Question on whether climate is chaotic or not

[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" )

 

[Astronuc]

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.

I think folks need to be careful and refrain from making statements about others' comments or others' motivations.

It's one thing to cite published statements, but it becomes hearsay to make an unsubstantiated claim about what another party said or wrote privately.


Certainly the public has a poor understanding of chaos and predictability. The climate models might do a good job in predicting trends - within uncertainty.

Obviously, if some data have been excluded such that the measurements are 'made' to agree with models, i.e., the data are intentionally and artificially biased, then there is a big problem with the data integrity and models.

 

[Coldcall]

I think folks need to be careful and refrain from making statements about others' comments or others' motivations.

It's one thing to cite published statements, but it becomes hearsay to make an unsubstantiated claim about what another party said or wrote privately.


Certainly the public has a poor understanding of chaos and predictability. The climate models might do a good job in predicting trends - within uncertainty.

Obviously, if some data have been excluded such that the measurements are 'made' to agree with models, i.e., the data are intentionally and artificially biased, then there is a big problem with the data integrity and models.

Okay well i have referenced multiple evidence showing these climate models are not credible from any scientific perspective. I can do no more than point people at the actual science.

I mean no disrespect to Gavin, but the fact he won't define the basic physics underlying his idealisation of the climate *system* is very disturbing. It has also become apparent that most of these climate modellers have no background in non-linnear dynamics as has been pointed out by many engineers who use complex models idealising something from the real-world.

In fact its is interesting how so many working engineers are sceptics. But not surprising since engineers actually have to work with real-world problems which require real results that can be proven or falsified.

 

[vanesch]

I have been playing a bit around, and just as a pedagogical illustration and nothing more, I've been doing the following.

I took the Lorenz attractor (see http://en.wikipedia.org/wiki/Lorenz_system) and took the source code there as a starting point, and adapted it to the free matlab-like environment scilab (see http://www.scilab.org/ where you can download it for different systems). I prefer scilab over octave because it has a better windows-implementation as far as I know.

The Lorenz attractor is a very well known chaotic system, as a function of 3 parameters, sigma, rho and beta (see wiki for an explanation).

If you calculate a solution to the Lorenz system starting out from arbitrary starting conditions, you get a solution, and given that the system is chaotic, each different initial condition will give you a wildly different solution.

But then I calculated, along a solution, an average (here the average of x(1) * x(2), but you could think up any quantity based upon the state of the lorenz system).

It turns out that that average is, even though calculated on the basis of a solution to a chaotic system, rather "stable".

Next I calculated that average for different Lorenz systems, where I varied one of the parameters, namely sigma, from 7 to 15 (in steps of 0.2) and calculated the average of my "interesting quantity" x(1) * x(2) for each of these. This gives me a (somewhat noisy) dependency of my "interesting quantity" on sigma.

I did that several times, and I find rather comparable evolutions.

So I can conclude that even though the underlying system is chaotic, I can say things about the dependency of my average "interesting quantity" as a function of a parameter (sigma).

Here's the code:

// Lorenz Attractor equations solved by ODE Solve
// x' = sigma*(y-x)
// y' = x*(rho - z) - y
// z' = x*y - beta*z
function dx = lorenzatt(T,X);
    global rho;
    global sigma;
    global b;
    dx = zeros(3,1);
    dx(1) = sigma*(X(2) - X(1));
    dx(2) = X(1)*(rho - X(3)) - X(2);
    dx(3) = X(1)*X(2) - b*X(3);
endfunction
// Using LSODE to solve the ODE system.
clear all
global rho;
global sigma;
global b;
k = 1;
ssig = 7:0.2:15;
for sigma = ssig
  rho = 28; 
  // sigma = 10; 
  b = 8/3;
  t = 0:0.01:100; X0 = rand(3,1);
  X=ode(X0,0,t,lorenzatt);
  // param3d(X(1,:),X(2,:),X(3,:))
  uu(k) = mean(X(1,:).*X(2,:));
  k = k + 1;
end;
plot(ssig,uu,'g')

 

[Coldcall]

Vanesch,

"It turns out that that average is, even though calculated on the basis of a solution to a chaotic system, rather "stable"."

Thats a good point though because chaotic systems are stable. Chaotic behaviour has nothing to do with instability. The term chaos refers to the unpredictability because of sensitive initial conditions.

Hence why we define some chaotic systems as self-organising because they appear able to maintain a status quo (within a limit cycle) creating long term stability through positive and negative feedbacks. What better example do we have than a climate system that has remained stable for some billions of years.

The agw proponents would have us believe this climate stability is now endangered by our moderate increase in Co2 emissions. Maybe they are right, but i suspect they are not.

 

[vanesch]

Vanesch,

"It turns out that that average is, even though calculated on the basis of a solution to a chaotic system, rather "stable"."

Thats a good point though because chaotic systems are stable. Chaotic behaviour has nothing to do with instability. The term chaos refers to the unpredictability because of sensitive initial conditions.

I think you are pretty confused about what "chaotic" actually means. It has a rather well-defined mathematical meaning, which has been discussed before in this thread.

You don't seem to have noted what this little example illustrates. It illustrates that you can have a chaotic system (the Lorenz system here, a very simplistic "weather forecaster"), of which certain average quantities (here taken to be < x1 x2 > ) which correspond to "climate" which is "average weather" are nevertheless rather well-defined and can be calculated, and moreover, of which these averages can be calculated as a function of a varying external parameter (here sigma). Nevertheless, all the "solutions" to the lorenz system that I calculated were "wrong" simply because it is a chaotic system and that my computer has finite numerical resolution. So all these numerical solutions have deviated from the "true" solution after small time intervals (although within these time intervals, they were each time rather good approximations).
But even with these "wrong" solutions, I could calculate a rather well-defined average, which was reproducible, which didn't vary wildly with initial conditions, and which had a smooth dependency on sigma.

So for this chaotic "weather" I could calculate rather well-defined "climate", and I could also calculate the influence of a changing boundary condition (sigma) on "climate" - even though the underlying "weather" is totally chaotic.
(again, I need to emphasise that this is a toy example for illustrative purposes only, and has nothing to do with a real climate system).

Hence why we define some chaotic systems as self-organising because they appear able to maintain a status quo (within a limit cycle) creating long term stability through positive and negative feedbacks. What better example do we have than a climate system that has remained stable for some billions of years.

Don't confuse issues please, so-called self-organisation has nothing to do with the definition of a chaotic system as we take it here.

The agw proponents would have us believe this climate stability is now endangered by our moderate increase in Co2 emissions. Maybe they are right, but i suspect they are not.

Absolutely not. You should maybe try to understand what the scientific AGW claim is. It is not about "rendering the climate chaotic", or "rendering the climate instable" or something of the kind. It is about changing the climate under the influence of human activities. And changing the climate means "changing average weather".

These changes might be relatively large and we might not like the new "average weather".

So the whole idea is to try to estimate as well as we can, what will be the "new average weather" as a function of certain projections of human activities in the near future, and how much it will be different from the current "average weather".

So for the near-term projections (next century or so), any "chaotic behaviour" of the climate system itself doesn't really matter - and these are the only projections that matter on the level of political and societal decision making.

There can be an academic question of whether on the very long run, the 30-year weather average itself (climate) has a chaotic dynamics - in other words, whether the chaotic behavior of the underlying weather dynamics has very slow components that exhibit themselves a chaotic dynamics. I guess that's an open question, but it has nothing to do with the social implications of AGW. The little bit of trajectory that we need to find out about, namely the next century or so, has nothing to do with this potential very-long-term behaviour of the weather/climate system.