There is an interesting review of the book here. Unfortunately the book is a little pricey over here so I might wait until I’m next at a decent scientific library to have a trawl through it! He also has some interesting papers on the topic (here) – these papers were controversial at the time, although carry many citations.

Following this up led to an interesting bibliography on 1/f noise here.

The real world is also only a single realisation that may also not be typical (whatever typical means in this context). Yet we are busily fitting our models to churn that out as the central result. This is a very important issue …

It is actually THE single most important issue .
It is the same question that the cosmology asks : “Why is the Universe like it is ?” .
Here too we have a single realisation .
However the cosmologists are bright enough to have seen that the question of probability of realisation à priori is at best undefined and at worst absurd .
In any case they know that even by using all natural laws we know and having numerical models running for eternity we would not be able to stick a number on this particular Universe we have .

Actually it is interesting to look at the “physics” of a well documented climate model like CAM 3.0 .
Not because of the content that contrarily to a widespread myth is not complex but rather simple and boring .
It is interesting to see what the underlying assumptions/beliefs/hopes are .
There is a dynamical core and a sauce .
Let’s forget the sauce for every cook has his own receipt and it is anyway irrelevant for what follows .

The construction of the dynamical core consists to play with conservation laws f.ex Navier Stokes .
Basically it means to change variables by calling them generalised coordinates and transform the relevant equations to a more manageable form .
Anybody with understanding of analytic geometry and PDE theory can follow very easily what they do – no rocket science involved .
Once there , some form of discretisation is chosen and the thing coded on a computer .
What does the computer produce ?
A climate .
Certainly it produces a climate that is not absurd . Certainly it is a climate that looks possible .

However since Dan Hughes showed me some papers about the constructal theory whose details I had the opportunity to discover , I have seen that with a very small number of very basic principles it was possible to develop a quite impressive “climate model” .
No computer necessary , only pen and paper and yet you get all the circulation features right (Hadley cells , polar cells) and the model even predicts their location and dynamics .
Of course all “details” were wrong and many assumptions debatable but the fact stays that even a model that had no continents ,
no GHG , no clouds , no sun variability , produced something that looked like a climate .
It appeared also certain that with a little sauce it would easily incorporate more details if somebody wished so .

What I infer from that and what is also very consistent with the chaos theory is that the sole existence of conservation laws and the permanence of the geometry and of the mass distribution imposes on the dynamics of the system such severe constraints that given a set of initial conditions , ANY model that respects these laws would produce a climate .
Now the enlightening point by looking at the CAM 3.0 documentation is that the people are convinced that they produce THE climate .
They even use rather strong statements in the semi lagrangian section by talking about high predictive skills despite the use of coarse resolution .
They certainly believe that playing with N-S and changing variables , they have actually solved the problem .
Of course if they took a step back , they would realise that people have been “playing” with N-S these last 100 + years and the problem is still not solved on the fundamental level let alone at the discrete numerical level .

I am convinced that there is an infinity of solutions to the continuous equations representing the dynamics of the earth/atmosphere system .
Therefore there can’t be any uniform convergence of a numerical run to THE solution and interestingly hindcasting doesn’t make any sense because there is no reason that a model starting with the correct initial conditions 20 000 years ago finishes NECESSARILY with the observed state of today .
Follows also that a numerical trajectory cannot have a probability of realisation .
The only thing that we will be able to say once we stop wasting money on deterministic schemes that won’t work , is that all the trajectories are located within a strange attractor that may have a large number of attractor bassins .
The Earth during the last 4.5 billions years has wandered through the attractor whose topology depends on the millions of “details” that the modellers consider irrelevant .
If we have some insight in this topology , we will perhaps be able to make modest statements regading the rates of divergence of trajectories depending on the initial point chosen within the attractor .
The state the Earth is in today is no more probable than any other , possibly very different , as long as it is situated within the attractor .
And to close the loop – for an initial value problem the time scale is everything and with increasing time the system may but must not rapidly swap from one attraction bassin to another .

Of course, proof entails an atmosphere measured at 800 ppmv and proof the anomaly reflects temperature.

Or as my dad once told me while we were bowling, “Good luck with that, fanboy.”

The real world is also only a single realisation that may also not be typical

Exactly. The models should be fit* to Earth’s own ensemble. But all we have is one realization. If you overfit to that realization, you will be wrong about the ensemble. That is a certainty.

I do not think Gavin Schmidt et al understand this. I hope and pray that I am wrong.

*And don’t tell the models are “determined by physics” and not tuned to scenarios. This is a lie that I have heard told by true believing alarmists on many occasions. There is wide uncertainty on some parameters and this gives the modelers free regin to overfit those parameters to the single stochastic realization of modern earth climate.

Does this falsify AGW? No. Does it suggest the estimated sensitivities may be biased low or high? Yes.

Tom, I fully agree that there is considerable evidence to support the idea that weather is an initial value problem with exponential error growth. I start from this premise rather than justify it because I believe both AGW supporters and AGW sceptics agree on this point. This makes it a good place to start a debate, in order to find why we draw different conclusions from the same premise. My use of the word “if” is really due to habit, it is just my naturally cautious way of expressing the premise of a logical argument. (I blame the modal logic that I had to study as part of my university work!)

Bender made an excellent point on another thread which ties in with this nicely as well. Dr. Curry argued on the feedback thread that single model runs (what I would refer to as realisations) were not informative due to the fact that a single run could look very different due to natural variability. I was still in lurk mode and bit my tongue, but the good dr. bender made the point very well elsewhere. The real world is also only a single realisation that may also not be typical (whatever typical means in this context). Yet we are busily fitting our models to churn that out as the central result. This is a very important issue, and hopefully someone in the mainstream will wake up and smell the coffee on this point. The presence of fractional variability in climate makes this a fundamental problem.

PS. Watching closely for Dr. Browning’s review. Should be interesting.

In both of the above examples, the clustering (large-scale variability) follows directly from the fine-scale variability. If the fine-scale variability (i.e., the weather) is an initial value problem with exponential error growth, attempting to predict large-scale behaviour of the system within the natural variability would be an exercise in futility.

Yes and YES !
However why do you write “… IF the weather is an initial value problem …” ?
It is an initial value problem and I know of nothing that would suggest otherwise .
From that follows then that the clustering (or self similarity) forbids to operate some cut offs in the time scales by arbitrary considerations of “randomness below , signal above” .
L.Motl has challenged some post on RC blathering about “weather vs climate differences” by asking at what time scale climate emerges from the noise and what physical process governs that transition .
My take on it is that climate emerges after around 50 years because that is a typical time length of human awareness .
Shorter we don’t know enough and longer we forgot too much

All the convection modes (ENSO,PDO,NAO,THC,etc) are in some sense real. But what are they? You can’t predict the temperature of the flows through those pathways over time (over weeks & months, yes). You can’t say how robust those pathways are spatially because they haven’t been studied that long and their driving forces are not that well understood. How on earth do you judge whether a GCMs internal climate variability/weather noise is appropriate when you don’t know how the actual system is behaving? And if you can’t get a fix on the internal noise, how do you get a fix on the external signal?

The 20th “century” warming “trend” is actually two warming phases lasting only 30 years long each (broken by “aersol cooling” in teh 60s and 70s?). Given the uncertainty on the solar forcing, its effects on dominant pathways such as ENSO, the process by which surface heat is taken to the ocean depths … given the spectacular failure of the GCMs in the Arctic during both of these warming phases … I can’t help being skeptical of the way “weather noise” (which in my books includes ENSO,PDO,NAO,etc.) is encapsulated in the GCMs.

The questions I ask at RC on this issue go unanswered. Why? If Spence_UK can understand what I am saying, why can the gatekeepers not? Are they in denial?

Questions, questions.

I’m pretty sure that “Allan variance” in this context is the same thing as the wavelet decomposition of variance by scale that I’ve used in several posts e.g. my discussion of the VZ pseudoproxies.

Haar wavelet variance with fractional freq. deviates, if I remember correctly

As per post 62 , Gavin and Hansen are doing fine if global temp Allan variance looks similar to last figure in that post. Maybe that’s one reason why Mann hand-crafted astronomical forcing to the hockey stick . See the Allan variance before and after ‘the fix’:

( http://signals.auditblogs.com/files/2008/02/co2fix_allan.png )