Question on whether climate is chaotic or not

[Astronuc]

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?

In the context of Earth's climate, I wondering at what point one takes the initial, or perhaps more appropriately, the reference time. The climate has constantly changed - sometimes slowly, sometimes abruptly.

In the context of today's climate, do we look back 100 years, 200 years, 400 years, 1000 years, 5000, 10,000, 100,000, 1 million, 10 million.

Also - what is the system (which defines statepoints) and what are the inputs, and more importantly - what are the 'natural' inputs/perturbations, and what are the 'anthropogenic inputs/perturbations - and what are the relative magnitudes of these inputs/perturbations?

 

[Xnn]

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.

Okay;

Then how can we answer the question if we don't know if
there are tipping points or how close we are to them?

 

[turbo]

PBS hosts a nice article on weather, climate, and chaos:

http://www.pbs.org/kcet/wiredscience/blogs/2007/10/climate-chaos-and-confusion.html

The explanation of how weather and climate are described by the illustration of Lorentz attractors is a good one, IMO, though greatly simplified, since weather and climate have a LOT of variables.

 

[seycyrus]

Okay;
Then how can we answer the question if we don't know if
there are tipping points or how close we are to them?

We really need for that nonlinear-mathematician friend of a poster to swing by ...Maybe if we are lucky, he will be a "Chaotician" (I cringed when they used that word in Jurasic Park)

Perhaps your question reflects the uncertainty the one scientist in question (Gavin??) meant to reflect upon when he said it "might" be chaotic.

How does one label a natural system as chaotic when one cannot formulate and solve expressions that correctly model the observed behavior? Does being able to model the sensitivity to initial conditions suffice to say that the natural system being modeled is chaotic? Not in a strict mathematical sense.

It's more straightforward for a simpler system. One can write down the equations for a double pendulum and compare the results with a *physical* double pendulum. One notes the behavior of the real beast and says
"Look at that pendulum go! It's all crazy-like!"
and then
"Wow, when I map out the trajectories in phase space solved from my equations of motion they get pretty crazy too! Why, they look just like that swinging contraption!"
and then
"I can show that these equations describe a chaotic system, therefore it seems fair to induce that the *real* double pendulum is chaotic."

But doing it for the weather ...

I'm liking the *might be* answer more and more.

 

[turbo]

I'm liking the *might be* answer more and more.

I think I'd like that answer even more if it were qualified with *on some scales*. Certainly the Younger Dryas event shows that global climate can take some pretty rapid swings. It brought on an ice age in the northern hemisphere, and much warmer temperatures in the southern hemisphere, so the results of that event were divergent N-S.

 

[Astronuc]

Then how can we answer the question if we don't know if
there are tipping points or how close we are to them?

That's the proverbial $64 million or now $64 billion (or maybe it's $6.4 trillion) question.

In order to know how to procede, one needs to understand the path/trajectory and the tipping points/pitfalls. If one makes the wrong assessment and/or wrong prediction, things might get dicier.

 

[Andre]

I was trying to shed some light on that but the post about that got deleted.

 

[Xnn]

Personally, I'm not fond of "We don't know" as an answer.

Here is an article from Scientific America which suggest that the
Earths climate becomes chaotic at around 1000 ppm CO2.
Fortunately, that is not expected to occur for at least 200 years.

http://www.scientificamerican.com/article.cfm?id=impact-from-the-deep

 

[vanesch]

Okay;

Then how can we answer the question if we don't know if
there are tipping points or how close we are to them?

But there are 3 different aspects:

- chaotic behaviour of the inherent dynamics of climate
- eventual existence of bifurcations (tipping points)
- relatively short term (a few centuries) predictability.

They are not related. The system can be chaotic with Lyapunov exponents which are of the order of 1/1 million years for instance, which would mean that predictability over centuries or hundreds of millennia isn't going to be a problem by this chaotic dynamics.

Bifurcations don't mean necessarily chaos, and even less "unpredictability". A beam under compression has a bifurcation point (from a certain stress onwards, it will bulge). That doesn't mean we can't calculate beam deformation.

So the argument "they say there might be tipping points, but then it is chaotic, and hence we can't make any predictions" is full of invalid inferences.

Let's first find out the dynamics already !

 

[Coldcall]

PBS hosts a nice article on weather, climate, and chaos:

http://www.pbs.org/kcet/wiredscience/blogs/2007/10/climate-chaos-and-confusion.html

The explanation of how weather and climate are described by the illustration of Lorentz attractors is a good one, IMO, though greatly simplified, since weather and climate have a LOT of variables.

Actually I've read that blog before and Alexi Tekhasski has some interesting points contrary to the author of that blog. Just read some of the comment below re Lorenz attractor.

As that pro-agw blog shows there is a concerted effort by the some in the agw community, including Gavin Schmidt at RC, who for some odd reason, don't want the climate system labelled as chaotic. However the silly part is that their models are indeed non-linear with all the inherent problems about initial conditions.

My whole point has always been that:

1) I am highly suspicious of any scientist who claims a computer model is based on an "unknown" physics. (in other words, if one can't explain the underying physics how can one be confident of the model?) I think i hold a reasonable position and if we were discussing most other scientific (less trendy)topics i think most would agree with that stance.

2) Any computer model which needs to virtualise the real climate system in a realistic capacity probably needs an infinite amount of variables and factors for which we are today probably aware of only a tiny fraction. The current models are just way too primitive to accomplish that.

3) I don't accept this idea (often stated by some in the agw community) that while these computer models may not be able to predict shorterm climate, they can predict long-term averages. This goes against very fundamental science known and demonstrated in chaotic systems, which states that small inaacuracies in initial condiions grow exponentially and irregularly the longer the clock runs. Remember that climate is longterm weather, no mattter what sort of clever semantic one wants to use to define "climate".

4) The climate is open ended and affected by cosmic phenomenom so the idea we can create and idealisation of the climate in a model is a non-starter.

So I am not arguing that Co2 does not affect the climate or we are not having climate change, or perhaps even some warming depending on what time scale one uses as a boundary.

I'm simply saying that with our current knowledge of the scientific fundamentals which MUST be adhered to in any theory, there is too large an uncertainty and unpredictability factor for claiming anything is settled.

That is how i am sceptical.

PS: The burden of proof is on the computer models to confirm and validate their predictions as with any scientific theory. They have not done so, and in fact, their models did NOT predict the post 98 cooling period. So those models have failed at the first hurdle.

 

[Coldcall]

Some professional references for some of my points above:

[moderator note: blogs do not count as references][/color]

http://rsta.royalsocietypublishing.org/content/365/1857/2145

Another paper challenging the predictability of these models. Len Smith, one of the authors from LSE works on climate models and is constantly trying to get his colleagues to tone donw the hubris about predictability.

"Over the last 20 years, climate models have been developed to an impressive level of complexity. They are core tools in the study of the interactions of many climatic processes and justifiably provide an additional strand in the argument that anthropogenic climate change is a critical global problem. Over a similar period, there has been growing interest in the interpretation and probabilistic analysis of the output of computer models; particularly, models of natural systems. The results of these areas of research are being sought and utilized in the development of policy, in other academic disciplines, and more generally in societal decision making. Here, our focus is solely on complex climate models as predictive tools on decadal and longer time scales. We argue for a reassessment of the role of such models when used for this purpose and a reconsideration of strategies for model development and experimental design. Building on more generic work, we categorize sources of uncertainty as they relate to this specific problem and discuss experimental strategies available for their quantification. Complex climate models, as predictive tools for many variables and scales, cannot be meaningfully calibrated because they are simulating a never before experienced state of the system; the problem is one of extrapolation. It is therefore inappropriate to apply any of the currently available generic techniques which utilize observations to calibrate or weight models to produce forecast probabilities for the real world. To do so is misleading to the users of climate science in wider society. In this context, we discuss where we derive confidence in climate forecasts and present some concepts to aid discussion and communicate the state-of-the-art. Effective communication of the underlying assumptions and sources of forecast uncertainty is critical in the interaction between climate science, the impacts communities and society in general".

 

[Coldcall]

But there are 3 different aspects:

- chaotic behaviour of the inherent dynamics of climate
- eventual existence of bifurcations (tipping points)
- relatively short term (a few centuries) predictability.

They are not related. The system can be chaotic with Lyapunov exponents which are of the order of 1/1 million years for instance, which would mean that predictability over centuries or hundreds of millennia isn't going to be a problem by this chaotic dynamics.

Bifurcations don't mean necessarily chaos, and even less "unpredictability". A beam under compression has a bifurcation point (from a certain stress onwards, it will bulge). That doesn't mean we can't calculate beam deformation.

So the argument "they say there might be tipping points, but then it is chaotic, and hence we can't make any predictions" is full of invalid inferences.

Let's first find out the dynamics already !

Sorry but i think your point about:

"The system can be chaotic with Lyapunov exponents which are of the order of 1/1 million years for instance, which would mean that predictability over centuries or hundreds of millennia isn't going to be a problem by this chaotic dynamics."

Is wrong form a foundational perspective re chaos. In any complex open ended system in a state of non-equlibirum there is just no way you can expect super longterm predictions to be accurate without having actually run the model for that amount of time then observed correlations with what really emerged from that chaotic system. And the model must be not an idealisation but an exact simulation of all the factors that will effect that chaotic system. The initial conditions must be known to an almost infinite degree of accuracy. All these things are an impossibility from the perspective of known and tested scientific theory of chaos.

What you are suggesting is that we freeze reality as it stands today and extraploate that into the future ad infinitum idealising a status quo. Whereas we know this is not practical nor useful in predicting long range behaviour of a chaotic system open to external influences of which we have little information.

Im sorry but every text on chaos theory will support my view. I suggest any of the books by Davies, Gribbin's (Complexity), Ian Stewart, and even Gleicks original book on chaos theory.

 

[Coldcall]

Personally, I'm not fond of "We don't know" as an answer.

Here is an article from Scientific America which suggest that the
Earths climate becomes chaotic at around 1000 ppm CO2.
Fortunately, that is not expected to occur for at least 200 years.

http://www.scientificamerican.com/article.cfm?id=impact-from-the-deep

"We don't know" is the answer Gavin at RC has provided every time he is asked to define the physics behind a) the climate system. and b) his models.

If one cannot define the physics any idea of accurate predictions is just a logical fallacy.

However, the truth is that their models are chaotic. Its a mystery why they won't admit it, but my suspicion is that they won't admit it because they know what it implies for any hopes of accurate prediction.

Actually the IPCC report has a section called Basic Science where they state this unpredictability in the oddly semantic "surprises". But then they go on to ignore the basic fundamental science and pretend the uncertainty is less than 10%! That is a figure they have pulled out of the air. Its a nonsense.

 

[D H]

Sorry but i think your point about:

The system can be chaotic with Lyapunov exponents which are of the order of 1/1 million years for instance, which would mean that predictability over centuries or hundreds of millennia isn't going to be a problem by this chaotic dynamics.

Is wrong form a foundational perspective re chaos. In any complex open ended system in a state of non-equlibirum there is just no way you can expect super longterm predictions to be accurate without having actually run the model for that amount of time then observed correlations with what really emerged from that chaotic system. And the model must be not an idealisation but an exact simulation of all the factors that will effect that chaotic system. The initial conditions must be known to an almost infinite degree of accuracy. All these things are an impossibility from the perspective of known and tested scientific theory of chaos.

Did you read what vanesch wrote? A chaotic system can be quite predictable over time scales much less than the system's Lyapunov time. The solar system is chaotic with a Lyapunov time of 5 to 10 million years. (See the article cited in post #49.) That means that predictions of the state of the solar system over centuries, or even hundreds of millennia can be quite accurate. Problems with the predictions do appear, but only when on the scale of millions of years or longer.

Bringing this back to the discussion of the climate, *if* climate is chaotic, then it can still be quite predictable over time scales of human interest (decades to a century or so) so long as the climate's Lyapunov time is a millennia or more.

 

[Coldcall]

Did you read what vanesch wrote? A chaotic system can be quite predictable over time scales much less than the system's Lyapunov time. The solar system is chaotic with a Lyapunov time of 5 to 10 million years. (See the article cited in post #49.) That means that predictions of the state of the solar system over centuries, or even hundreds of millennia can be quite accurate. Problems with the predictions do appear, but only when on the scale of millions of years or longer.

Bringing this back to the discussion of the climate, *if* climate is chaotic, then it can still be quite predictable over time scales of human interest (decades to a century or so) so long as the climate's Lyapunov time is a millennia or more.

Yes i read what he said very carefully and disagree, for the fundamental points i have raised.

You say they can be "quite accurate". What does that mean? Its not enough to say we can more or less approximate within some defined margin of error. The only way to prove that assertion that "quite accurate" will be good enough is by running the model and making predictions. None of this has yet been done.

You guys are talking about idealisations. Thats not how the real universe works.

I would be convinced that "quite accurate" is good enough for our purposes if predictions were made, confirmed and validated.

Are we not in our right to insist that if agw is to be taken seriously as a science that the correct methodology and process take place to validate or falsify it?

 

[billiards]

Yes i read what he said very carefully and disagree, for the fundamental points i have raised.

You say they can be "quite accurate". What does that mean? Its not enough to say we can more or less approximate within some defined margin of error. The only way to prove that assertion that "quite accurate" will be good enough is by running the model and making predictions. None of this has yet been done.

You guys are talking about idealisations. Thats not how the real universe works.

I would be convinced that "quite accurate" is good enough for our purposes if predictions were made, confirmed and validated.

Are we not in our right to insist that if agw is to be taken seriously as a science that the correct methodology and process take place to validate or falsify it?

Climate models are not meant to be predictive. They are adopting the methodology commonly adopted in the Earth Sciences (and other sciences for that matter) of using a simple model to better understand the behaviour of a complex system.

 

[D H]

You are making multiple claims, Coldcall, and you are mixing them up. You are being a bit chaotic.

Here is what I think your claims are. Correct me if I'm wrong.

• From post #64, "However, the truth is that their models are chaotic. Its a mystery why they won't admit it, but my suspicion is that they won't admit it because they know what it implies for any hopes of accurate prediction."
  
  Claim #1: The climate is a chaotic system and hence is unpredictable (period). In particular, climate is unpredictable over the time span of immediate interest -- the present to 100 years from now.
• From post #66, "The only way to prove that assertion that "quite accurate" will be good enough is by running the model and making predictions. None of this has yet been done."
  
  Claim #2: Climate scientists don't have models and don't make predictions.
• From post #61, "The climate is open ended and affected by cosmic phenomenom so the idea we can create and idealisation of the climate in a model is a non-starter."
  
  Claim #3: Creating a model of the climate is a hopeless endeavor. There are too many "unknown unknowns."
• Also from post #61, "Any computer model which needs to virtualise the real climate system in a realistic capacity probably needs an infinite amount of variables and factors for which we are today probably aware of only a tiny fraction."
  
  Claim #4: A model of the climate is beyond the scope of modern science. There are too many "known unknowns."

This is a just start; you are making more claims than that. This is a problem. Let's keep this thread to claim #1. Raise those other claims in some other thread. Too many issues in a single thread makes for a chaotic discussion.

 

[Coldcall]

You are making multiple claims, Coldcall, and you are mixing them up. You are being a bit chaotic.

Here is what I think your claims are. Correct me if I'm wrong.

• From post #64, "However, the truth is that their models are chaotic. Its a mystery why they won't admit it, but my suspicion is that they won't admit it because they know what it implies for any hopes of accurate prediction."
  
  Claim #1: The climate is a chaotic system and hence is unpredictable (period). In particular, climate is unpredictable over the time span of immediate interest -- the present to 100 years from now.
  
• From post #66, "The only way to prove that assertion that "quite accurate" will be good enough is by running the model and making predictions. None of this has yet been done."
  
  Claim #2: Climate scientists don't have models and don't make predictions.
  
• From post #61, "The climate is open ended and affected by cosmic phenomenom so the idea we can create and idealisation of the climate in a model is a non-starter."
  
  Claim #3: Creating a model of the climate is a hopeless endeavor. There are too many "unknown unknowns."
  
• Also from post #61, "Any computer model which needs to virtualise the real climate system in a realistic capacity probably needs an infinite amount of variables and factors for which we are today probably aware of only a tiny fraction."
  
  Claim #4: A model of the climate is beyond the scope of modern science. There are too many "known unknowns."

This is a just start; you are making more claims than that. This is a problem. Let's keep this thread to claim #1. Raise those other claims in some other thread. Too many issues in a single thread makes for a chaotic discussion.

Well actually most of those statements revolve around the same question. I've just tried to artciulate them in different ways because there appears to be some misunderstandings about what I am trying to get at.

Look, don't take it from me. Here are a load of papers looking at prediction in chaotic systems, and they asll say the same thing, long-term prediction is next to impossible.

http://www.engineeringletters.com/issues_v15/issue_1/EL_15_1_10.pdf

http://sciencelinks.jp/j-east/article/200118/000020011801A0278369.php

http://www.springerlink.com/content/g074k6037tr76906/

http://www.jstor.org/pss/2290510

http://personalpages.to.infn.it/~boffetta/Papers/bc98.pdf

By the way the one called personal pages is a paper, but if its not good enough because the link isn't to anything institutional then delete by all means.

But going back to the original point, as youve requested:

I stand by the statemement that climate is a chaotic system and all the same rules of chaotic systems should apply. As the papers and books i have references will all tell you the same thing about the unpredictability of long term forecasts and it does not matter the system, if its chaotic they all behave this way.

But this is exactly why Gavin at RC won't commit one way or another, because admitting the chaotic nature of the climate basically puts his models into the same problem territory as any other chaotic system.

I don't see how anyone can not notice the game being played with this reticence to admit the chaotic nature of the climate.

 

[Coldcall]

Climate models are not meant to be predictive. They are adopting the methodology commonly adopted in the Earth Sciences (and other sciences for that matter) of using a simple model to better understand the behaviour of a complex system.

You can't expect a simplistic model to accurately describe what will happen in the future re a complex choatic system. But if what you are saying is true then their whole theory is flawed from the start.

Also please don't tell me they are not meant to make predictions because that's exactly what they have done re Co2 forcing in the next decades.

 

[Coldcall]

I've got to leave for the day but i just ask everyone that if they have any referential evidence of a sucessful longterm predictions in chaotic systems please post it.

So far all i have seen in an attempt to contradict the fundamental known science of chaos theory are "could" or "may" or other caveated statements with no proof.

If someone thinks they can overturn chaos physics going back to Poincare please show me the evidence as the burden of proof lies squarely with the detractors.

Of course that doesn't settle the argument over whether climate is chaotic but i think if you ask any scientists properly involved with chaotic systems they will tell you it is indeed chaotic. It seems the only people arguing otherwise are agw proponents.

Gotta go for now.

 

[D H]

Well actually most of those statements revolve around the same question.

No, they don't. They are very distinct issues.

The first claim *must* be the sole focus of discussion of this thread:

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".

That alone is not particularly fruitful. I'd suggest "whether climate is chaotic or not, and if it is, what that says about the predictability of the climate".

Those other claims are off-topic. By coming back to those issues you are risking having this thread re-locked.

 

[seycyrus]

Let us explore this concept of being able to predict future behavior of a chaotic system. When it is claimed that this is possible, are we talking about a prediction *within* certain bounds, i.e. the phase space outlined by the estrange attractor? if so, I don't think we can consider that as "predictability" in the classical sense. I don't think that phase space is swept in a continuous fashion, but rather, by jumps.

It has been some years, but isn't the Lyapunov time scale sort of calculated *after* you have a pretty good handle on the dynamics of your system? I recall writing a program to model a bacteria population. Lyapunov was related to the onset of initial and subsequent bifurcation.

I'm not certain that calculating the Lyapunov factor for the weather or the climate can be done in a suitable sufficient way to satisfy mathematicians.

On a side note, why are people once again resorting to the tired old "You don't understand chaos theory" argument. I think it is pretty evident that unless you have done substantial work in this field, everyone falls into that category.

It's not like we are talking about a well understood phenomenon, like friction *snork*.

 

[D H]

I've got to leave for the day but i just ask everyone that if they have any referential evidence of a sucessful longterm predictions in chaotic systems please post it.

It depends totally on what you mean by "longterm". If by that you mean long on a human timescale, then the answer is absolutely yes. If on the other hand you mean long compared to the Lyapunov time for a chaotic system, the answer is of course no.

This is why the issue of the Lyapunov exponent for the climate is critical to this discussion. Suppose for example that the climate is chaotic but that the climactic Lyapunov time scale is on the order of millennia or more. If this is case, that the climate is chaotic is irrelevant to the question of whether the climate is predictable.

You asked for "referential evidence of a sucessful longterm predictions in chaotic systems." As has been mentioned before, the solar system is chaotic on a time scale of five to ten million years or so. Compared to that time scale, the seven thousand years or so that people have been trying to predict what is going in the sky is a blink of the eye.

It takes several years between the launch of a deep space probe and the probe's arrival at the target destination. New Horizons, for example, was launched in January 2006 and won't reach Pluto until July 2015. This mission required that mission planners to have very accurate predictions of where Pluto will be in 2015 back in the early 2000s. Another example is the Cassini probe. Cassini was *huge*. A direct flight to Saturn was well beyond the capability of 1997 rocket technology (or today's technology, for that matter). The probe instead swung by Venus twice, then came back to Earth, then swung by Jupiter, and finally reached Saturn 6 3/4 years after launch. If the mission planners did not have *extremely* accurate predictions of where the planets would be at the times of the flybys those gravity assists would not have worked.

The US' Jet Propulsion Laboratory and Russia's St. Petersburg Institute of Applied Astronomy are in a bit of a friendly competition to see who can do a better job of modeling the behavior of the solar system. Both groups have developed very precise ephemerides. JPL's Development Ephemerides and the Institute's Ephemerides of Planets and the Moon are essential in planning long term space missions. See http://iau-comm4.jpl.nasa.gov/relateds.html for papers on both.


Bottom line: What do you mean by "longterm"?

 

[Astronuc]

I'd suggest "whether climate is chaotic or not, and if it is, what that says about the predictability of the climate".

I concur.

 

[seycyrus]

...

You asked for "referential evidence of a sucessful longterm predictions in chaotic systems." As has been mentioned before, the solar system is chaotic on a time scale of five to ten million years or so. Compared to that time scale, the seven thousand years or so that people have been trying to predict what is going in the sky is a blink of the eye.

I don't think that is helpful. Certainly he understands that we can launch craft to other planets, and predict when the next eclipse will occur.

Since he will be gone for a day or so, I'll speak for him and ask a question that I think is relative to your solar system example.

What evidence do we have that the solar system is chaotic? The fact that some of the equations we use to model astronomical phenomena suggest chaos?

Can't we say that *everything* is chaotic, just with necessarily large Lyapunov time scales?

 

[Andre]

Anyway, http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=1120981322&_sort=r&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=5f1e7157e44025dc05d6a32cc4313057 is long overdue according to our predictions.

So if we can't predict solar cycles, chaotic or not, if climate is forced by solar cycles, how to deal with that?

 

[D H]

On a side note, why are people once again resorting to the tired old "You don't understand chaos theory" argument. I think it is pretty evident that unless you have done substantial work in this field, everyone falls into that category.

Were it not for some chaotic events in my personal life a *long* time ago, that was exactly where my career was heading.

I presented my interpretation of Coldcall's claims in post #68. He replied in post #69 and did not argue with my interpretation. Key here is claim #1, which I interpreted as

From post #64, "However, the truth is that their models are chaotic. Its a mystery why they won't admit it, but my suspicion is that they won't admit it because they know what it implies for any hopes of accurate prediction."

Claim #1: The climate is a chaotic system and hence is unpredictable (period). In particular, climate is unpredictable over the time span of immediate interest -- the present to 100 years from now.

If that is a true characterization of Coldcall's views, it does indeed demonstrate a lack of understanding of chaos theory.

=============================

What evidence do we have that the solar system is chaotic? The fact that some of the equations we use to model astronomical phenomena suggest chaos?

See the article cited in post #49. Also see http://www.imcce.fr/Equipes/ASD/preprints/prep.2003/th2002_laskar.pdf[/url], [url]http://www.astronomynow.com/090616Planetarypileuppossibleinnextfivebillionyears.html[/url], [url]http://books.google.com/books?id=LkXhPwAACAAJ[/url], [url]http://books.google.com/books?id=shYNuW0B0fsC[/url], [url]http://books.google.com/books?id=7YkDhZCCLR4C[/URL], ... Google "chaos in the solar system" for more.

 

[seycyrus]

Were it not for some chaotic events in my personal life a *long* time ago, that was exactly where my career was heading.

Yeah, it seems like you know what you are talking about.

If that is a true characterization of Coldcall's views, it does indeed demonstrate a lack of understanding of chaos theory.

Chaos theory seems to me to be one of those topics that everyone and his brother is ready to jump at anyone else and claim that "they don't understand it.", regardless of their own experience in the field.

See the article cited in post #49. Also see http://www.imcce.fr/Equipes/ASD/preprints/prep.2003/th2002_laskar.pdf[/url], [url]http://www.astronomynow.com/090616Planetarypileuppossibleinnextfivebillionyears.html[/url], [url]http://books.google.com/books?id=LkXhPwAACAAJ[/url], [url]http://books.google.com/books?id=shYNuW0B0fsC[/url], [url]http://books.google.com/books?id=7YkDhZCCLR4C[/URL], ... Google "chaos in the solar system" for more.[/QUOTE]

I will look at these articles.
EDIT: Not to be terribly ungrateful, but of those links you posted there, the first is as you hinted, the second doesn't seem to discuss the topic, and the other 3 are books. I guess you are telling me that it is well understood to be true?

Has a similar analysis been done to show that the weather is chaotic?

 

[D H]

Has a similar analysis been done to show that the weather is chaotic?

Whether the weather is chaotic is pretty much where chaos theory in its modern form started. (This ignores Poincaré's work, ergodic theory and KAM theory.) Lorenz tried to cut some time off a computer simulation by restarting it with the printed out conditions from the middle of a prior run. Much to his surprise, the restarted run rather quickly diverged from the rest of that prior run.

The weather most definitely is chaotic. It fits the concept to a T:

• It is highly sensitive to initial conditions. Lorenz failed short-cut, and his analysis of why it did not work was what started chaos theory. Weather modeling was in its infancy in the early 1960s. The assumption before Lorenz' discovery was that with enough information we could predict the weather for a long time. Lorenz showed that this assumption was a pipe dream. A one or (maybe) two week forecast is about as good as we can ever hope to get.
• It is topologically mixing. The historical record of the weather in your home town on December 3 undoubtedly shows a wide range of behavior. If the climate were unchanging, the weather on a succession of December 3rds would come arbitrarily close to any point in that range.
• Its periodic orbits are dense. The weather has a periodic orbit; next July will be hot (assuming your are in the northern hemisphere) and next December it will once again be cold. Next December 3rd you might be hit with a snowstorm, a late warm spell, or anything in between. That's partly because of the topological mixing. That's not a complete picture, however. There is an obvious autocorrelation to the weather.

One way to look at climate is that the climate describes the attractor around which the weather currently orbits. Unlike simple chaotic systems, this is not a stationary attractor. The weather in aggregate, the climate, from 100 years ago is different from the climate of today. Climate is a characterization of the weather, and this characterization is itself a dynamical system.

 

[Astronuc]

Anyway, http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_ArticleListID=1120981322&_sort=r&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=5f1e7157e44025dc05d6a32cc4313057 is long overdue according to our predictions.

So if we can't predict solar cycles, chaotic or not, if climate is forced by solar cycles, how to deal with that?

Yes - at the moment attention is on the quiescence of the sun although Cycle 24 is not significantly delayed - yet. Perhaps is off to a slow start. But it has folks wondering.

Another site - http://sidc.oma.be/index.php

http://sidc.oma.be/sunspot-index-graphics/sidc_graphics.php

http://sidc.oma.be/html/wolfjmms.html

 

[vanesch]

Sorry but i think your point about:

"The system can be chaotic with Lyapunov exponents which are of the order of 1/1 million years for instance, which would mean that predictability over centuries or hundreds of millennia isn't going to be a problem by this chaotic dynamics."

Is wrong form a foundational perspective re chaos. In any complex open ended system in a state of non-equlibirum there is just no way you can expect super longterm predictions to be accurate without having actually run the model for that amount of time then observed correlations with what really emerged from that chaotic system.

We should first define what we understand by "system" here. If we understand by "system", one or other well-defined model (and not the "actual" climate), then, depending exactly on how it is formulated, it is entirely possible to find out. You could find it out formally, if it is just a set of differential equations for instance. But probably the climate models we are talking about are not simply a set of explicit differential equations, but are more involved, and probably come down to implicitly formulated integro-differential equations with table-form functions in it.
It is then of course still possible to run the model "for millions of years" (in simulation time), and try to find out numerically what are the Lyapunov exponents around certain working points - however, most of these models don't even make sense over millions of years (probably continental drift is not implemented in them, for instance).

If you mean "the real climate" we don't even know whether it has a well-defined deterministic dynamics. After all, to have a well-defined climate dynamics, we must make the assumption that the "climate" (as long-term average of weather) has its own state variables and its own internal dynamical equations which pertain only to these state variables and "external input functions". It is not said that this dynamics exists other than in some coarse form, with finite precision. In that case, we cannot make any statement about whether this system is "chaotic".

And the model must be not an idealisation but an exact simulation of all the factors that will effect that chaotic system.

Every model is of course an idealization. And we're considering the model, with all its simplifications, of course, as a system.

The initial conditions must be known to an almost infinite degree of accuracy. All these things are an impossibility from the perspective of known and tested scientific theory of chaos.

No, not at all. I don't know why you say this. I have the impression that you confuse "predictions by a chaotic model beyond the time scale where chaos sets in (infinite precision of initial conditions)", "the accuracy of the model in describing a real-world phenomenon" (tested scientific theory), and "the possibility of finding out whether a certain dynamical model is in fact chaotic or not" (which is not really difficult).

 

[seycyrus]

Whether the weather is chaotic is pretty much where chaos theory in its modern form started. (This ignores Poincaré's work, ergodic theory and KAM theory.) Lorenz tried to cut some time off a computer simulation by restarting it with the printed out conditions from the middle of a prior run. Much to his surprise, the restarted run rather quickly diverged from the rest of that prior run.

I have taken courses in Chaos theory. Even tho it has been some time, I am familiar with lorenz etc.

The weather most definitely is chaotic. It fits the concept to a T:

The papers on the chaos of the solar system shows deviations from classical theory which could be accounted for using chaos theory. I was wondering about a similar analysis for the weather. Has a Lyapunov time scale for the weather been theorized from anything besides observation?

[*]It is topologically mixing. The historical record of the weather in your home town on December 3 undoubtedly shows a wide range of behavior. If the climate were unchanging,..

This seems to be an odd caveat (bolded) to add, since we are after all talking about the weather, which is linked to climate. sort of seems like you are saying *If the average behavior of the weather (the climate) does not change, the future weather will be close to what it is today.*

... Unlike simple chaotic systems, this is not a stationary attractor.

How does one differentiate between a system with a single (or perhaps multiple) non-stationary attractor, and say a system with multiple stationary attractors?

 

[D H]

This seems to be an odd caveat (bolded) to add, since we are after all talking about the weather, which is linked to climate. sort of seems like you are saying *If the average behavior of the weather (the climate) does not change, the future weather will be close to what it is today.*

I'll try again. The weather's autocorrelation function has a long tail. Things like El Ninos stick around for a while. For the sake of argument, assume the autocorrelation function effectively zeros out after a decade. Now imagine a perfect weather/climate simulator. A zillion parallel Earths would do. Start this simulator with tiny, tiny variations in the initial state and run it for ten years. The state of the weather at the end of that ten year period will cover the possible range of conditions for that date.

We only have one real weather/climate machine (the real Earth), and only a finite amount of time before the climate does change. The states covered by that real weather/climate machine on successive December 3rds will not cover the space before the climate moves the weather to a slightly different attractor.

 

[Xnn]

"We don't know" is the answer Gavin at RC has provided every time he is asked to define the physics behind a) the climate system. and b) his models.

If one cannot define the physics any idea of accurate predictions is just a logical fallacy.

However, the truth is that their models are chaotic. Its a mystery why they won't admit it, but my suspicion is that they won't admit it because they know what it implies for any hopes of accurate prediction.

Actually the IPCC report has a section called Basic Science where they state this unpredictability in the oddly semantic "surprises". But then they go on to ignore the basic fundamental science and pretend the uncertainty is less than 10%! That is a figure they have pulled out of the air. Its a nonsense.

They may not be operating the models near conditions suspected to be chaotic either.
Likewise, the current actual climate of the Earth is not necessarily near a choatic region.

If the models do contain chaotic features, then that will eventually be detected, examined, understood and corrected if needed. All the models would then need to be revised to contain the chaotic feature.

For example, if it's clearly proven that the Earth's climate becomes chaotic at around 1000 ppm CO2 or less than 100 ppm, then the models will have to be designed to incorporate that.

 

[Coldcall]

Vanesch,

RE: Defining the climate system

Yes i agree its important to define the boundaries of such a system. And while i am not expert enough to make that definition and I am sure people here can do much better at that sort of thing; however i do believe that you've hit the nail on the head in a way which supports my argument about the uncertainties.

The fact is that the actual climate modellers themselves have not fulfilled this defintion re the climate, otherwise they could agree on whether it was chaotic or not, or at least make a partial definition so we could look at the foundational science which then incorporates that defined or partly defined system.

But without that definition we are really running into problems re; what are the factors, variables and initial conditions which encompass that system. So the lack of deifnition is another reason why i am sceptical that those models can tell us anything which can carry the sort of credibility and validation required in most scientific subjects.

So if its not yet defined, and the underlying science or physics is not yet defined (as is the case currently), how can we be making such conclusions about temerpature tipping points and the like?

Its okay for you to argue that because we have yet to define these issues we cannot categorically state that the climate is chaotic, but that creates even more uncertainty about the science itself.

"Every model is of course an idealization. And we're considering the model, with all its simplifications, of course, as a system."

Exactly. Poincare's n-body problem and Chaos theory demonstrated that idealisation of complex systems is a slippery slope, and really should not be simplified or taken lightly. It seems to me that those lessons have now been forgotten and this is why i am so shocked that learned scientists are in fact indirectly trying to overturn centures of science by pretending we can accurately predict those types of systems.

Worse still, so that they can sort of sidestep the whole issue re uncertainty, they refuse to use the term "chaotic" when it comes to climate. I find this whole strategy deplorable, especially when it appears to only cater for political expediency and dumbing down science in order to bamboozle the masses.

 

[Coldcall]

I have taken courses in Chaos theory. Even tho it has been some time, I am familiar with lorenz etc.



The papers on the chaos of the solar system shows deviations from classical theory which could be accounted for using chaos theory. I was wondering about a similar analysis for the weather. Has a Lyapunov time scale for the weather been theorized from anything besides observation?



This seems to be an odd caveat (bolded) to add, since we are after all talking about the weather, which is linked to climate. sort of seems like you are saying *If the average behavior of the weather (the climate) does not change, the future weather will be close to what it is today.*



How does one differentiate between a system with a single (or perhaps multiple) non-stationary attractor, and say a system with multiple stationary attractors?

Thanks for your input. At least i did not get here today to be swamped by an avalanche of posts condeming me to oblivion!

 

[vanesch]

The fact is that the actual climate modellers themselves have not fulfilled this defintion re the climate, otherwise they could agree on whether it was chaotic or not, or at least make a partial definition so we could look at the foundational science which then incorporates that defined or partly defined system.

I would hope they know what they've put in their computer model. They have not been typing random lines of code, right ?

Honestly, concerning computer climate models, I really don't see the problem. Those that wrote that code surely did define a system, with well-defined parameters and so on. If you have a computer model, surely you can find out whether, in the range of interest of parameters and time scale, you are suffering from chaotic behaviour. Otherwise you would not be able to get any presentable results out! It would wildly vary, from the moment you change the slightest bit.

So it is not possible that actually used models over the time scale and in the parameter zone they are used, exhibit chaotic behaviour.

But without that definition we are really running into problems re; what are the factors, variables and initial conditions which encompass that system. So the lack of deifnition is another reason why i am sceptical that those models can tell us anything which can carry the sort of credibility and validation required in most scientific subjects.

For sure those writing the code of a computer model know exactly what variables they are using in their code, no ? So I don't understand your objection.

As to whether that model is close enough to reality to say something sensible about it, that's an entirely different matter.

Here's some reading material concerning this.

http://www.iop.org/activity/policy/Publications/file_4147.pdf

 

[Coldcall]

Vanesch,

"I would hope they know what they've put in their computer model. They have not been typing random lines of code, right ?"

Good question. Considering some of the comments in the harry_readme file of the CRU emails one wonders about the quality and validation of the input data for Jones's models. Though no I am not saying their inputs were just random code :-)

"So it is not possible that actually used models over the time scale and in the parameter zone they are used, exhibit chaotic behaviour"

I respectfully disagree. The timeframe involved may be arbritray depending on ones definition of a full climate cycle. I believe they speak of 30 years usually (correct me if I am wrong). But even if one uses a shorter timeframe such as 10 years the system will exhibit chaotic behaviour within the first few seconds (depending on how accurately you are measuring the initial conditions and then comparing them to what actually transpired in the real world).

So there is a sort of paradox which is that the more accurate one wants to be about initial conditions the quicker one will observe divergence from reality, because of the more granular observations and measurements being conducted.

Its that difference to reality (unpredictability) which is a symptom of the chaotic behaviour.

hence agw proponents don't want climate defined as chaotic. Its easy to see why. Seriously its almost like they have created a whole new law of physics which has no foundational support other than the rules they have applied for their models.

 

[Xnn]

hence agw proponents don't want climate defined as chaotic. Its easy to see why. Seriously its almost like they have created a whole new law of physics which has no foundational support other than the rules they have applied for their models.

That is not a fair statement.

The models are built on a fondation of physics; just like the climate.
The models are designed to replicate the physics as accurately as possible
within computational limitations.

A good modeler isn't going to just willy nilly build chaos into a model.
It needs to be an outcome of the particulars and the physics.

 

[Coldcall]

That is not a fair statement.

The models are built on a fondation of physics; just like the climate.
The models are designed to replicate the physics as accurately as possible
within computational limitations.

A good modeler isn't going to just willy nilly build chaos into a model.
It needs to be an outcome of the particulars and the physics.

Perhaps you are right and i am being somewhat unfair. Sorry.

However, the chaos is a natural result of the system they are attempting to model, so to simulate it even simplistically, means they need to bite the bullet and fess up on the chaotic nature of the thing they are modelling.

 

[D H]

No they don't. You don't invent chaos. You discover it after the fact. People used models of ever increasing fidelity of solar system dynamics for a long time before discovering that the solar system is chaotic.

You are assuming the climate is chaotic. Since the climate is in a sense a descriptor of the strange attractor of a chaotic system, what exactly does it mean for the climate to be chaotic? The strange attractors themselves have meta strange attractors? That is something outside the realm of chaos theory.

 

[Coldcall]

Is the weather a sub-set of the climate or is it the other way round? I only ask because if we can agree it is the former, then i think that would add much weight to the argument the climate is indeed chaotic.

Just a thought.

 

[Coldcall]

No they don't. You don't invent chaos. You discover it after the fact. People used models of ever increasing fidelity of solar system dynamics for a long time before discovering that the solar system is chaotic.

Who is this directed at? I ask because i never said anything about inventing chaos?

 

[Xnn]

Cllimate models already have their own set of weather; and it's chaotic!

That is covered in FAQ section on Models at Real Climate.

 

[D H]

Is the weather a sub-set of the climate or is it the other way round? I only ask because if we can agree it is the former, then i think that would add much weight to the argument the climate is indeed chaotic.

Neither. The climate is a meta descriptor of the weather. They are different things.

By way of analogy, is medicine a subset of particle physics? In a sense yes, but not really. Medicine, for the most part, is far removed from particle physics. Explaining how the body changes over decades in terms of the standard model of physics would be a fruitless endeavor.

Another analogy: Consider a simple chaotic system with a fixed strange attractor. That attractor is fixed, so it is not chaotic. Yet it describes a chaotic system. Just because the system it describes is chaotic does not mean the characterization of the attractor is chaotic.

 

[Astronuc]

Maybe we need a separate thread on the effects of volcanic eruptions on climate.

A massive volcanic eruption that occurred in the distant past killed off much of central India's forests and may have pushed humans to the brink of extinction, according to a new study that adds evidence to a controversial topic.

The Toba eruption, which took place on the island of Sumatra in Indonesia about 73,000 years ago, released an estimated 800 cubic kilometers of ash into the atmosphere that blanketed the skies and blocked out sunlight for six years. In the aftermath, global temperatures dropped by as much as 16 degrees centigrade (28 degrees Fahrenheit) and life on Earth plunged deeper into an ice age that lasted around 1,800 years.

http://news.yahoo.com/s/livescience/20091204/sc_livescience/ancientvolcanosdevastatingeffectsconfirmed

But was the baseline (equilibrium) before and after the same.

 

[vanesch]

Vanesch,

"I would hope they know what they've put in their computer model. They have not been typing random lines of code, right ?"

Good question. Considering some of the comments in the harry_readme file of the CRU emails one wonders about the quality and validation of the input data for Jones's models. Though no I am not saying their inputs were just random code :-)

Reconstruction of indicators of past climate have nothing to do with climate models.

"So it is not possible that actually used models over the time scale and in the parameter zone they are used, exhibit chaotic behaviour"

I respectfully disagree. The timeframe involved may be arbritray depending on ones definition of a full climate cycle. I believe they speak of 30 years usually (correct me if I am wrong). But even if one uses a shorter timeframe such as 10 years the system will exhibit chaotic behaviour within the first few seconds (depending on how accurately you are measuring the initial conditions and then comparing them to what actually transpired in the real world).

I have no idea what that might mean. A "full climate cycle" must be something that is way longer than the defining time of over how long we have to average weather to even define climate. If that period is 30 years, then 30 years is just ONE single "climate point". The next single point is then 60 years later. In a century, we have about 3 "climate state points" (of course, we will work with moving averages, and we can then interpolate between them to have a continuous curve).

Climate dynamics - strictly speaking - is then the dynamical equation which will have us the first climate point (right now) evolve in the second one (30 years from now) and which will have the second one evolve in the third one (60 years from now).

By definition, you cannot have better time resolution in climate dynamics. A climate cycle must contain many "climate points" and hence must have a period that is several hundreds of years, at least.

Its that difference to reality (unpredictability) which is a symptom of the chaotic behaviour.

Imagine that you have a weather forcast program. You introduce into it, actual initial conditions. You let it compute the weather for the next 20 years. Of course, it will not predict the day-to-day weather accurately after a few days, because of, exactly, that chaotic behaviour of weather. But if you take the average of that weather over your computed time series, you will find certain average evolutions for temperature, precipitation etc... over the year.
Now, do the same, but start out from different (randomly generated) initial conditions. You will have 20 years of imaginary weather (again). Take the average. Chances are, your average is not very different from your first run.

Do this 1000 times (that is, do 1000 times a 20 - year weather forecast), each time with different initial conditions. Calculate averages each time.

If those "time averages" are more or less comparable, you can say that you have a rather robust climate estimate, independent of the exact initial conditions, right ? So although the exact succession of rain, sunshine, wind and so on will be totally different for those 1000 runs, the averages calculated will maybe be rather comparable. And probably also comparable to the real climate if the weather forecasting program is any good.

Mind you, it could be that each time you get wildly different averages. In that case, your weather forecasting engine doesn't allow you to estimate climate. But if the averages are more or less the same, it does.

This allows you already to estimate (static) climate from a weather forecasting program - even though the weather forecasting itself is chaotic, the statistical properties (the averages) can be well-defined (or not).

 

[Coldcall]

Vanesch and DH,

Thats for the posts guys but I'm afraid you are both skirting around the fundamental science on which any attempt to predict the climate must be based.

But don't take my word for it. Check out these papers which put those climate models to the test. They overiding findings is that they are not credible:

http://www.itia.ntua.gr/getfile/850/3/documents/2008EGU_ClimatePredictionPrSm.pdf

http://www.sciencemag.org/cgi/content/abstract/318/5850/629

http://www.atypon-link.com/IAHS/doi/pdf/10.1623/hysj.53.4.671?cookieSet=1

Further more, the IPCC reports have buried the high level of unpredictability in the Science section. Remember their projections (as they like to call predictions) are based on these GLCs which they claim show a moderate increase in Co2 will cause a NET positive feedback affect causing run-away warming!

However if the GLCs are not credible as predicitive tools then the whole scientific case is flawed.

So if you guys want to prove that we should rely on these GLCs please provide references of papers demonstrating a high degree of accurate prediction. There are none that i can find, except for ones putting forward hypothesis on how they might be able to become a little more accurate.

 

[Coldcall]

Cllimate models already have their own set of weather; and it's chaotic!

That is covered in FAQ section on Models at Real Climate.

Problem is gavin from RC, and in fact most climate modellers don't want to accept that the climate is a chaotic system because it would falsify the predictive potential of their climate models.

So they play semantic games by sidestepping the elephant in the room.

 

[D H]

Vanesch and DH,

Thats for the posts guys but I'm afraid you are both skirting around the fundamental science on which any attempt to predict the climate must be based.

But don't take my word for it. Check out these papers which put those climate models to the test. They overiding findings is that they are not credible: ...

Guilty as charged. The reason is simple: Those issues are not germane to this thread. A common rule to almost all internet forums is to stay on-topic. That certainly is a rule here at PF. The general issue of the accuracy of climate models is not the topic of this thread. Start a new thread on that issue if it gets you all hot and bothered, or find an existing thread where that issue is the central topic.

You cited three papers. The first and third paper (http://www.atypon-link.com/IAHS/doi/abs/10.1623/hysj.53.4.671" ) represent this kind of off-topic discussion. These papers have nothing to do per se with the topic of this thread. There are plenty of reasons why climate models might be less accurate than desired. Those two articles claim that climate models are erroneous as evidenced by comparisons between predictions to outcomes. That's all fine and dandy. However, those articles did not attribute this "wrongness" to the chaotic nature of climate. They are off-topic. Discuss them elsewhere.

The second paper, Roe, G.H., and M.B. Baker, 2007: Why is climate sensitivity so unpredictable? Science, 318, 629-632, (http://earthweb.ess.washington.edu/roe/Publications/RoeBaker_Science07.pdf" ; no paywall) is closer to the subject of this thread. Nonlinear dynamics, and feedback loops in particular, are afterall one of the hallmarks of chaotic systems. However, to argue that this paper means that climatology is a fruitless endeavor is a misrepresentation of the paper. The paper does not say that, and the authors are definitely of the opposite opinion.

In fact, the authors wrote a followup article to the article published in Science. The title: "The shape of things to come: why is climate sensitivity so predictable?" (emphasis mine).

Baker, M.B., and G.H. Roe, 2009: The shape of things to come: why is climate change so predictable? J. Climate. 22, 4574-4589. (http://earthweb.ess.washington.edu/roe/Publications/BakerRoe_Predictable_Jclim09.pdf" )