With the risk of being monotonous, I will repeat here a few of my theses which are related to this discussion:

1. Records which seem to exhibit long range dependence (LRD) should not be handled with the ease of typical statistical processing. LDR implies dramatically increased uncertainty and classical statistics can yield quite misleading results if LRD is not taken into account in statistical estimations. This extends to derivative time series (e.g. by differencing) and to transformed statistics (e.g. power spectrum). In this respect short records of say 20 years do not provide sufficient information to study processes which might exhibit LRD. (See details in Koutsoyiannis, 2003, and Cohn and Lins, 2005).

2. Nonstationarity and stationarity are not properties of a time series but of a mathematical process that models the time series. In this respect it is not possible to infer nonstationarity or stationarity merely from data. Some reasoning is also needed about (1) why a stationarity hypothesis cannot be valid for the process at hand; (2) what has caused the change of behaviour (in time); (3) whether this change is deterministically known (for instance a random change in the mean of a stationary model results in a composite model that is again stationary). (See details in Koutsoyiannis, 2006a).

3. The power spectrum is very helpful in detecting periodicities and choosing a cyclostationary against a stationary model (e.g. for monthly temperature). But it cannot be used to reveal whether a process without specific periodicities is stationary or nonstationary. Besides, it can lead to very misleading results in the presence of LRD. (I am preparing a paper about this — I hope to publish it in the next decade).

4. Asymptotic behaviours (e.g. the Hurst behaviour and the estimation of the Hurst exponent, the long distribution tails, the entropic dimensions) should not be detected in the “body” of a graph but in the appropriate “tail”. Otherwise (e.g. by neglecting the slope in the tail and taking an average slope in a graph with varying slopes), there is high risk to obtain mistaken results. (This I have demonstrated for entropic dimensions is an older paper that was published only recently: Koutsoyiannis, 2006b).

5. Obviously the climatic system is not characterized by a single feedback loop (e.g. a negative one, which perhaps would introduce anti-persistence); rather several feedback mechanisms, positive and negative, act simultaneously. I have tried to demonstrate that in a system with a positive and a negative feedback component whose parameters vary in time as if they obey some feedbacks themselves, the resulting time series can exhibit LRD even though the dynamics are fully deterministic ( Koutsoyiannis, 2006c).

From the difficulties I had to publish the above referenced papers and from what I see in the mainstream literature, I understand that there are not many who think that these theses are correct. So I am very grateful and happy that this blog discusses positively these ideas.

Now, coming to the papers that Onar brought into discussion, I leave it to the reader to decide whether or not these papers fall into some of the problems that I wrote into the above five points.

Anyone got anything to say about Juckes citing Wahl and Ammann

In any case, I do not believe H is an indication of sensitivity. In particular, although I am intrigued by your statement:

If Kàƒ⣲ner is correct in his analysis then it should be possible to test it right now: positive feedback dominated climate models should have a Hurst exponent > 0,5. If they do but reality has an exponent lower than 0,5 then this pretty much falsifies the whole thing, no?

I do not think it is correct.

Perhaps Koutsoyiannis or Kàƒ⣲ner himself might have a comment on this?

thanks for all these interesting references. Reading Benestad’s views was particularly illuminating.
It was shocking to discover that he really do believe that they understand climate very well, and that he is so impressed by the fact that climate models fit the data very quite well. (thereby revealing a thorough lack of understanding of the profound role of uncertainty in multivariable systems)

However, despite lots of interesting comments I am still at a loss about the physical interpretation of the Kàƒ⣲ner papers. Basically, he interprets the Hurst exponent as a measure of negative versus positive feedbacks in the system. A Hurst exponent between 0 and 0,5 implies non-stationary anti-persistence, whereas a Hurst exponent greater than 0,5 implies persistence. Kàƒ⣲ner finds H-values significantly lower than 0,5, implying anti-persistence and in his interpretation, negative feedbacks dominating the climate system. This seems logical, but I need to get a handle of what this means in practice. In particular, what would be extremely interesting to find out is what the Hurst exponent of climate models are. If Kàƒ⣲ner is correct in his analysis then it should be possible to test it right now: positive feedback dominated climate models should have a Hurst exponent > 0,5. If they do but reality has an exponent lower than 0,5 then this pretty much falsifies the whole thing, no?

Although, in order to put confidence into such a finding I would like to see the Hurst exponent calculated for a range of climate
sensitivites, all the way from a Lindzenesque 0,3 C/doubling to a doomsday 6 C/doubling. If Kàƒ⣲ner is correct, then a all climate models with a sensitivity lower than ~1 C/doubling should have a Hurst exponent lower than 0,5. ~1 C/doubling (i.e. zero overall feedbacks) should give H=0,5, and sensitivities 1-6 should give H>0,5.

Has anyone done this? If not, why the hell not? As far as I can tell it should be possible to use H to measure the climate sensitivity statistically by mapping the empirical value of H onto the climate model which best matches that value. Comments?

Although a little way off topic (SteveM, feel free to move this with the above post), this type of article is of great interest and although not specifically audited, these approaches have been discussed on this site:

The Mandelbrot and Wallis paper referenced by Olavi is discussed here.

Along similar lines, Cohn and Lins is discussed here.

I would also recommend reviewing some of Demetris Koutsoyiannis’ work, discussed here. Demetris has been on this site and has an impressive knowledge on these topics.

Suffice to say many of the people here are of the opinion that the statistical models commonly applied in climate science are not up to the job. ARIMA, FARIMA and FGN (fractional gaussian noise) being posited as much better models. Very little work seems to be done by mainstream climate scientists in this area.

this is surely not the right article to make this request, but this one seems as good as any. Feel free to delete or move this to its appropriate place. My request is as follows:

Olavi Kàƒ⣲ner has done a lot of remarkable studies of negative versus positive feedbacks in climate. Reading his papers I find no fault in his methodology, but I am no statistics expert. Even so I find it puzzling that this work of his has not received any more attention as it is potentially a blockbuster. Then again… Anyways, his two main articles are On non-stationarity and anti-persistency in global temperature series and Some examples of negative feedback in the Earth climate system, both very interesting.

What I would like to see is 1) a comment from statistical experts here on ClimateAudit on the validity of this approach, 2) as a bonus an audit of the results.

At the moment I would be more than happy with just 1. If I understand the results of these papers correctly then a) the claim about positive versus negative climate feedbacks is not something that we need to wait far into the future to see unfolding, it can be measured now, using statistical techniques, and b) the result from the second paper implies that there are negative feedbacks in the climate system everywhere on Earth, but that they are weaker in the tropics. That in itself seems like a highly significant finding.

Comments?