Demetris Koutsoyiannis emails to point me to his new paper. Markonis and Koutsoyiannis (Surveys of Geophysics) takes a look at climate variability over periods spanning nine orders of magnitude.
We overview studies of the natural variability of past climate, as seen from available proxy information, and its attribution to deterministic or stochastic controls. Furthermore, we characterize this variability over the widest possible range of scales that the available information allows, and we try to connect the deterministic Milankovitch cycles with the Hurst–Kolmogorov (HK) stochastic dynamics. To this aim, we analyse two instrumental series of global temperature and eight proxy series with varying lengths from 2 thousand to 500 million years. In our analysis, we use a simple tool, the climacogram, which is the logarithmic plot of standard deviation versus time scale, and its slope can be used to identify the presence of HK dynamics. By superimposing the climacograms of the different series, we obtain an impressive overview of the variability for time scales spanning almost nine orders of magnitude—from 1 month to 50 million years. An overall climacogram slope of −0.08 supports the presence of HK dynamics with Hurst coefficient of at least 0.92. The orbital forcing (Milankovitch cycles) is also evident in the combined climacogram at time scales between 10 and 100 thousand years. While orbital forcing favours predictability at the scales it acts, the overview of climate variability at all scales suggests a big picture of irregular change and uncertainty of Earth’s climate.
There is an interesting link to a discussion at BH here. That conversation ended when Prof Koutsoyiannis told commenters that he was unable to respond to further questions since the answers were contained in a draft paper that he had going through the peer review process at the time:
As per the “opportunity” to discuss the scientific part, I am afraid it must wait some time. We have produced some results related to your questions, but I do not wish to discuss them before we have them officially published. In this case the peer review may take some months or years, considering the necessary rejections.
This paper is the result. The discussion thread dates back a year, so you can see that the peer review process has been at least that long. The paper was rejected by Geophysical Research Letters and Nature Geoscience (the peer review comments are available here) although as DK notes in the discussion thread, those of his papers rejected by mainstream climate journals tend to be the ones most cited after finding a home in some less "plugged" publication.
(Hurst Kolmogorov dynamics are explained here)