Chaotic Systems are not Predictable

Although the climate definition you've given above doesn't allow for chaotic behaviors, it seems that the nonlinear PDEs that we use to model the climate do. How do we reconcile the two?

Hi Sean

The mathematics of chaos are over my head, but climate models do not exhibit chaotic behaviour in multi-decadal temperature trends. There is a very technical and extensive discussion over at the original blog on a related thread, where Gavin Schmidt weighs in, you might get your answers there. One point that sticks in my mind is that weather prediction is an initial conditions problem where as climate prediction is a boundary condition problem. You may know more than I what the technical significance of that is WRT the PDEs used in climate models.

"Climate is generally viewed as an average of weather patterns over some meaningful time period."

Meaningful for who? Civilization is a speck of time in the history of the planet. How could you even possibly say that 30 years is a meaningful number? I know that is what textbooks use, but it's completely arbitrary. Maybe 1 week is meaningful to a bee, but we can't predict that weather either.

Rafi, I think for the case of AGW, by CO2, a shorter period could be useful. Long enough to see CO2 climb by some amount and then see global temps work in sync with it.

So for a shorter period, say 30 years (Gavin requires at least 30 years for "climate" to be defined), we saw CO2 increase from 1979 to 1999 and global temps rose with it. For 1999 to 2009 CO2 also rose and we have seen global temps fall. Now the experts will analyze that and tell us what it means.

Quote: "So for a shorter period, say 30 years (Gavin requires at least 30 years for "climate" to be defined), we saw CO2 increase from 1979 to 1999 and global temps rose with it. For 1999 to 2009 CO2 also rose and we have seen global temps fall. Now the experts will analyze that and tell us what it means."

Well, the period from 1999 to 2009 may be answered by a few comments based upon data and extrapolations from such data:

1.) 1998 was warmer due to El Nino.
2.) CO2 has a logarhythmic nature, meaning that as more CO2 is pumped into the atmosphere, it takes that much more to have a positive effect in warming.
3.) Yearly changes in global mean temperature do not change the overall warming trend.
4.)Cloud dynamics as of late have shown alterations in the overall greenhouse effect, reducing the amount of radiation (temporarily) being held at or near the Earth's surface.
5.) Thermohaline slowing/shutdown may also be altering heat transfer as well.

As far as 30 years being used to define climate; I agree from the perspective of applying a mathematical trend line, heck we can even look at 50, 60, 70, 100 years, etc for a trend line, however, 5 years can be seen as climate, so as long as caution is used in not attempting to eliminate the trend.

Although the discussion is thoughtfully presented here, certain elements are incorrect.

Mathematical definition of what the essential elements of chaotic systems are very clearly described, and each of the principle elements is present in the interconnection of atmospheric elements that constitute "climate." One can dislike the fact that climate is chaotic - but one must accept that the definitions apply.

The suggestion that perturbations in a system will cause a change in a certain direction does not disprove that climate is chaotic. The appropriate question to ask about one perturbation or another is - how much? Always the same? This is the part which is not clearly predictable.

A mistake is made here in inferring an identity between chaotic and stochastic (random) system. Chaotic systems are not random at all. No physical system could be clearly random.

Glacial/interglacial cycles occur regularly for long periods, and then stop and restart. That's a common characteristic of chaotic systems - apparent stability, then wild instability, then a reappearance of stability.

Chaos theory has certain things to say about the limits on predictability. One may suppose that one knows ALL of the parameters at one time point - a daunting amount of information - but be unable to extrapolate to a later time.
Again, "broadly deterministic responses to forcings" does not prove a system non-chaotic.

Similarly, chaos theory has certain restrictions upon what can be known by means of statistical analysis, such as "averaging," etc. These measures may have some retrospective validity, but little or no predictive utility.

Good run at it, though.

Hi B. Troglodyte,

Thanks for the thoughtful and substantive comment. I have no doubt you know much more about chaos theory than I, but your assertion that climate is chaotic needs a bit more justification. One thing I have read that may be relevant is that weather prediction is an initial conditions problem, whereas climate prediction is a boundaries problem. So even though they both deal with interconnection of atmospheric elements, they are in fact fundamentally different.

You may be interested in some very technical discussion (over my head, I freely admit) that went on on another article at my original site here:
http://illconsidered.blogspot.com/2006/03/models-are-unproven.html

Thank you for the kind reply. I have glanced at the reference page, and will go through it carefully.

As I understand it, all that it takes for a system to truly BE chaotic and operate in a chaotic manner is:

a) small differences in STARTING conditions get amplified into bigger differences in later outcomes due to the nature of the systems. That's the "Butterfly Effect."

b) The system "topologically spans the space," which simply means that you CAN get there from here. Pretty much all roads in the Western Hemisphere are connected - you can drive to Rio Janeiro from anywhere in the US.

c) The elements are close enough to interact with each other.

Further elements are of interest to mathematicians, and state interesting and useful things; but can add to the confusing nature of the topic to observers - things such as nonlinear differential equations and attractors and such.

If one looks at physical conditions of the atmosphere, within a very broad boundary of earth and space, there are no intervening walls or boundaries. The atmosphere is "topologically transitive" - you can get there from here.

The Wikipedia reference (Chaos Theory) is quite good, but offers the conditions of chaos in a more mathematical way, less easy to comprehend:
"A it must be sensitive to initial conditions,
B it must be topologically mixing, and
C its periodic orbits must be dense."

Gavin certainly offers some interesting insight into a question which has troubled me - how valid it to use statistical methods in presenting the results of chaotic systems? He discusses Liapunov functions, which are a bit over my head, and seems to state that the averages converge. I'm just not sure how this could tell us much.

I think that the concept of "Chaos" gets tossed about as a political chip, when it might actually tell us something about how the system works. My bias is that it affects the toughest part of the AGW debate - balancing degree of certainty with degree of response - which is a hard thing, indeed.

AGW is a good test of whether we deserve the label "civilized" or not. It strikes at the heart of our self-admiring claim to be an "intelligent life force." We might be forced, in fact, to show our chips and act intelligently - are we up to it?

Then I guess where the climate might escape the category of chaotic would be on point A. Climate models, at least, are not sensitive to initial conditions, in fact that is one of the ways they "kick the tires" so to speak. If a model initialized with a variety of starting conditions does not always come to an equilibrium state given static forcings it is taken as a problem. Of course, that is the model, not the reality.

Again, I would like to emphasis that spatial and temporal scale is central to this question. I think the evidence is very good that for global indicators like average surface temperature and on timescales greater than ~30 years and less than several thousand, the climate system does not exhibit the properties of a chaotic system. Looking back over geological history and into the distant future we could well find different characteristics.

Bringing this back to the level of policy choices, I think you agree that this is hardly a reassurance and a reason keep poking the hornet's nest!

It is important to understand what sensitivity to initial conditions means in chaos theory and what it does not. Chaos theory has many examples of strange attractors such as the Lorenz attractor. These attractors are considered chaotic because if you calculate them out to a certain period of time or a certain number of iterations, then you calculate them to the same period of time or number of iterations with slightly different starting values, you get a very different result and how the result will vary isn't easily predictable from how the starting conditions varied. However, they are considered attractors because they have a characteristic behavior that is not dependent on their initial conditions. Typically when producing an image of a strange attractor, you pick a starting point at random, then you draw the values covered over a certain range of iterations/time, and if that range is long enough your picture of the strange attractor will look like anyone else's, because it covered roughly the same values, though maybe in a different order. So in that sense they are very predictable and not at all sensitive to initial conditions.

I'd imagine climate models are in this way similar to Lorenz's models that produced the butterfly effect. You change the initial conditions a little, and on a specific day in 2080 when Miami had blue skies and Iowa was suffering a severe drought, now Miami is getting hit by a class 5 hurricane and Iowa is flooding. But that's weather, not climate. We're interested in the amount of rainfall Iowa gets in a year, the average summer temp, the average winter temp, as well as statistical distributions for these, not the weather on any given day. And that is far more predictable, and models that produce the kind of chaos seen in weather will nonetheless give predictions about climate.

Basically, if climate were as unpredictable as weather, there would be no such thing as climate. We would not be able to say this summer, "when winter comes it will be colder"... weather is not predictable even one month out so how can we say what will happen half a year from now? But climate remains predictable, ice ages don't happen at random and they don't happen in a decade.

The signature of chaotic climate involves large flucuations followed by transition to a new stable state. Transition points to new states have been identified in 1910, the mid 1940's, the mid 1970's and 1998/2001.

Ocean and atmosphere data suggest that this is very real - note the big flucuation around the turn of the millenium and the seeming but surprising transtition to a stable but cooler state subsequently?

@Robert Indigo Ellison: what cooler state? The last decade has been the warmest decade in the history of our temperature measurements.

RIE is talling about the steep run-up to 1998, then a stall to a plateau slightly below the peak. But yes, the warmest decade, but not ramping up.

I know what RIE is talking about, and he's wrong.

trying to follow but doesn't this call for a thread switch?

Skip

Marco,
Please enlighten us, for it all seems to follow what is familiar.

Skip,
All seems *chaotic*, what are you driving at?

PaulinMI: it really is not that hard. He's referring to the various "warm, then cold, then warm" oscillations brought forward by e.g. Don Easterbrook (and a host of others). Based on that they propose a "cooling" for the next x-years. There is no mechanistic explanation, nor any proper statistical handling of these supposed oscillations, and if they are supposed to have such major influences, their influence would show up on a shorter time-scale, too. They don't. Ergo: hypothesis rejected, start again.

Note also that RIE refers to *regimes*, which means he himself would have to dismiss using one year (1998) as a reference point. But then, by extending that same logic, the current proposed 'cool' period isn't 'cool', since it is much warmer than the previous period.

I'd imagine climate models are in this way similar to Lorenz's models that produced the butterfly effect.

Marco,
Thanks for that explanation.
Please note in post 11 RIE does not mention "regimes", but single point transition dates, all of which are clearly visible on a temp data graph over the years mentioned.

[In discussing a graph, is it not appropriate to mention a "point" to describe the location of interest?]

He also mentions a "cooler state", and I assumed he meant "than the peak". He did not mention cooling for the next years. Again, this higher temp plateau is clearly visible as above historic temps. This describes the time/temp data graph quite well, and does not claim cooling from an unknown source. But rather the continued step-wise escalation of temperatures.

One could also assume that this break from a constant rise does not mean AGW is over, but continuing in the way expected.

Thanks for the flattery, Marco, but my concern was not that sophisticated--at least not in terms of knowing the theorists' names.

It just looked to me like it was turning into another 1998-was-the-hottest-year-on-record schpiel.

Skip

skip,
Does it matter how and which data is looked at to determine the hottest year ?
http://woodfortrees.org/plot/wti/last:160/plot/wti/last:160

http://woodfortrees.org/plot/wti/last:160/trend/plot/wti/last:160/plot/…

Hands up those who are familiar with the term 'outlier'.

Dappledwater - (puts hand up)

Well, it's settled then.
(hands up)

Hand up . . . different thread?

Skip

This describes the time/temp data graph quite well, and does not claim cooling from an unknown source. But rather the continued step-wise escalation of temperatures.

I think the basic definition of climate as a weather average is wrong. Rather weather is an expression of climate.

The nature of climate as a dynamically complex system is not in question. Not in the IPCC, realclimate or anywhere else.

Climate is chaotic. Models - just like Lorenz's original three equations - are chaotic and the results are - or should be - expressed as a probability distribution. Ensemble projections are used to average out emergent properties. Complex systems are theoretically determinant - modellers are looking for 2000 times more computing power - but practically incalcuable.

You may indeed change one parameter and get a short term change. Volcanoes cause cooling in the very short term, changing solar intensities changes temperature a little. Yet if the changes exceed a threshold value climate is precipitatied flucuation and then into a new state. And yes - greenhouse gases are included in these ordered forcings.

Climate behaves as a nonlinear oscillator on scales from ENSO to ice ages and beyond.

I will refer to this paper.

http://www.nosams.whoi.edu/PDFs/papers/tsonis-grl_newtheoryforclimatesh…

No regimes - no cycles - simply shifts in climate after a critical threshold is reached. Climate should be viewed - in terms of complex system theory - as a forced nonlinear oscillator. There is no such thing as simple causality in climate.

Ice ages are indeed the result of climate behaving as a non-linear oecillator. Climate doesn't simply respond to orbital changes but as a result of energy changes cascading through ice, clouds, winds, atmosphere oceans and biosphere.

There is a new theory of climate - http://www.nosams.whoi.edu/PDFs/papers/tsonis-grl_newtheoryforclimatesh… - it goes beyond the simple physics of gases and radiation to modern physics of complex systems. It views climate on decadal timescales as an emergent property of complex and dynamic Earth systems.

Is chaos predictable? It is not predictable if there is another climate shift in the next decade or so, one a few decades after that and so on. Chaos theory explains why there has been no warming since 1998. This must deserve to be the next line in sceptical argument â except that they donât seem to understand it or realise it doesn't let us off the carbon hook. But the temperatures stubbornly refuse to rise and thus the battle is lost and it will be another generation or 2 before action is taken.

I am, at any rate, missing the point of science that needs to be definitive and have scary answers (e.g. James Hansen and the Venus scenario). This is particularly the case where science is synthesis rather than hypothesis and experiment.

There are three real human questions about climate.

1. Should we continue to change the composition of the atmosphere? No.
2. What is the cheapest and most effective way to transition economies - I call this the organisational and technological path - it is said by economist Bjorn Lomborg's Copenhagen Consensus Group to be 300 times more cost effective than cap and trade methods.

Organisational methods could include such things as this geo-engineering proposal - http://dirt.asla.org/2009/11/20/new-geoengineering-idea-turning-deserts… - for carbon sequestration involving afforestation of deserts in Africa and Australia. A mega project in greening the Sahel has potential not only to sequester carbon but to bring safe water, sewerage, power, education and health services to the heart of Africa. The proposal would have some ecological show stoppers in Australia - but a project to restore carbon stores to pre-European levels in Australian soils has as well productivity, fire risk and conservation benefits. It is easily possible to do something other than an inefficient, complex and market distorting government imposed limit on carbon emissions. This latter approach seems to stem in good part from a sincere desire, based on the limits to growth of the Club of Rome or similar, to reduce global wealth to some ostensibly sustainable level. An approach likely to be counter productive with respect to both population and conservation. Population growth declines and environmental standards increase with increasing GDP.

There are a number of technologies that are available and in use, are 10 years or less away or can be delivered within 20 years. Thin (and therefore cheap) solar panels are a dream source for many of the world's poorest who don't have adequate energy supplies. Generation 4 nuclear plants have a 40 year development history and are being built and operated now. A new model designed at Los Alamos - the US government laboratory famous (or infamous) for the first atomic bomb - will be available commercially from 2013. Generation 4 nuclear plants can't melt down, are modular and flexible, can't be used for weapons production, use a range of nuclear materials (conventional nuclear waste, uranium, thorium and recycled weapons plutonium) providing virtually limitless fuels, burn two orders of magnitude more efficiently than conventional reactors and create much shorter lived wastes (hundreds of years rather than hundreds of millennia). Endless energy for endless purposes through clever fuel processing and materials. The Gen 4 International Forum - which Australia should join given our huge nuclear fuels advantage - has a technology roadmap for 6 different designs for different purposes to be delivered by 2030. In the interim there are Gen 3 and 3+ technologies to go on with. These are perfectly adequate in many locations and applications - and indeed there are hundreds of these plants ordered or under construction.

Geothermal, wind farms, solar concentrators, algal biofuels, oil recovery from waste, co-generation, carbon efficiency, coal to gas conversion, coal seam methane production to name a few more examples. There are technologies available now that are cost effective and others where costs are coming down and technologies are improving. This is not market magic - but the inevitable outcome of the rapid rate of technological innovation. Instead of spending trillions on carbon regulation - spend, mostly by the private sector, a fraction of that on research and development and create better and cheaper energy options for the world.

3. What does the science say?

Technology and organisation having changed the trajectory - science (having done the job of provisionally warning) can return to being fun explorations of the universe around us. I am particularly fond of trying to reconcile evolutionary theory with the space/time continuum but some people just don't have a sense of humour.

RIE

"Climate is chaotic"

Of course it is mate. That's why:

(1)sometimes boreal summers begin in Dec, sometimes March. It's hard to predict year to year with all that chaos.
(2)as you amble further north or south on the globe, it sometimes gets hotter, sometimes colder, hey, sometimes its 25 deg C all the way to Vostok. Never can tell......
(3)the prevailing winds that sweep the globe in an unending howl between 50-75 deg latitude south, with no great landmass to impede them, sometimes stop for a cup of tea and then turn around and go the other way for a year or two
(4)if you're living at 700m altitude and you're feeling the cold, you never know whether to head for sea level or climb to 4000m for reprieve.
(5)as you move further from any given sun there seems to be no correlation between how close a planet is to its parent star and how warm or cool that planet gets on its star-facing side
(6)and on.... and on..... and on.......

Research your subject before you start with your rank amateur ramblings. You might even learn something. An area's climate doesn't stop being the average of its weather just because you say so.

Start here:
geosci.uchicago.edu/~rtp1/ClimateBook/ClimateBook.html

To add one very specific point to what Matt said about RIE's post ... in his very first paragraph RIE says

new theory of climate [...] views climate on decadal timescales as an emergent property of complex and dynamic Earth systems.

Um, that's what the best models in use by mainstream climatologists already do. Decadal and shorter variations emerge from the simulation runs every time, and have statistical properties similar to known variations like the ENSO. Unfortunately, the models *don't* predict the exact evolution of such variations, but that's why we call them chaotic - or at least semi-chaotic.

All this quarreling about what "climate" or "weather" might be is a struggle about words. Let's just forget about it and turn to statements like "According to all currently known facts and mechanisms, the mean surface temperature in 2100 will be in the range of 2 to 8 °C higher than today, with the probability maximum at 5°C." Basically these kind of probability statements are all we have in our hands. So now anybody may come and tell me, that climate is defined by a 10 year period, a 50 year period or a 100 year period - it doesn't change a bit to what we know (knowledge, as always in science, understood as probability distribution.)

In climate research and modelling, we should recognize that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.

Bob

And from that I take it that you are a climate change denier, and your position is that, because we supposedly cannot predict the future, we should do nothing.

Would that be a reasonable summary of your worldview? If not, please let me know where I have it wrong so we can have a rational discussion.

It's amazing that Bob Grant appears to have posted a comment without reading the post in question.

From the OP (my bold): "Now, I know that quite a few people believe that climate is a chaotic system, and maybe on some large scale levels, it is. But it is not chaotic on anything approaching the kinds of time scales humans need to be mindful of. Frankly, I have never heard any objective argument supporting that notion, only arguments that take that as a given. Certainly the march of the seasons is nice and regular, and determined directly by the orbital inclination of the earth. If a large volcanic eruption occurs, the global temperature drops for a few years quite predictably. Diurnal cycles show the very direct influence of insolation changes on the system. Clearly, if you turn down the sun, the temperature drops. Clearly, if you throw a bunch of SO2 into the stratosphere, the temperature drops. Clearly, if you turn the surface completely white, the temperature drops. And clearly, if you double the amount of an important GHG in the atmosphere, the temperature rises."

mandas & Chris,

Sorry about that. I forgot the citation:

"In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible."

- Intergovernmental Panel on Climate Change

http://ipcc.ch/ipccreports/tar/wg1/505.htm

You should be reading the FAR, but never mind.

What is the answer to mandas's question in post 34, Bob? You selected out this quote from the IPCC. Does this mean you accept their findings?

Surprisingly enough, the complete paragraph from which Bob extracted his little gem gives good details of what the writers are really getting at ....

In sum, a strategy must recognise what is possible. In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible. The most we can expect to achieve is the prediction of the probability distribution of the system�s future possible states by the generation of ensembles of model solutions. This reduces climate change to the discernment of significant differences in the statistics of such ensembles. The generation of such model ensembles will require the dedication of greatly increased computer resources and the application of new methods of model diagnosis. Addressing adequately the statistical nature of climate is computationally intensive, but such statistical information is essential.

Oh look. That's exactly what analysis, models and reports have done for the last umpty years.

I expect this was supposed to be interesting or contentious or something-other-than-boring. But it's not.

skip / adelady

It would appear that my assessment of Bob was 100% accurate. He is a denier - but a bad one at that.

He demonstrated one of the traits of a denier - quote mining. But he did provide us with the link so we could read the ENTIRE quote, and not just the selected piece he used to try and prove his case.

Some advice Bob. If you want to get better with your anti-science denialism, don't reference your sources. It just makes you look foolish when we check. And we will check.

On the plus side, maybe there is hope for Bob. If he keeps referencing from legitimate sources, maybe some science and evidence may actually seep into his brain.