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« Lord Turnbull advises caution | Main | Wegman paper retracted »
Monday
May162011

Non-linear system is linear

Only in climateland - Willis Eschenbach's post at WUWT is very interesting. He shows that the output of a major climate model is essentially just a lagged linear combination of its inputs. This is kind of odd when what they are modelling is a non-linear system.

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Reader Comments (29)

Willis' post is only about the metric of global mean temperature. Isaac Held makes the same point here http://www.gfdl.noaa.gov/blog/isaac-held/2011/03/05/2-linearity-of-the-forced-response/ and the same understanding has underpinned the use of Wigley's MAGICC to simulate GCMs, I don't see that there is anything all that "odd" about this, though it's definitely not publicized in IPCC.

May 16, 2011 at 1:03 PM | Unregistered CommenterSteve McIntyre

I don't find Willis's result particularly surprising. Look at it from the perspective of the energy in the terrestrial system, incorporating land, ocean and atmosphere. The forcings which Willis used -- solar, greenhouse gases, and volcanic effects -- represent additional energy input (above the initial equilibrium value). Energy leaves via infrared radiation, and this increases according to temperature. At a very coarse level, the additional energy is convertible into a temperature increase, which increases the outgoing energy until balance is achieved. All of the interesting non-linear effects (weather) re-distribute the energy between different components of the terrestrial system, e.g. tropical/poles, ocean/atmosphere. Feedback cycles such as increased cloud formation due to increased temperature exist, but can be taken to have an average effect, which is included as part of Willis's "lambda" factor, determined post hoc. Willis's "tau" factor is the (globally-averaged) relaxation time in the cycle of heating the atmosphere until it achieves radiation balance.

It's the averaging (of the global temperature) which smooths out the considerable variations which we observe over regions and seasons.

May 16, 2011 at 1:43 PM | Unregistered CommenterHaroldW

HaroldW

Well put.

May 16, 2011 at 2:14 PM | Unregistered CommenterBBD

HaroldW writes:

"All of the interesting non-linear effects (weather) re-distribute the energy between different components of the terrestrial system, e.g. tropical/poles, ocean/atmosphere. Feedback cycles such as increased cloud formation due to increased temperature exist, but can be taken to have an average effect, which is included as part of Willis's "lambda" factor, determined post hoc."

To assume that this is how the model works is to assume your conclusion in your premisses. Given Willis' challenge, the response needed from the modelers is that there is some internal complexity involving several terms that are not eliminable from the model. But none of the modelers have explained their list of primitive predicates and why even one of the predicates is not eliminable. Until such explanations are given, Willis point is made: the models are a black box whose output is a linear transformation on inputs. After all, science is criticism and sceptics need for modelers to explain the structure of their models so that we can criticize them. That is the only way science advances.

May 16, 2011 at 5:53 PM | Unregistered CommenterTheo Goodwin

Theo Goodwin

Have a look at the link to Isaac Held's GFDL blog that Steven McIntyre provides in comment #1.

May 16, 2011 at 6:06 PM | Unregistered CommenterBBD

Why, BBD,
Shouldn't we need to explicitly state why it is necessary to incorporate complexity into a climate model if a simple linear equation gives the same output?

Consider a person walking. From a distance, all one can percieve is a mass propogating on plain land. Only on closer examination, is revealed a complex musculoskeletal system, coordinated by multiple spinal reflexes and cerebellar feedback loops and a functioning vestibular system, all completely essential to the simple act of walking.

Understanding and reproducing all these subsystems is necessary and perhaps interesting, to someone who wants to build a walking robot. It is not at all so, if all one wants to calculate is how far and in what direction the walking person did go.

If you start building a walking robot when I ask you the latter question, it is most definitely not an obvious thing why you started doing so.

Isaac Held, in this instance, is a walking robot builder. His post addresses the internal queston of the apparent linearity of model outputs, not the question of why it is needed to model at all, if their output is linear. His answers about the why his complex robot can only accomplish the simple task of tottering along in a straight line from A to B will be unsatisfactory to the question of why it is necessary to build such a complex, delicate machine if all one wants to do is simply translate from A to B.

Therefore, simply sending people on hand-wavy wild goose chases will not serve our purpose here.

May 17, 2011 at 4:58 AM | Unregistered CommenterShub

On any short timescale you can approximate a non-linear system with a linear system.

What would be interesting is a factor analysis of the many time-series. I've not looked at the Willis calculations as they are excel spreadsheets so they are highly obfusticated. ClimateAudit is redoing them in 'R' which will help, but converting the analysis to use factor-analysis in 'R' will be best.

May 17, 2011 at 9:46 AM | Unregistered CommenterJerry

Some posters seem to have missed the point of Willis' 'black box' statistical exercise, which (to me) was to point up the essential simplicity of the black box model which seems entirely unrelated to the Climate Scientists' absolute need for computers with mega-terrabyte capacity to run their models and acheive an adequate level of accuracy. John Lockwood's recent statement about the preferrence of models over direct observation seems to reinforce Willis' point.
Or have I missed something?

May 17, 2011 at 9:52 AM | Unregistered CommenterAlexander K

Shub

Therefore, simply sending people on hand-wavy wild goose chases will not serve our purpose here.

Please, do tell that to Steve McIntyre, who originally posted the (helpful, illuminating) link to Held's blog.

May 17, 2011 at 1:18 PM | Unregistered CommenterBBD

Commenters should never assign homework. It leads to exactly this situation. BBD, if you have a point that is explained or supported by a post by someone else on another blog, you should make your point and support it in your own words before sending commenters to the other blog. What we are doing here is debating. If you refuse to speak your mind then you are not participating. Then you have the "whatever" to berate someone for not doing the homework you assigned. Excuse me, but I am American and do not recognize a noble class or a higher class of any sort.

May 17, 2011 at 1:57 PM | Unregistered CommenterTheo Goodwin

Theo Goodwin

I was attempting to be constructive by pointing to a relevant link. Not 'assigning homework'.

And this:

Excuse me, but I am American and do not recognize a noble class or a higher class of any sort.

Does not support your claim to be doing this:

What we are doing here is debating.

If you want a serious conversation, then be serious.

May 17, 2011 at 2:33 PM | Unregistered CommenterBBD

Theo G, while I agree with you, I have to say that I much prefer discussions to debates - implying a focus on pooling of knowledge rather than attempting to prove someone 'wrong'?

May 17, 2011 at 2:34 PM | Unregistered CommenterChuckles

Theo Goodwin

Then you have the "whatever" to berate someone for not doing the homework you assigned.
.

What are you talking about? Where do I 'berate' you? The more I read your last, the odder it looks.

May 17, 2011 at 2:44 PM | Unregistered CommenterBBD

Complex dynamic systems incorporating three or more interacting variables are inherently chaotic/fractal, non-random but indeterminate (Lorenz, 1960; Mandelbrot, 1974). Despite micro-scale approximations analogous to decomposing a circle's circumference into infinitesimal chords, such non-linear systems are not amenable to extrapolation via y-intercept and Slope.

Due to sensitive dependence on initial conditions (Lorenz's notorious "butterfly effect"), over-simplified "climate models" thus compound micro-minuscule errors to become entirely useless, fatally flawed by very nature. Conveniently ignoring this reality means that even the most massive computational exercises fall to pieces in short order, becoming not just wrong but cyclically inverted-- ridiculously, 180-degrees wrong.

AGW hysterics aka the Green Gang of extreme-reactionary Luddite thanatists --cf: Ehrlich, Holdren, Keith Farnish, plus pilot-fish such as Briffa, Hansen, Jones, Mann, Trenberth et al.-- by mathematical/physical definition cannot be other than egregious canonical frauds. Not objective, rational, scientific debate but "Argumentum verecundiam" is their sole stock-in-trade, and on that basis they will lose out every time.

May 17, 2011 at 4:39 PM | Unregistered CommenterJohn Blake

John Blake

You say:

Due to sensitive dependence on initial conditions (Lorenz's notorious "butterfly effect"), over-simplified "climate models" thus compound micro-minuscule errors to become entirely useless, fatally flawed by very nature. Conveniently ignoring this reality means that even the most massive computational exercises fall to pieces in short order, becoming not just wrong but cyclically inverted-- ridiculously, 180-degrees wrong.

Why then is the multi-model mean referenced by AR4 approximately 0.2C/decade (1979 - present) and observations show approximately 0.15C/decade over the same period?

While this is clear evidence that the MMM is biased high, does not the broad agreement in trend invalidate your strongly worded critique of GCMs?

Could you perhaps explain what I have not understood here?

Please do not misunderstand. I am as cautious about what we may learn from the output of GCMs as many here, but you argue that they are "cyclically inverted-- ridiculously, 180-degrees wrong" and I see no evidence of that.

May 17, 2011 at 6:33 PM | Unregistered CommenterBBD

BBD
In all the hand-waving, you have managed to not answer Theo's original question. I'm not saying you have to,...but you haven't

Instead you asked to go and read a web page, and then told him that he was not being serious.

May 17, 2011 at 6:43 PM | Unregistered CommenterShub

Shub

Blatant distortion, even by your standards. Stop it. It makes you look bad.

May 17, 2011 at 6:56 PM | Unregistered CommenterBBD

And why not have a go at Steve McIntyre and HaroldW while you are at it?

Surely you have no special motive for attacking me? Or do you ;-)

May 17, 2011 at 6:59 PM | Unregistered CommenterBBD

Shub

Just one more thing.

Why, if you feel so strongly that there is a problem with the GCMs, do you not take it up with Isaac Held? I'm sure he'd be more than happy to discuss the detail with you.

May 17, 2011 at 7:04 PM | Unregistered CommenterBBD

Calm down BBD, your in danger of becomming a gate keeper. "peace dude".

May 17, 2011 at 10:43 PM | Unregistered CommenterGreg Cavanagh

BBD, you are coming across as bit self-righteous, shrill and judgemental on this thread. I usally enjoy your comments, but not at the moment.

May 18, 2011 at 1:20 PM | Unregistered CommenterAlexander K

Alexander K

Please, go back to the beginning of the thread and read it carefully.

You (like several others here) have been misdirected by Shub at 4:58pm May 17. His calculated intervention set off Theo Goodwin, (who I was trying to help and did not at any point 'berate' - read the thread).

Then I responded to John Blake, and Shub has another go. Then I got irritated - which was fair enough.

Just read it all again, please. Same goes for Greg Cavanagh.

May 18, 2011 at 1:30 PM | Unregistered CommenterBBD

BBD, I read the entire thread quite carefully. I haven't been misdirected by anyone, let alone Shub, and I AM capable of thinking for myself. I thought very carefully before writing as I was quite nervous of offending you, but I am now more than slightly irritated by your tone. I was initially, surprising as it may seem to you, attempting to be helpful.

May 18, 2011 at 3:16 PM | Unregistered CommenterAlexander K

Alexander K

Er, hang on.

What tone? This is getting very strange. I respectfully request that you re-read the thread and you bite my head off. Why?

Everything I have said is self-evident and there to be seen by all. Starting with the way Shub carefully poisoned the thread.

Perhaps you are unaware that he and I have had a protracted disagreement (see Jones Live Blog) and that he is continuing that here? Rather pettily, IMO.

May 18, 2011 at 3:57 PM | Unregistered CommenterBBD

Please, note the use of commas to denote respectful requests, eg:

Please, go back to the beginning of the thread and read it carefully.

and:

Just read it all again, please.

If I've written carelessly, then I freely apologise. But you do seem to have the wrong end of the stick.

May 18, 2011 at 4:01 PM | Unregistered CommenterBBD

BBD, I have read the entire thing again and have no idea how I (and others) was expected to know that you and Shub were doing a 'handbags at dawn' thing with each other. Okay, I metaphorically opened my big mouth thinking I was helping smooth something over that made you step aside from your usual thoughtful persona. My apologies. I hope normal (adult) discussions can resume.

May 18, 2011 at 9:07 PM | Unregistered CommenterAlexander K

Alexander K

Thank you for the above and I'm sorry I compounded things with careless writing.

May 18, 2011 at 11:03 PM | Unregistered CommenterBBD

Hey BBD
I didn't poison anything. I ran into Theo in the WUWT thread by Willis and he seemed to agree with me. When he posted the concept here, (that we need to explicate why we need complex models if simple linear ones provide similar output), your initial post did seem like a 'homework assignment'. So I just chimed in, because unlike WUWT or even CA, it becomes possible to have a focused discussion here sometimes. Moreover partly taking your advice, I have looked at the CA thread and I did feel Steven Mosher's comments and a few others' there are also similar - somewhat avoidant of confronting the actual implication of Willis' findings.

We need to actively confront the implications here, to the extent our puny minds can. For eg., I cannot simply shake away the cognitive destructive interference that occurs from digesting what Willis describes. I cannot honestly say that Isaac Held, or Mosher or anyone has convinced me otherwise. Look at McIntyre's comments to Bart V for example, he says something I completely agree with as well.

May 19, 2011 at 12:23 AM | Unregistered CommenterShub

Just to be explicit, I did not 'pick' on you, here, because of the uhi/tlt/jones thing. I knew it would look like that, but it was not.

May 19, 2011 at 12:27 AM | Unregistered CommenterShub

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