Bart on Chaos in weather and climate forecasting
Bart R | February 9, 2011 at 9:58 pm |
Now you’re making me think back to the days when I studied and did equations and the like.
Best I can offer are suggestions.
1. Period doubling is offers us a signature, a highly reliable prediction of Chaos Theory to indicate a) whether we’re seeing actual Chaos, and b) what step in the transition we have encountered between orderly, turbulent and chaotic; it c) also gives us information on scale and d) points like an arrow to the suspect inputs and relevant domains.
The inputs and relevant domains I’ve seen argued are such things as CO2 levels, solar and cosmic effects, and much smaller influences like land use on temperature, variability of cloud formation, precipitation, variability of extreme events, rate old meteorological records are broken (ie one expects the rate of new record setting to be logarithmic at best, so linearity would be Chaotic on some scale). I imagine a clever Chaos analyst could correlate period doubling signatures to rank the significant inputs.
2. What isn’t Chaotic is really important. Is there something that the chaotic state always collapses back to, as a ground state?
Those things that can’t stay Chaotic long and are subject to reversion are really helpful in that they become semi-predictable.
(Wow am I rusty, used to be able to rattle this stuff off like a gattling gun. You need a current hot quarterback, not a former benchwarmer.)
3. What scales (time, geography, temperature range, etc) things do and don’t exhibit Chaos traits is also meaningful to analysis of what is going to become less predictable and how soon. Suppose we’re entering a domain where for some regions of the planet seasons become truly meaningless? We don’t know that this hasn’t happened before, how could we? We would want to know if we might be approaching it now, and Chaos Theory has some strong tools for identifying such patterns.
Suppose Earth is about to generate an equivalent of the Great Eye of Saturn, a standing storm covering a huge fraction of the planet and lasting centuries? That’s alarmism to non-mathematicians, of course, but wow wouldn’t it be such an awesomely cool mathematical event to be present for? Sadly, really not likely for so many reasons. But it’d be awesome.
4. Resonances: we can establish something much more powerful than correlation, if we can show that the profile in terms of chaos measures for two possibly related phenomena match. Are our thermometers biased by changes in the way measurements are taken and the places they happen, or do the profiles of periodicity and so forth correspond?
5. Attractors are really fun! I don’t recall the reference, but I recall that self-motivated complex systems at equilibrium, for example imagine a solar system with three stars and 17 planets where unlikely though it may seem the ‘orbits’ have entered a course that doesn’t result in everything all collapsing, even with highly erratic planetary paths exchanging between all three stars.. That system would have attractos exhibiting some sort of, if not pattern, non-vanishingness. Attractors in a system with a new disturbance, however, do vanish and move and spontaneously appear. Liken this to new CO2 emissions and look at what happens in the climate with its historical attractors.
6. Better things to measure. We measure all this by anomaly? Just anomaly? Really? That’s scandalous. (I know, I’m being freakishly blinkered; there are many, many non-anomaly measures, so why focus on just temperature?) Chaos Theory can identify whether groups of observations fit orderly, turbulent or chaotic sets, and whether those states are changing.. which would be interesting.
At least, maybe some of this sort of might work. With equations.
If only we had a Hydrologist.