Guest Post by Willis Eschenbach
Figure 1. The Experimental Setup
I keep reading statements in various places about how it is indisputable “simple physics” that if we increase the amount of atmospheric CO2, it will inevitably warm the planet. Here’s a typical example:
In the hyperbolic language that has infested the debate, researchers have been accused of everything from ditching the scientific method to participating in a vast conspiracy. But the basic concepts of the greenhouse effect is a matter of simple physics and chemistry, and have been part of the scientific dialog for roughly a century.
Here’s another:
The important thing is that we know how greenhouse gases affect climate. It has even been predicted hundred years ago by Arrhenius. It is simple physics.
Unfortunately, while the physics is simple, the climate is far from simple. It is one of the more complex systems that we have ever studied. The climate is a tera-watt scale planetary sized heat engine. It is driven by both terrestrial and extra-terrestrial forcings, a number of which are unknown, and many of which are poorly understood and/or difficult to measure. It is inherently chaotic and turbulent, two conditions for which we have few mathematical tools.
The climate is composed of six major subsystems — atmosphere, ocean, cryosphere, lithosphere, biosphere, and electrosphere. All of these subsystems are imperfectly understood. Each of these subsystems has its own known and unknown internal and external forcings, feedbacks, resonances, and cyclical variations. In addition, each subsystem affects all of the other subsystems through a variety of known and unknown forcings and feedbacks.
Then there is the problem of scale. Climate has crucially important processes at physical scales from the molecular to the planetary and at temporal scales from milliseconds to millennia.
As a result of this almost unimaginable complexity, simple physics is simply inadequate to predict the effect of a change in one of the hundreds and hundreds of things that affect the climate. I will give two examples of why “simple physics” doesn’t work with the climate — a river, and a block of steel. I’ll start with a thought experiment with the block of steel.
Suppose that I want to find out about how temperature affects solids. I take a 75 kg block of steel, and I put the bottom end of it in a bucket of hot water. I duct tape a thermometer to the top end in the best experimental fashion, and I start recording how the temperature changes with time. At first, nothing happens. So I wait. And soon, the temperature of the other end of the block of steel starts rising. Hey, simple physics, right?
To verify my results, I try the experiment with a block of copper. I get the same result, the end of the block that’s not in the hot water soon begins to warm up. I try it with a block of glass, same thing. My tentative conclusion is that simple physics says that if you heat one end of a solid, the other end will eventually heat up as well.
So I look around for a final test. Not seeing anything obvious, I have a flash of insight. I weigh about 75 kg. So I sit with my feet in the bucket of hot water, put the thermometer in my mouth, and wait for my head to heat up. This experimental setup is shown in Figure 1 above.
After all, simple physics is my guideline, I know what’s going to happen, I just have to wait.
And wait … and wait …
As our thought experiment shows, simple physics may simply not work when applied to a complex system. The problem is that there are feedback mechanisms that negate the effect of the hot water on my cold toes. My body has a preferential temperature which is not set by the external forcings.
For a more nuanced view of what is happening, let’s consider the second example, a river. Again, a thought experiment.
I take a sheet of plywood, and I cover it with some earth. I tilt it up so it slopes from one edge to the other. For our thought experiment, we’ll imagine that this is a hill that goes down to the ocean.
I place a steel ball at the top edge of the earth-covered plywood, and I watch what happens. It rolls, as simple physics predicts, straight down to the lower edge. I try it with a wooden ball, and get the same result. I figure maybe it’s because of the shape of the object.
So I make a small wooden sled, and put it on the plywood. Again, it slides straight down to the ocean. I try it with a miniature steel shed, same result. It goes directly downhill to the ocean as well. Simple physics, understood by Isaac Newton.
As a final test, I take a hose and I start running some water down from the top edge of my hill to make a model river. To my surprise, although the model river starts straight down the hill, it soon starts to wander. Before long, it has formed a meandering stream, which changes its course with time. Sections of the river form long loops, the channel changes, loops are cut off, new channels form, and after while we get something like this:
Figure 2. Meanders, oxbow bends, and oxbow lakes in a river system. Note the old channels where the river used to run.
The most amazing part is that the process never stops. No matter how long we run the river experiment, the channel continues to change. What’s going on here?
Well, the first thing that we can conclude is that, just as in our experiment with the steel block, simple physics simply doesn’t work in this situation. Simple physics says that things roll straight downhill, and clearly, that ain’t happening here … it is obvious we need better tools to analyze the flow of the river.
Are there mathematical tools that we can use to understand this system? Yes, but they are not simple. The breakthrough came in the 1990’s, with the discovery by Adrian Bejan of the Constructal Law. The Constructal Law applies to all flow systems which are far from equilibrium, like a river or the climate.
It turns out that these types of flow systems are not passive systems which can take up any configuration. Instead, they actively strive to maximize some aspect of the system. For the river, as for the climate, the system strives to maximize the sum of the energy moved and the energy lost through turbulence. See the discussion of these principles here, here, here, and here. There is also a website devoted to various applications of the Constructal Law here.
There are several conclusions that we can make from the application of the Constructal Law to flow systems:
1. Any flow system far from equilibrium is not free to take up any form as the climate models assume. Instead, it has a preferential state which it works actively to approach.
2. This preferential state, however, is never achieved. Instead, the system constantly overshoots and undershoots that state, and does not settle down to one final form. The system never stops modifying its internal aspects to move towards the preferential state.
3. The results of changes in such a flow system are often counterintuitive. For example, suppose we want to shorten the river. Simple physics says it should be easy. So we cut through an oxbow bend, and it makes the river shorter … but only for a little while. Soon the river readjusts, and some other part of the river becomes longer. The length of the river is actively maintained by the system. Contrary to our simplistic assumptions, the length of the river is not changed by our actions.
So that’s the problem with “simple physics” and the climate. For example, simple physics predicts a simple linear relationship between the climate forcings and the temperature. People seriously believe that a change of X in the forcings will lead inevitably to a chance of A * X in the temperature. This is called the “climate sensitivity”, and is a fundamental assumption in the climate models. The IPCC says that if CO2 doubles, we will get a rise of around 3C in the global temperature. However, there is absolutely no evidence to support that claim, only computer models. But the models assume this relationship, so they cannot be used to establish the relationship.
However, as rivers clearly show, there is no such simple relationship in a flow system far from equilibrium. We can’t cut through an oxbow to shorten the river, it just lengthens elsewhere to maintain the same total length. Instead of being affected by a change in the forcings, the system sets its own preferential operating conditions (e.g. length, temperature, etc.) based on the natural constraints and flow possibilities and other parameters of the system.
Final conclusion? Because climate is a flow system far from equilibrium, it is ruled by the Constructal Law. As a result, there is no physics-based reason to assume that increasing CO2 will make a large difference to the global temperature, and the Constructal Law gives us reason to think that it may make no difference at all. In any case, regardless of Arrhenius, the “simple physics” relationship between CO2 and global temperature is something that we cannot simply assume to be true.
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Steve Milesworthy (04:41:00)
Can the climate shift 1.5 – 4.5C? Certainly, although it seems that it has not reached the high end of that in the last ten thousand years.
We are so used to the stability of the climate that this doesn’t strike us as odd. We stand around and dispute about the fact that a hugely complex system has seen a temperature change of 0.6C in a century, as if the size of that were what is significan.
But to me, it is nothing short of amazing that the climate has kept the planet within a range of plus or minus half a freaking degree in a century. You think you could design a system to do that? and Me, if I were trying to design such a system as the planetary climate, I wouldn’t try to keep it in balance using something as sensitive and unpredictable as clouds.
You are right that that system works too slowly to keep the temperature stable in the short term. Again I recommend that people look at my article at this link. It details a system which works, not on the millennial timescale, but on the daily timescale.
You miss my point. What I’m trying to get across is that complex systems are not like balls on a billiard table, which move a distance X in direction Y if force Z is applied. That is the foolish assumption upon which the mountain of GCMs are built, that if CO2 goes up by Z, the temperature will move a distance X in direction Y. Complex systems don’t work that way.
Instead, complex systems spontaneously evolve to maximize or minimize some particular aspects of the system. Because of this they do not move in a predictable direction in response to a given forcing. If you cut through an oxbow, it does not shorten the river.
I, like you, don’t expect the constructal law to tell us that the temperature of the earth cannot change. However, it certainly tells us that the climate system is not free willy-nilly to take up any temperature at all, because it is constantly adapting to maximize some aspects of the system. This means that there is no magical knob, CO2 or otherwise, that we can twist to reset the temperature.
And it tells us that there is almost certainly a temperature governing system at work, one good enough to regulate the planetary temperature to within half a degree per century. At the link above I have posted my ideas on how that governing system works. I’m more than happy to have folks either poke holes in my theory or propose their own. But the idea that there is no temperature governing system at all flies in the face of experience, history, and the constructal law.
Thank you all for looking into the Constructal Law and discussing it.
The latest design-in-nature discovery from the constructal law is the prediction of the “physics phenomenon” of golden-ratio appearances, and the union of it with animal design (locomotion, cognition, getting smarter, pleasure)….
… all for moving mass currents more easily on earth, just like the design of global climate and circulation.
See the top box at http://www.constructal.org, and this week’s article in Physics Today and The Guardian, UK :
http://blogs.physicstoday.org/newspicks/2009/12/why-the-golden-ratio-pleases-t.html
http://www.guardian.co.uk/artanddesign/2009/dec/28/golden-ratio-us-academic/print
Adrian Bejan (12:19:44) :
The latest design-in-nature discovery from the constructal law is the prediction of the “physics phenomenon” of golden-ratio appearances…”
Fascinating. And here, we all thought Dan Brown was making it all up.
Interesting, now that I think of it, that regular TV is too narrow at 4:3, and widescreen at 16:9 is closer to the GR and seems to be more pleasing to the eye.
Mark Duigon (07:04:56), thanks for raising interesting objections.
Say what? My example is useless because water in a concrete ditch doesn’t meander?
Let me get this straight. Your claim is that my example is useless because if conditions were 100% different from what I gave as my example, the results would be different??
I’m sorry, but that makes no sense.
But in any case, even pure water flowing down a sheet of glass does not flow straight downhill, it forms meanders … surely as a hydrologist you must be aware of this phenomenon.
My point is that an active system like a river does not change at random. As the Constructal Law specifies, it is constantly adapting to maximize some aspect of the system. Because of this, “simple physics”, which does not allow for the active adaptation and directed change of the system, is inadequate to predict what will happen in response to a change. See Rereke Whakaaro (19:51:42) above for an example.
Well, it seems that we are using a different meaning of “simple physics”. Yes, we can say that self-organized criticality can be described as “simple physics”, and that chaotic systems orbiting around a strange attractor can be described as “simple physics”, and that the systems of the human body can be described as “simple physics” plus “simple chemistry”, and that the Constructal Law is just “simple physics” … but that’s a most curious definition of “simple”.
My point is that unlike a simple system like billiard balls on a table, complex systems do not respond linearly to forces that impinge on them. Unlike a block of steel, my body does not respond linearly to heating my feet. Unlike a piece of rope, when I cut through a bend in a river, the river readjusts so that it maintains about the same length. I am using that difference as the distinction between “simple physics” and “the physics of complex flow systems”.
The basic rule of models is that all models are wrong, but some models are useful. Like scientists in a host of disciplines, you as a hydrologist employ useful models. (As an aside, many hydrological computer models do not use “simple physics”, but instead use simple heuristics because the simple physics is either unknown or mathematically intractable … but I digress.)
Because you use useful models in your work, you (like other scientists) are predisposed to assume that climate models are also useful … which is a bridge too far. Tell me the truth — as a hydrologist, could your models predict the change in the average position of a river system a hundred years from now assuming that the river flow slowly increases by say 50% over that time?
Because that is what you are asking us to believe about the climate models, that they can tell us the average temperature a hundred years from now assuming that CO2 increases by say 50% over that time. Me, I have written (not used, but written) far too many computer models to give that claim the slightest credence.
The problem is that the climate, as a complex flow system ruled by the constructal law, is constantly adapting to maximize certain aspects of the system. Now if you can point to a single climate model that does that, you’ll have a point. If not …
Unfortunately, even including that active adaptation process in the model is only a necessary but not sufficient requirement for an accurate model. The claim is often made that despite the dismal failure of weather models in forecasting weather one month ahead, climate models can forecast climate a century ahead. Given that the known problem with forecasting weather is that it is chaotic and our current models can’t handle chaos for … excrement, I am astounded that people believe that climate forecasts will be successful, but there you are.
I say this because we have no evidence that climate is any less chaotic than weather, and according to no less an authority than Mandelbrot himself, we have evidence that it is just as chaotic as the weather … which bodes extremely ill for any long-range climate forecasting.
The programmers of the present generation of models make the most bozo linear assumption, which is that increasing CO2 will increase temperature linearly with the log of CO2 … “simple physics”, right? They then program a slew of different models that all embody that “simple physics” assumption. And guess what these models show will happen when CO2 increases? Yep, your guess is right.
And to add insult to injury, the modelers then claim that the fact that all of the models predict increasing temperature with increasing CO2 is proof that the models are correct, that that agreement between models should increase our confidence in their forecasts … riiiiight.
So Mark, if you think that current climate models tell us anything more than the assumptions of the programmers writ large, I’ve got bad news for you …
Thanks for the questions and objections,
w.
Adrian Bejan (12:19:44), first, many thanks for your comments on this thread, it is an honor.
A question along those lines, if you don’t mind. I have often cited your work on the application of the Constructal Law to global climate (available here).
Since bifurcations are the essence of chaos, of course my single question above is actually two-fold. First, I had heard through the grapevine that you were doing further work along those lines. Any truth to that, or is it just another ghost of the intartubes?
Second, is anyone else working along those lines, using the Constructal Law to elucidate many of these climate mysteries?
All the best to you, your work has been a great inspiration to me which has unlocked many mysteries (and of course, pointed out many new locked mysteries, the unending joy of science).
w.
@ur momisugly ThinkingBeing (10:02:11) :
“The bottom line is that deniers want to believe that we will be saved by magic, that somewhere Mother Nature has a secret negative feedback waiting to save us from ourselves. “Alarmists” don’t want to trust to magic.”
=====================================
it’s not about beliefs, magic or secrets. it’s about science.
you might even call it critical “thinking”. guess you’ve stopped.
The central importance of non-equilbrium pattern formation / dynamic chaos (call it what you will) to climate has been an “emergent” theme at WUWT, and Dr Eschenbach’s excellent and concise article advances this further.
It is indeed to be hoped that Dr Bejan would join others such as Tsonis to develop new analytic and descriptive tools for climate based fundamentally on non-linear theory. They are much needed.
The chaotic non-linear / non-equilibrium pattern formation aspect of climate is sometimes presented as if it was a side-salad or peripheral issue to climate. But it is the main course. It needs to become the dominant paradigm for real progress in understanding to be made. For the damage done by the AGW movement to begin to be undone.
The following is an example I have come across in my own research, of how a chaotic nonlinear paradigm radically changes the role and significance of an important system parameter: feedback, negative or positive. (It is repeated here from an earlier post.) Feedbacks are at the centre of the debates about climate dynamics and so-called “forcings”. A chaotic nonlinear (CN) paradigm results in predicted outcomes (yes some of us still believe science should make testable predictions) that are diametrically, 180 degrees, opposed to the predictions of a linear reductionistic-mechanistic (LRM) paradigm.
How do the CN and LMR paradigms differ in relation to their interpretation of feedbacks?
Negative feedbacks, in the LRM paradigm, basically oppose any force causing a change with a force reversing the change, so that status quo returns. Anti AGW scientists and commentators like negative feedbacks since they can be expected to oppose AGW.
Positive feedbacks – again according to LRM – on the other hand result in runaway self-reinforcing change, and are thus popular with the AGW proponents. In fact the basis of the AGW position is arguing how a small CO2 forcing can initiate positive feedbacks with the help of water vapour and other factors.
In a nutshell: negative feedbacks return the system to status quo, while positive feedback drives sustained unidirectional change. This is the LRM paradigm.
The CN paradigm is quite different. Here, negative feedback is given another name: friction. Friction is when a forced change sets in motion processes which act to oppose the change. (“Dissipation” and “damping” are also terms with similar meaning.) And in non-linear, non-equilibrium dynamic systems, friction has one major outcome: it stimulates the emergence of pattern formation. A system becomes fruitful with rich emergent patterns when it is far from equilibrium and in the bifurcating non-linear regime and friction is present in the system.
The literature is replete with experimental studies substantiating this thoroughly well-established theory. (“friction + pattern + formation + non-linear” in Google scholar just yielded 15500 hits). Examples of such systems include:
The classic Belousov-Zhabotinsky reaction,
Rayleigh-Benaud convection,
Catalysed CO oxidation on a Pt surface,
Coastline formation by sea currents on sand,
The formation of pattern in mammalian trabecular bone,
And many more. So while negative feedback causes a simple return to status quo (whatever that is) in the LMR paradigm, negative feedback or friction causes the emergence of pattern and structure in the CN paradigm.
What about positive feedback?
Positive feedback in the CN paradigm does one thing: it kills emergent pattern. Feedbacks have to be suppressed in order for rich and complex patterns to emerge. The Pt-catalysed oxidation of CO, studied by Matthias Bertram and others shows this clearly [2]. (This is the reaction that happens in your car’s catalytic converter.) The system generates rich and complex geometric spatial patterns, but these collapse into a set of uniform sinusoidal oscillations when the gas pressures are adjusted to increase feedback in the system. Another, biomedical study shows that in the biochemical regulation of bone turnover, inactivation of the gene for OPG which acts against osteoblast-osteoclast coupling (feedback by yet another name) results in a debilitating genetic bone disorder where complex trabecular bone pattern collapses into an abnormal and pathological series of parallel plates [3].
So while in the LRM paradigm positive feedback is what produces unidirectional sustained change, in the CN paradigm, it reduces complex and pattern-rich structure into simple periodic structure. So it actually opposes sustained change.
Oscillations by the way are the norm for a planetary ocean and atmosphere system such as ours which is under continuous periodic forcing from the Milankovitch, solar and other cycles, and which in response – as a dynamically chaotic / non-linear system – generates intrinsic oscillations of its own. The type of feedbacks in the system determine the nature of the oscillations. Negative feedbacks (friction or damping) result in complex pattern with for instance log-log power law scales of magnitude. Positive feedback, by contrast, reduces oscillation to a simple wave.
If you want to see a nice video of emergent pattern in a non-equilibrium system under periodic forcing, please go to:
http://chaos.ph.utexas.edu/research/vibrated_cornstarch.htm
and click on the link for “see a movie”.
Note that by emergent structure in the climate context one can include things like ice ages, El Nino and La Nina ocean current events, Pacific and Atlantic and other oceanic oscillations, the MWP, the LIA, the CWP, and others.
Richard Lindzen has examined clearly the issue of positive and negative feedbacks in the earth’s radiative balance [1] involving among other things the ERBE satellite measured fluxes at various wavelengths. Lindzen points out that negative feedbacks are generally underestimated, since systems will try to return to equilibrium via negative feedbacks. Basic thermodynamics dictates that applied forces induce opposing forces.
Thus complexity and rich emergent pattern can be expected as the order of the day.
[1] Richard S. Lindzen and Yong-Sang Choi, Geophysical Research Letters, July 14, 2009.
[2] Bertram M et al. Pattern formation on the edge of chaos: Experiments with CO oxidation on a Pt(110) surface under global delayed feedback. Phys. Rev. E 67(3) 036208 (2003)
[3] Salmon PL. Loss of Chaotic Trabecular Structure in OPG-Deficient Juvenile Pagets Disease Patients Indicates a Chaogenic Role for OPG in Nonlinear Pattern Formation of Trabecular Bone. J. Bone Miner. Res., 2004; 19 (5): 695-702.
None of the crude models we used when I was active in air pollution research 30 years ago made such linear assumptions. Since then, every model I’ve looked at has gotten much more complex, especially as computing power has grown.
Which model is it you claim makes a linear assumption, without qualifications? Got a citation on the description of that model?
Such a crude model would be at least crudely accurate, however. What confounding operations of science would make it less than crudely accurate?
REPLY: Sorry Ed, but your assumption of a linear model being “crudely accurate” is wrong. The CO2 induced LWIR return response in the atmosphere with increasing concentration is logarithmic, and we are already fairly close to saturation of the effect at 388PPM of CO2 concentration as seen below.
Also, observation still doesn’t match the modeling, and falls short for the effect. Now go write an angry/silly post about it dissing me. We love the entertainment here, and we are counting on you to deliver. 😉 HNY!
– Anthony
Ed Darrell (19:42:03)
All of the models, as far as I know, are built around the ideas that
∆F = α log2(C1/C0)
and
∆T = λ ∆F
where C1 is current CO2 concentration, C0 is starting CO2 concentration, log2 is the logarithm to the base 2, alpha is the proportionality factor between forcing and CO2 concentration, T is temperature, F is forcing, and lambda is the climate sensitivity.
In English, this says that the change (∆) in forcing is linearly related to the logarithm of the change in CO2 concentration, and the temperature is linearly related to the change in forcing.
Substituting we get
∆T = λ α log2(C1/C0)
In other words, as I said above, they assume a linear relationship between the log of CO2 concentration and temperature.
The IPCC says that the values are
α = 3.7
and
λ = 2 to 4.5, central value of 3
This gives us (using the central value for lambda)
∆T = 11.1 log2(C1/C0)
In other words, the models posit a linear relationship between log CO2 and temperature, as I said above.
The IPCC FAR, for example, says:
(FAR Chapter 2 p. 133)
and
(Ibid p. 140)
All of this is so widely known, I am curious why you would question it.
You close by saying:
The modelers do not say that their results are “crudely accurate”. Quite the contrary, they say that they are supernaturally accurate, so accurate that we can use them to forecast the climate 100 years from now (although paradoxically, not accurate enough to forecast for a single decade). Go figure …
What would make them “less than crudely accurate”? Ummm … well, we could start with the fact that they ignore both the Constructal Law and thunderstorms, both of which are central to the climate question …
u.k.(us) (16:52:32) :
“it’s not about beliefs, magic or secrets. it’s about science.
you might even call it critical “thinking”. guess you’ve stopped.
Actually, “ThinkingBeing” wants to believe that we will be doomed by magic.
Willis Eschenbach (21:40:44) :
A good reply.
I would add that in addition, all the Navier Stokes solutions etc entering the calculations are also taken to a linear approximation over the grid dimensions in the models, and all the unknowns that are taken as average are also in essence the first term of a linear expansion in other unknown solutions of equations. Linear assumptions are all over the place in the models, when it is well known that in coupled differential equations the solutions are highly non linear.
Happy New Year and carry on the good fight.
Ed Darrell (19:42:03)
“None of the crude models we used when I was active in air pollution research 30 years ago made such linear assumptions. Since then, every model I’ve looked at has gotten much more complex, especially as computing power has grown.”
It is important to clarify the word “complex” and distinguish between “complex” in the specific sense that there is an involvement in spontaneous non-equilibrium / nonlinear pattern formation under well characterised system parameters (with bifurcation leading to emergent e.g. fractal pattern etc.), and on the other hand “complex” in a general sense just meaning “there’s lots of things in it”. A classic example of a system that is complex in the second sense is the “Heath-Robinsonian machine” from fiction – see the link below (not a bad analogy for current general circulation models):
http://blogs.guardian.co.uk/digitalcontent/heath9sep2008.jpg
This latter type of complexity does not in itself guarantee efficiency or correctness of modelled results. The first type of complexity is more appropriate for climate modelling. But one cant just rely on or hope for the accidental appearance of such nonlinear chaos pattern dynamics in a model possessing the Heath-Robinsonian type of complexity. You must create the models based on an understanding of such systems – the Constructal Law might not be a bad place to start.
phlogiston (19:41:14) : posted a link that appears to be broken regarding a video of vibrated cornstarch, as an example of an
Here is another link that hopefully works:
Then Hamlet is wrong:
PS: If ones body is not solid, but gaseous or liquid, or some combination thereof, it would make no difference to WE’s hypothesis. Whatever state the body is in, it should transmit heat, if only “simple physics” applies.
Noaaprogrammer (21:45:04) :
Considering the hydrothermal activity between the oceans and the Earth’s interior, one would think that over time, the molton core would eventually cool and solidify….
Seems OT, but I’ll take a shot at an answer…Over quite a depth range within the Earth heat transfer from the interior is by conduction. This process is so darned slow that most of the Earth’s original heat from its formation is still in place.There is also heat generated by radioactive decay in the crust (perhaps in the core as well), which is substantial enough to supply all heat flow currently leaving the surface. The core will not solidify any time soon in the geological sense of that term.
How would the increase in Earth’s mass and consequent increase in core pressure and heat over 8 million years compare with the dissipation of the Earth’s interior heat over the same time?…
The pressure-volume work done by the added mass is nil compared to the heat flow from the interior, which in turn s nil compared to the solar and LW flux at the surface.
jt (21:54:39) :
People keep making the point that Climate is Chaotic as if that meant Climate is unpredictable on any scale. However, there are kinds of chaotic systems which operate around “attractors” so that they repeat their configurations in quasi-periodic fashion. I would be interested in comments from mathematically knowledgeable persons about whether such kinds of chaos have been found, or are likely to be found, in the systems which generate climate, and, if so, what kinds of quasi-periodicity have been found or are expected.
There are only two obvious short periods of forcing for the climate system, diurnal and annual (in the tropics the annual forcing is actually annual plus twice per year), so if everything were to respond linearly those would be the only periods we would observe in the response. However, we observe all sorts of responses that are somewhat aperiodic, unpredictable, and also have periods unlike this forcing; so may be chaotic. For starters there is El Nino, which has a period between 3 and 7 years, and a host of other long period responses like the PDO. These are good candidates for chaotic orbits around attractors. There is also a variation in the index cycle that appears now and then around 30 days period and is another reasonable candidate.
Phil (11:22:10)
Thanks for this Phil, it is indeed the same video I linked to earlier. (I copied from an earlier posting and neglected to check if the link was still active.)
Thanks for sort of avoiding the answer, Anthony. I have a real job and had hoped to look up the paper so I could read the research that makes the point. I don’t have all day to spend in the library, nor good access to a research library to track this stuff down.
As you can see, I’m long out of the research, and some of the jargon fails me. But someone had said the “alarmists” make a “bozo linear assumption.” That’s the piece I’d really like to read.
Fortunately for WUWC, you’re not government funded. At least that protects you from an FOIA request.
In the absence of anyone offering any citation that the “alarmists” make a linear assumption, I’ll continue to presume they don’t.
So, Anthony, you’re arguing that a logarithmic model works better — that makes sense — but the models used for forecasting by the “alarmists,” don’t get it right.
Can you offer a suggestion of where the “alarmists” published their incorrect model? Can you offer a citation on the model you claim to be correct?
Ed Darrell:
“Can you offer a suggestion of where the “alarmists” published their incorrect model? Can you offer a citation on the model you claim to be correct?”
“Alarmist bozo linear assumption” [black line]: click [graph by Bill Illis]
Dear Willis,
Please note that the geometry of rivers’ meanders is discussed in A. Bejan, “Shape and Structure, from Engineering to Nature”, Cambridge University Press, 2000.
See § (a) Meanders, p. 117, Chap. 6.1 Ducts and rivers.
Roughly, a river can be modeled as finite-size elastic column in end-to-end compression, and it will develop a resistive bending moment, and the buckling wavelength will be proportional to the river width.
More articles and news on constructal theory here: http://www.constructal.org
Twitter: http://twitter.com/constructal
Constructal.org Webmaster (23:00:42),
Very interesting site, thanks for posting. Now I get to do some more reading on a subject that I didn’t even know existed a month ago. Thanks to Willis, too.
WUWT is a fascinating resource!
Constructal.org Webmaster (23:00:42)
Many thanks for the links, I linked to your web page above. I have been fighting for some time to get people to start using the Constructal Law when they are attempting to understand climate … it’s taking longer than I thought, but there is incremental progress.