that we can't call it chaotic because the tipping points happen on larger time scales.

Do you see what i mean?

 

[Hepth]

Nevertheless, predictions go nowhere when when it is based on flawed interpretations of proxies of the climate of the past.

Or when your analysis and models can change faster than the time needed to test predictions. At least the advancements from it (modeling) will benefit us one way or another.

 

[Coldcall]

Exactly, and that's also the big problem. Everybody does. The general picture is lacking if you can only think for your own expertise and have to rely on others like CRU personel for the rest.

I'm certainly no expert on chaos theory and non-linear system, however i am facinated by them from a layman's perspective and have read just about every book on the subject.

So for me, i have always been sceptical of the level of certainty declared in these climate models as i know that they MUST inherently be based on chaotic physics as is just about every other natureally occurring system in the universe. I will happily eat humble pie if someone can prove to me that climate systems are not chaotic. I'll feel really stupid but i'll eat the pie :-)

However i do agree with you, and follow both WUWT and Climate Audit, who have i think been really unfairly labelled as cranks. But I'm not knoweldgable enough on the Co2 - temp link to comment other than i have noted the apparent problems with causality dynamic between the two in the historical record - as best we can make out.

 

[Coldcall]

That's a perfect "gotcha" question because demanding a yes or no answer assumes a dichotomy in a complex situation. It is quite possible that climate is chaotic on small scales, yet more predictable on larger scales or over time, or when observations are averaged, etc, etc. That's what the models are for.

How can a chaotic system be more accurately predictable over longer time spans when those intial condition errors grow exponentially? I'm not sure you understand how small inaccuracies turn into very large disturbances the longer the clock is running.Thats just chaos theory 101.

 

[D H]

Chaotic systems are not predictable with any level of certainty at which one can rule out surprise behaviour.

That is wrong.

I suggest you read up on the n-body problem because it is unsolvable (from any practical perspective)

That is also wrong.

But let me ask you : is climate a chaotic system?

This question is irrelevant if the timescale at which chaos ensues is far beyond the scope of the timescale of human concern.

 

[Xnn]

Coldcall;

I have a Math Professor buddy that specializes in Choas theory who might be able to help explain. However, my impression is that while weather is clearly choatic, the climate is not depending on how climate is defined.

In other words, over longer time periods, choatic properties diminish.

 

[turbo]

How can a chaotic system be more accurately predictable over longer time spans when those intial condition errors grow exponentially? I'm not sure you understand how small inaccuracies turn into very large disturbances the longer the clock is running.Thats just chaos theory 101.

And that statement shows a fundamental misunderstanding of natural systems, which have feedback mechanisms, damping factors, etc.

 

[seycyrus]

And that statement shows a fundamental misunderstanding of natural systems, which have feedback mechanisms, damping factors, etc.

But his statement concerns an understanding of chaotic systems. I think it is apparent that chaotic systems do necessarily contain feedback mechanisms, IIRC.

He is asking whether this natural system can be classified as a chaotic system. Does it meet the strict definition regarding sensitivity to initial conditions, density of strange attractors, and mixed topology?

I like the answer that seems to be "weather is chaotic, but climate is not". Certainly food for thought.

Regarding the one guys, ambiguous sounding answer (it *might* be). Perhaps he is merely voicing his uncertainty whether the weather can be *proven* to meet the strict definition.

 

[Sorry!]

I think that's enough about chaos system in regard to the climate. I kept noticing it come up in the Politics forums but the person was told to discuss it here so I thought I would have a looksie. D H best answered the post about chaos theory that keeps popping up in these threads. Coldcall your understanding of chaos theory is completely off-base my man.

You strike me as a layman who read in such and such a philosophical physics book then this and that out of context (or maybe, most likely actually, the book/article didn't explain it properly) and you think that's what it is. (Without any more research.) I remember running into the exact same problem you have when I took a philosophy course and we got into the subject of Philosophy of Science and we started learnin all these different theories... the best thing to do is ALWAYS check up EVERYTHING.

EDIT: Well then looks like you already admitted most of this anyways:

I'm certainly no expert on chaos theory and non-linear system, however i am facinated by them from a layman's perspective and have read just about every book on the subject.

Read some more.

 

[D H]

I like the answer that seems to be "weather is chaotic, but climate is not". Certainly food for thought.

On a very long time scale, I cannot see how climate can be anything but chaotic. The Earth's axial tilt, argument of perihelion, and orbital eccentricity are climate drivers. On a long time scale those orbital parameters are chaotic because the solar system is chaotic. The Sun was once thought to be highly stable. However, other stars of the same type, age, chemical makeup, and size as the Sun have been observed to have chaotic output; there is no reason to think our Sun is any different.

That is on a *long* time scale, of course. On a short time scale, there is no reason (yet) to think that climate is not predictable (so long as we / Mother Nature don't flip the climate to some other stable attractor any time soon.)

 

[seycyrus]

On a very long time scale, I cannot see how climate can be anything but chaotic. The Earth's axial tilt, argument of perihelion, and orbital eccentricity are climate drivers. On a long time scale those orbital parameters are chaotic because the solar system is chaotic. The Sun was once thought to be highly stable.

I concede this point. I had not considered such exo-planetary influences as being climate drivers. This is a rather broad scope. However, see below.

However, other stars of the same type, age, chemical makeup, and size as the Sun have been observed to have chaotic output; there is no reason to think our Sun is any different.

Is it correct that multiple interacting chaotic systems MUST combine/interact to form another chaotic system?

...climate is not predictable (so long as we / Mother Nature don't flip the climate to some other stable attractor any time soon.)

The size of the delta required to flip to another attractor and the required time scale involved is really what is being discussed. I think the OP was trying to address this.

Are you not *sorta* in agreement with the OP? I believe the OP is expressing confusion over some scientists inability to classify the climate as a chaotic system.

 

[D H]

IAre you not *sorta* in agreement with the OP? I believe the OP is expressing confusion over some scientists inability to classify the climate as a chaotic system.

No. I was talking about the mainstream AGW claims, e.g. post #23, the predicted warming cited in the IPCC, etc. Those claims do not assume climate is chaotic. They do assume that climate is predictable in the short-term (10-100 years is short-term in climate science). I believe the OP was coming in with a misperception of chaos theory and with a hidden agenda based on this misperception, to wit:

"If the climate is chaotic, then why are you climate scientists pretending you can model climate?" For example, this post (emphasis mine):

Okay but i don't get how that answers my question re climate and chaos, and the fact that there appears a need for agw to argue that climate is not chaotic (hence predictable), ...

The OP continues with

but then they claim that a little more Co2 (initial condition) will cause tipping point leading to run-away gw.

The claims of a "tipping point" are pure alarmism, in my opinion, and those alarmists have about the same amount of scientific credibility as those who say global warming doesn't exist (period). That "tipping point" stuff does form a nice basis for science fiction movies --- and for scaring the masses.

 

[Astronuc]

Of course climate is chaotic given that the inputs are chaotic.

Look at solar cycles - which are mostly, but not precisely periodice (~ 11 years).

Look at volcanic eruptions - which are relatively random events - some of which have a dramatic impact on climate.

But one can have bounded chaos, which means one cannot predict the trajetory precisely, because one cannot predict the future, besides the fact that there is still much we do not know.

 

[sylas]

Of course climate is chaotic given that the inputs are chaotic.

I tend to use the word "chaotic" to mean arbitrarily small changes in input can lead to large changes in output.

The notion of "tipping" point is related but not quite the same. It refers to cases where a system can slip from one comparatively stable condition to another as you pass a certain threshhold. A system with hysteresis, for example, has tipping points.

The clearest example of tipping points so far in this thread would be the ice ages. The evidence is not completely conclusive, but it is widely considered that ice ages over the Quaternary period, which we can see in the graphs of the thread, are caused by small changes in Earth's orbit; and moving in or out of an ice age occurs as a tipping point is passed, leading to a cascade of changes in the whole climate system that together raise, or lower, temperatures more than one would expect from the orbital changes alone.

The Quaternary contrasts with more stable conditions earlier in the Cenozoic, and one major hypothesis for this relates to the particular arrangements of land masses, which contribute to the conditions that allow for the tipping point. Specifically identified features have been the almost enclosed northern Arctic ocean and the existence of a contrasting case in the South, with a free passage for ocean circulations around the Southern Antarctic oceans.

Look at solar cycles - which are mostly, but not precisely periodice (~ 11 years).

Look at volcanic eruptions - which are relatively random events - some of which have a dramatic impact on climate.

But one can have bounded chaos, which means one cannot predict the trajetory precisely, because one cannot predict the future, besides the fact that there is still much we do not know.

Yes indeed. The 11 year solar cycles are poorly understood, but they are periodic, not chaotic. They also have a comparatively small impact. There may be stronger impacts from longer term and much more mysterious cycles, in which the 11 year cycle may be totally suppressed. This is often proposed as a factor in the "little ice age". Interestingly, the 11 year cycle seems to be particularly slow getting started for the next solar maximum at present.

Volcanic eruptions do have a dramatic impact; though it tends to be in the form of random "spikes" that then die away in the years following an eruption; or the decades following an eruption if it is a big one. The very fact that there is a recovery after an eruption indicates that the climate system itself is not chaotic, even though the input may be unpredictable.

The frequency of eruptions world wide can vary; a period of time with comparatively few major eruptions is sometimes proposed as a contributing factor for the rise in temperatures in the early part of the twentieth century.

The comment about "bounded chaos" is particularly important. Weather is certainly chaotic. Climate, however, is usually defined as the range (or bound) within weather is found. The bound itself is not obviously chaotic at all. It may have tipping points -- as we see suggested in the ice ages -- but the response seems to be much too regular to be truly chaotic, in the normal sense of the word.

In my view, the evidence shows that climate is complex, and hard to predict; that it does have tipping points although it is very hard to identify them precisely; but it is not actually chaotic, as the word is usually defined.

Cheers -- sylas

 

[Astronuc]

I tend to use the word "chaotic" to mean arbitrarily small changes in input can lead to large changes in output.

Chaos refers to predictability, where 'stability' refers to the impact of change on output.

The notion of "tipping" point is related but not quite the same. It refers to cases where a system can slip from one comparatively stable condition to another as you pass a certain threshhold. A system with hysteresis, for example, has tipping points.

Tipping point is different, and the real issue is one of desirable or compatible outcome with respect to the process.

Nature (a physical process) is self-regulating. The real issue with respect to 'climate change' is whether or not any change is compatible with human existence.

If climate change (warming or cooling) is occurring, then one has to consider at what point does it become incompatible with our currently way of living. This matter is a different topic.

However, the question (OP) is about whether climate is chaotic or not, and I believe we have demonstrated that it is.

The 11 year solar cycles are poorly understood, but they are periodic, not chaotic. They also have a comparatively small impact. There may be stronger impacts from longer term and much more mysterious cycles, in which the 11 year cycle may be totally suppressed. This is often proposed as a factor in the "little ice age". Interestingly, the 11 year cycle seems to be particularly slow getting started for the next solar maximum at present.

The Maunder minimum would represent an aperiodic (chaotic) event. And yes - the Sun is unusually quiescent at the moment - yet another aperiodic (and unpredictable) event. Who would have predicted that 11 years ago, let alone last year, or 6 months ago. Of course, it could return to it's more usual trend in the next few days, weeks, months or years. But we just won't know until it happens.

Volcanic eruptions do have a dramatic impact; though it tends to be in the form of random "spikes" that then die away in the years following an eruption; or the decades following an eruption if it is a big one. The very fact that there is a recovery after an eruption indicates that the climate system itself is not chaotic, even though the input may be unpredictable.

Recovery on a different climate trajectory.

Another term for chaotic is 'noisy', and the 'noisiness' can be insignificant (even if not predicatible, but it's nevermind) or it can be significant.

 

[Astronuc]

Time out pending moderation. So save your thoughts.

Thread is re-opened. Please keep posts on-topic, which is about "whether climate is chaotic or not".

Claims and assertions must be supported by evidence from textbooks, scientific journals, and other peer-reviewed sources.

 

[seycyrus]

Of course climate is chaotic given that the inputs are chaotic.

I do not know if this is correct. Do chaotic inputs into a system *always* lead to chaos? Is this proven in chaos theory? This is the question I was trying to get at when I questioned D P.

I wonder about the human body as an example. I believe that certain subsystems are chaotic, but the whole is not...?

Is the current notion that the entire universe is chaotic, but simply riding along in an attractor?

Edit: I am reminded about a certain chapter intro in Hitchhikers guide to the Galaxy.

 

[Borek]

Vanesh already sumarized perfectly what I have on my mind when I hear words "weather", "climate", "chaos". My $0.02 is: single nuclear fission event is unpredictable, mass of the sample large enough after time t can be predicted with a very high precision. So I can imagine situation in which weather is chaotic as it is, but climate is quite predictable if you know how to describe it properly. Whether that's the case I have not the slightest idea.

 

[Andre]

Please keep posts on-topic, which is about "whether climate is chaotic or not".

However, the OP states:

...Their argument is more or less that because climate changes over longer periods they don't need to treat it like a chaotic system (with all the inherent unpredictability that comes with a chaotic system).

But then on the other hand, they claim that a moderate increase in Co2 will cause this "tipping point" to occur causing run-away global warming...

It appears that the intention was to discuss contradictions between chaotic behavior and triggering runaway conditions.

 

[vanesch]

Ok, let us get some definitions right.

Chaotic system: I think the wiki entry on it is pretty good.
http://en.wikipedia.org/wiki/Chaos_theory

A chaotic system is first of all a deterministic dynamical system that has initial conditions of its state one can specify and starts out from there.

The main property is indeed "sensitivity to initial conditions", but there's also another important condition, which is "topological mixing" (the image through dynamics of any open subset comes arbitrarily close to any point of the considered phase space). Sensitivity to initial conditions alone is not really sufficient, although if the phase space is bounded, sensitivity to initial conditions everywhere (usually or always?) also leads to mixing.

Divergent systems are sensitive on initial conditions, but not necessarily chaotic. A run-away system for instance, is not chaotic, because it lacks this mixing property.

So my personal "feel" for a chaotic system is that it "diverges but comes back pretty close but not exactly". I don't know how close that gut-feeling definition is in agreement with what is the right definition of a chaotic system.

Note that these properties are properties of the dynamics of the system, and have nothing to do with any properties of any input signal. So strictly speaking, a system is not chaotic because it receives external "chaotic" signals (you cannot really have "chaotic" signals, you can only have chaotic dynamics and eventually output signals of a chaotic system, but it is hard/impossible to find that out).

But it is worse: a dynamical system can also only be chaotic in certain subspaces of its phase space, and non-chaotic in others.

Related to this discussion are the questions of whether current climate models are chaotic in the range of validity and interest where they are used.

That really shouldn't be difficult to find out, by running those models with different initial conditions. Point is, most of these models are stochastic, so strictly speaking the definition of chaos doesn't even apply.

It is even pretty evident that running climate models cannot be chaotic exactly where they are used, because otherwise they would generate widely different results from run to run and it would not be possible to draw any conclusions from that.

In how much that this has anything to do with the real climate dynamics is very hard to tell. Historical data will probably (my opinion) not be of much use, as we probably don't know the external inputs.

 

[vanesch]

It appears that the intention was to discuss contradictions between chaotic behavior and triggering runaway conditions.

First of all, I don't think any serious climate scientists considers a run-away climate. But even a run-away climate would not be a chaotic dynamics.

A bifurcation in a dynamics is also not chaotic, but it is true that there is a small region of phase space that is then extremely sensitive to initial conditions, namely all the open sets around the trajectory that hits the bifurcation, because they are split in (at least) 2 pieces.

So a "tipping point" (= bifurcation ?) by itself would not indicate any chaos in climate dynamics by itself.

It is very well possible that long-term dynamics of the climate turns out to be chaotic, but that will be on a time scale much longer than what is of interest in the AGW debate.

Note for instance that the solar system is believed to be chaotic (see http://www.sciencemag.org/cgi/content/abstract/257/5066/56 ) but nevertheless allows for extreme precise predictions of orbits over millions of years.

 

[Astronuc]

Tipping point is about stability, and there seems to be some confusion between chaos and stability.

Chaos refers to uncertainty and noisiness in the system behavior.

I wasn't referring to the choatic or random inputs, but the response to those inputs.


Earth's climate is also not a closed system, and not only are the boundary conditions variable (noisy) and non-linear, the system itself is non-linear - but it's bounded somewhat - or at least part of the system is bounded.


Another matter is the definition of choas theory or chaotic system. Traditionally or conventially, "Chaos theory is an area of inquiry in mathematics, physics, and philosophy which studies the behavior of certain dynamical systems that are highly sensitive to initial conditions." What initial condition do we apply to today's climate?

Chaos also looks at system response/behavior to perturbations and noise (periodic and aperiodic), which also include perturbations to boundary conditions or transients, e.g. volcanic eruptions or meteoric impacts, or somewhat noisy inputs like solar-cycles. Add to this long term tectonic drift. The equilibrium shifts. The challenge is to determine why and attempt to predict weather and climate in the long term.

One can look at turbulence in a fluid. Locally the velocity changes constantly, but it is bounded by constraints, e.g. structure or limits on momentum and energy.

 

[Andre]

First of all, I don't think any serious climate scientists considers a run-away climate.

It seems that one of my posts got deleted that introduced somebody like that. Was that illegal?

 

[Monique]

To re-iterate Astronuc's words: let's keep it on the topic of whether the climate is chaotic or not and how that relates to the models Earth scientists use.
The OP explained himself: https://www.physicsforums.com/showpost.php?p=2468484&postcount=13

Off-topic posts were deleted to get the thread back on track.

 

[Astronuc]

One has to look into chaos as applied to multi-input, multi-output (MIMO) systems.

Perhaps the bifurcation is a more rigorously appropriate term.

Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family. Examples of such families are the integral curves of a family of vector fields or, the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour.

http://en.wikipedia.org/wiki/Bifurcation_theory

 

[Xnn]

OK; let's focus on the topic.

Wikipedia is not an acceptable source for this site.

So, where is the textbooks, scientific journals, and other peer-reviewed sources
that define a chaotic system?

So far, most post are just about opinion (some more reasoned than others).

 

[vanesch]

Wikipedia is not an acceptable source for this site.

So, where is the textbooks, scientific journals, and other peer-reviewed sources
that define a chaotic system?

We are talking here about elementary definitions of concepts in dynamics that have a clear meaning, so in as far as the Wiki article is serious, it is good enough a source for the clarification of such things, I would say. There is nothing controversial in these "claims" of elementary definitions, like chaotic system or what is a bifurcation. We're in the "let's get the definitions of the words right" stadium.

It corresponds pretty well to what I remember from reading the book "deterministic chaos" http://books.google.fr/books?id=WaEGkJ3XAtEC&lpg=PP1&ots=4tbrm7zFEv&dq=deterministic%20chaos&pg=PP1#v=onepage&q=&f=false which I have somewhere on my shelf but not at hand right now.

 

[Astronuc]

Don't know if this helps.

If the parameter V-m is increased even further, the behavior changes to an apparently random, erratic, and aperiodic waveform. This situation is illustrated in Figure 1.4. Such a bounded aperiodic behavior is known as chaos.

from Nonlinear Phenomena in Power Electronics: Bifurcations, Chaos, Control, and Applications
Soumitro Banerjee (Editor), George C. Verghese (Editor)
http://media.wiley.com/product_data/excerpt/38/07803538/0780353838.pdf

I was thinking IEEE would have a formal definition somewhere, for example

In this article, a nonlinear dynamical phenomena leading to bifurcation and chaos in power systems is explored using a sample power system. After giving an introduction to nonlinear dynamical power systems in section II a basic knowledge to nonlinear dynamics and chaos theory is given. Section III deals with bifurcation theory. In section IV a dynamical power system model has examined. In section V the theories are applied to a sample power system example and various bifurcation and chaotic phenomena are examined.

An application of chaos and bifurcation in nonlinear dynamical power systems
Kuru, L. Kuru, E. Yalcin, M.A.
http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=1344840
Intelligent Systems, 2004. Proceedings. 2004 2nd International IEEE Conference
Publication Date: 22-24 June 2004
Volume: 3, On page(s): 11- 15 Vol.3
ISSN:
ISBN: 0-7803-8278-1
INSPEC Accession Number: 8109177
Current Version Published: 2004-10-25


Another issue, and an important one, is - when does weather become climate?

Parts of North Africa (Algeria, Tunisia, Libya(?)) were once the bread basket of the Roman Empire. Now it's mostly desert.

More recently, the Horn of Africa (W. Somalia and E. Kenya) are suffering a third year of drought, but just to the north (N. Kenya and Uganda), they've had devastating floods.

Australia now has persistent drought in the south, and that's a lot different from when I lived there 43+ years ago.

 

[seycyrus]

A chaotic system is first of all a deterministic...

*deterministic* is also problematic in that is can be misconstrued, to imply arbitrary predictability. Certainly the system itself knows it's own dynamic evolution, but that doesn't help out any onlookers.

...Sensitivity to initial conditions alone is not really sufficient, although if the phase space is bounded, sensitivity to initial conditions everywhere (usually or always?) also leads to mixing.

In class,it was taught that neither *usually or always* can be assumed.

...So my personal "feel" for a chaotic system is that it "diverges but comes back pretty close but not exactly".

Eventually.

...So strictly speaking, a system is not chaotic because it receives external "chaotic" signals (you cannot really have "chaotic" signals, you can only have chaotic dynamics and eventually output signals of a chaotic system,

I was wondering about using those outputs of a chaotic system as inputs for another systems. I.E. the sun's output (postulated as chaotic) into the Earth's climate (questioning the chaosticity (woot woot!) of this system)

Thinking about it, I believe that such chaotic inputs cannot drive another system "chaotic". it is either chaotic or not from the get-go. Of course this just begs the question about whether it is correct to consider any systems as independent from another.

But it is worse: a dynamical system can also only be chaotic in certain subspaces of its phase space, and non-chaotic in others.

Difficulty amplified again by the requirement that the attractors be dense.

 

[Astronuc]

Try to define the Climate (system) statepoints, inputs and outputs.

Also try to define the climate system and it's boundaries.

 

[seycyrus]

OK; let's focus on the topic.

Wikipedia is not an acceptable source for this site.

So, where is the textbooks, scientific journals, and other peer-reviewed sources
that define a chaotic system?

So far, most post are just about opinion (some more reasoned than others).

Vanesch has got it right.

1) Sensitivity to initial conditions.

2) In the phase space around the attractors, it has to topologically mix.

3) The orbits are dense.

 

[Astronuc]

Interesting article - Chaos and stability of the solar system
http://www.pnas.org/content/98/22/12342.full

In its scientific usage, chaos is not a synonym for disorder, rather it describes the irregular behavior that can occur in deterministic dynamical systems, i.e., systems described by ordinary differential equations free of external random influences. Chaotic systems have two defining characteristics: they show order interspersed with randomness, and their evolution is extremely sensitive to initial conditions. Extreme sensitivity to initial conditions is quantified by the exponential divergence of nearby orbits. The rate of such divergence is characterized by the e-folding time scale called Lyapunov time. A second characteristic time scale is the escape time, which is the time for a major change in the orbit.

So if one applies the requirement that the evolution (of Earth's climate) is extremely sensitive (or at least sensitive) to 'initial conditions', then climate may not be chaotic. What are the initial conditions?

It does represent a dynamic with both periodic and aperiodic behaviors.

 

[seycyrus]

Interesting article - Chaos and stability of the solar system
http://www.pnas.org/content/98/22/12342.full

Nice find. I wonder what the lyapunov and escape time scales are for the weather/climate. I failed with google.

What are the initial conditions?

I always understood initial condition to be those you stipulate at t0, any t0. Or are you pointing out that we don't even know which variables are required inputs?