2011-07-02 05:45:20Chaos Theory & Climate Change
John Hartz
John Hartz
john.hartz@hotmail...
98.122.98.161

Given that the Earth's climate system behaves in a chaotic manner, can Chaos Theory be used, at least in part, to explain what,s going on?  

Do any of the climate models incorporate components od Chaos Theory?

Is the role of Chaos Theory addressed in any of the articles posted on SkS? (Based on a cursory serch, I suspect that the answer is "no".) 

2011-07-02 18:18:06short non-expert
jyyh
Otto Lehikoinen
otanle@hotmail...
85.77.32.144

AFAIK, all the models are "completely deterministic" so any chaotic results arise from the basic equations, which is why the modelers need to run several runs to get more robust results. The chaos inherent in the climate system is relevant in predicting local climates in short intervals, this is why the results of models are usually presented as 'average parameter during 2040-2060'. But I'm not an expert. I guess it might f.e. be possible to present a possibility some other location (than the one projected) will dry up based on chaos theory, but this would be a different calculation and not incorporated in the model. I guess this bugs the modelers quite a bit. Isaac Held's blog  has some more articles (#12 & #10 at least) on the models' performance in tricky subjects like chaotic behavior of weather and how they're showing in models.

2011-07-02 19:02:42
Dikran Marsupial
Gavin Cawley
gcc@cmp.uea.ac...
88.108.208.252

While weather is certainly chaotic, it doesn't necessarily follow that climate (long term statistical behaviour of the weather) is also chaotic.  If the physics of climate models is correct, they will exibit short term chaotic behaviour, but they can't be expected to be in phase with those actually observed on Earth.  However, this is not a problem as model projections are based on an ensemble of model runs, each of which will have differences in phase, so when the model runs are averaged out, the chaotic features cancel out and you are left with an estimate of "forced climate change", i.e. how the climate has responded to changes in forcings while ignoring the changes caused by chaotic variability.

AFAIK, climate models reproduce chaotic weather, but the forced response appears to be non-chaotic - if you repeatedly construct ensembles of model runs, the ensemble mean and spread is generally about the same each time.  Whether that is representative of the Earth cannot be easily determined without a stargate-type quantum mirror that would allow us access to parallel Earths! ;o)

2011-07-02 20:43:18
nealjking

nealjking@gmail...
91.33.98.246

Have you looked at:

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

2011-07-02 20:56:00
MarkR
Mark Richardson
m.t.richardson2@gmail...
134.225.187.197

"Chaos Theory" isn't so much something you build into a deterministic model, it's just a resulting behaviour of some systems.

 

It's just a tendency to diverge from very close initial conditions. An example of a chaotic climate might be that you would have one Earth with 1 W m-2 forcing and it warms by 0.5 C, and you have another Earth with 1.0001 W m-2 forcing and it warms by 5 C. That would be chaotic!

There is also a 'size' or 'rate' of chaos, and there are various ways of tracking this (such as the Lyapunov Characteristic Exponent, LCE). The movement of planets in the solar system is actually chaotic, so we can't tell whether in 6 billion years time a planet will be thrown out or not. But we can still predict with very good precision for hundreds of millions of years in the future - which is good enough!

 

Climate doesn't appear to be particularly chaotic, it seems to react pretty tightly to how much energy is available. But to account for chaos, climate models are run lots of times with very slightly different initial conditions. When you see a range of climate model outcomes (e.g. 1.1-1.9 C warming, best estimate 1.4 C) what you're getting are the statistics of lots of model runs and this fully accounts for any chaos in the models.

2011-07-02 21:27:31
Paul D

chillcast@googlemail...
82.18.130.183

I think Mark has pinpointed the issue.

Chaotic doesn't mean that a complex system can not be modeled, as in the solar system example.

Actually I think a simpler example is a double pendulum ??
The maths is well defined, but the output is chaotic.

I think climate is more predictable than a double pendulum, and climate is more complex. Anyway the point is that chaos would appear from the models output, you wouldn't program it in.

2011-07-02 23:47:31
Dikran Marsupial
Gavin Cawley
gcc@cmp.uea.ac...
88.108.196.254

@PaulD indeed ;o)

2011-07-03 00:28:18Muchos gracias...
John Hartz
John Hartz
john.hartz@hotmail...
98.122.98.161

to all of you for enlightening me on this issue. Perhaps I watched too many epsodes of "Numbers."

2011-07-05 17:55:52
Paul D

chillcast@googlemail...
82.18.130.183

Actually what does come out of the skeptic comments about Chaos are:

1. Attempts to confuse people reading their comments by stating that chaos means randomness and immense complexity, hence it is beyond the understanding of human brain and mind, which in turn means models won't work correctly until (if) we evolve with more brain capacity.

2. Others believe 1. because someone told them that and it sounds correct because the word chaos gives an impression of immense randomness. They then just regurgitate it.

2011-07-05 19:31:30
Riccardo

riccardoreitano@tiscali...
192.84.150.209

The layman idea of chaos is that anything may happen, an unbounded behaviour. On the contrary, chaotic systems may be bounded and even determistic, only they are very sensitive to the initial conditions. The double pendulum example used by Dikran is very appropiate.

Weather is chaotic, you may be wildely off in a one month forecast from now. Still, it is not unbounded, it will be august and I won't see freezing rivers in Sicily!

To expand Dikran's analogy, the double pendulum is weather. Immagine to add an upward translation of the pivot of the first pendulum and you have climate; you can't predict where the tip of the second pendulum will be but on average no doubt it will be higher.

An applet like the one for the double pendulum would be helpfull

2011-07-05 21:13:50
Dikran Marsupial
Gavin Cawley
gcc@cmp.uea.ac...
139.222.14.107

Riccardo, I have some ideas for an article based on the double pendulum with electromagnet (as described in the post I linked to earlier).  Ithink it can offer a useful analogy to many aspects of the way ensemble based climate projections are performed.  An applet would indeed be a good way to make it interactive.  Sadly it would need rather more time than I have at the moment.  I'd be happy to co-author an article with anybody who has the time to sort out the simulations etc.

2011-07-05 22:29:47
Paul D

chillcast@googlemail...
82.18.130.183

There are some apps around on the interweb.

Haven't tried them though. Just Google 'double pendulum simulator'.

2011-07-05 22:31:14
Riccardo

riccardoreitano@tiscali...
192.84.150.209

I'll give it a thought. Don't hold your breath though :)

2011-07-05 22:38:53
Paul D

chillcast@googlemail...
82.18.130.183

Java applet at Harvard uni:

http://www.math.harvard.edu/archive/21b_fall_03/doublependulum/index.html

2011-07-05 23:53:26New reference
John Hartz
John Hartz
john.hartz@hotmail...
98.122.98.161
 

scienceofdoom said on Models, On – and Off – the Catwalk – Part Three

July 5, 2011 at 10:22 am

In response to scienceofdoom on July 3, 2011 at 12:07 pm:

In Frontiers of Climate Modeling, Jeffrey Kiehl says: The study of the Earth’s climate system is motivated by the desire to understand the processes that determine the state of the climate and the possible ways in which this state may have changed in the past or may change in the future.. Earth’s climate system is [...]

There are many interesting papers out there. For example, from a name that people might recognize:

Can chaos and intransitivity lead to interannual variability?, EN Lorenz, Tellus (1990)

2011-07-06 01:58:58
John Hartz
John Hartz
john.hartz@hotmail...
98.122.98.161
 

scienceofdoom said on Models, On – and Off – the Catwalk – Part Three

July 5, 2011 at 8:10 am

In response to scienceofdoom on July 3, 2011 at 12:07 pm:

In Frontiers of Climate Modeling, Jeffrey Kiehl says: The study of the Earth’s climate system is motivated by the desire to understand the processes that determine the state of the climate and the possible ways in which this state may have changed in the past or may change in the future.. Earth’s climate system is [...]

eduardo:

I think the influence chaos for climate prediction is being in some sense overrated in some sense underrated. If the changes in the external forcing are large enough, chaos will not be that relevant to predict changes in the mean state..

..However, in the broad sense, if you change the energy balance by increasing the solar input or increasing greenhouse gases, temperatures tend to change. Chaos is a secondary agent. The annual cycle is a very obvious proof of this.

I think I am coming to understand this, probably somewhat slowly, through some simple (mathematical) experiments. Hopefully I will get around to demonstrating these points in a later article.

The key point seems to be how to assess this quantitatively.