I am currently rereading "Chaos" by Gleick, and hoping this time I will master it. So it would probably be better if I keep quiet at the moment.
But I see ENSO as a strange attractor, with quasi-random movement within bounds. I also think El Nino is one phase of the ENSO cycle, and that the idea of a permanent El Nino is as sensible as the sound made when clapping with one hand. Cheers, Alastair. On Feb 10, 9:27 pm, Robert Indigo Ellison <[email protected]> wrote: > Gear Alistair > > 'Most commonly applied to the mathematical study of dynamical > systems, a bifurcation occurs when a small smooth change made to the > parameter values (the bifurcation parameters) of a system causes a > sudden 'qualitative' or topological change in its behaviour.' > > But the term entering chaos does also seem to be used to used as an > equivalent to bifurcation. > > Slowing down refers to a state of maximum autocorrelation. That is > minimum change in values in a sliding window in a time series. > Oscillations tend to a minima - in detrended data in the case of Dakos > et al. For decadal climate shifts - I think we might be better off > looking at ENSO rather than surface temperature. Decadal scale > climate shifts are accompanied by large ENSO events (La Nina and El > Nino) and the oscillations then tend to a minima (slowing down) just > before another shift. > > I believe you can see hints of this pattern in the ENSO graph > approaching and following the 1998/2001 climate shift. > > http://ioc-goos-oopc.org/state_of_the_ocean/sur/pac/nino3.4.php > > Surface temperature changes are strongly correlated to ENSO - 70% > according to McLean et al (sorry can't help myself). But instead of > looking at decadal trends - detrend it and look at the magnitude of > interannual variations to detect autocorrelation maxima. > > Cheers > Robert > > On Feb 10, 10:14 pm, Alastair <[email protected]> wrote: > > > On Feb 9, 10:53 pm, Robert Indigo Ellison > > > <[email protected]> wrote: > > > >look at how we can describe and analyze > > > > systems in order to recognize and predict when they'll become > > > > chaotic...." > > > > One way of looking at trying to predict phase shifts is with > > > autocorrelation. > > > > I think perhaps the systems are always chaotic but the tipping point > > > is known as bifurcation. > > > I don't think so. The first bifurcation happens when the system > > enters chaos. > > > "Here, we analyze eight ancient abrupt climate shifts and show that > > they were all preceded by a characteristic slowing down of the > > fluctuations starting well before the actual shift. Such slowing down, > > measured as increased autocorrelation, can be mathematically shown to > > be a hallmark of tipping points. Therefore, our results imply > > independent empirical evidence for the idea that past abrupt shifts > > were associated with the passing of critical thresholds. Because the > > mechanism causing slowing down is fundamentally inherent to tipping > > points, it follows that our way to detect slowing down might be used > > as a universal early warning signal for upcoming catastrophic change > > > >http://www.pnas.org/content/105/38/14308.full > > > We have now entered a period when the temperature rise has slowed > > down. That is what they say happens as we are about to pass a tipping > > point :-! > > > Cheers, Alastair. > > -- You received this message because you are subscribed to the Google Groups Global Change ("globalchange") newsgroup. Global Change is a public, moderated venue for discussion of science, technology, economics and policy dimensions of global environmental change. Posts will be admitted to the list if and only if any moderator finds the submission to be constructive and/or interesting, on topic, and not gratuitously rude. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/globalchange
