Hi Judith,
Tsonis and colleagues used a network model to determine the ‘distance’ between the indices of major modes of NH climate variability. The distance is minimal at certain times – sychronisation -and then diverges again. At these times we have extreme ENSO events – ENSO dragon-kings in 1976/77 and 1998/2001 – after which climate settles into a new trajectory. So we have slowing down – autocorrelation increases in the ‘distance’ parameter – and noisy bifurcation.
It is not of much use to compare the Earth system to simple Lorenz attractors. The Earth system has a far more complex state topology and an infinite phase space. To say that it is not a simple Lorenz attractor which readily move between two attractors and it is therefore not chaotic is illogical. There are much complex systems that shift from state to state – and are ergodic in the sense that they will return to an original state if given enough time. Not a terribly usefull concept over time frames of anything but acdemic interest.
Tomas – I believe – distinguised between temporal chaos as embodied by models – and the spatio-temporal chaos of the Earth system. Intrinsically different dynamically complex systems. But they are still share properties with simple Lorenz atractors in the broad class of dynamically complex sysems. They are systems that are non-linearly sensitive to small changes in control variables.
I think Tsonis deserves a Nobel Prize for quantitatively showing how this works in modern climate records.
Robert I Ellsion
Chief Hydrologist