More chaos than you can shake a stick at.
Guest post by Andi Cockroft
(Anyone familiar with the Moody Blues should recognise the title – from “Higher and Higher”)
As some will have learned by now, I do not possess the scientific skills of the regular WUWT contributors to engage in in-depth evidential-based posts. Rather I like to think that just like the great unwashed masses, I have an intellect and an enquiring mind, and want here to share my musings and seek feedback to better help me (and hopefully other readers) understand some of the more complex subject matter. For my shortcomings I apologise. For raising questions requiring answers I do not!
Way back in January 2011, Phil Salmon posted here on WUWT “Is the ENSO a nonlinear oscillator of the Belousov-Zhabotinsky reaction type?” – His alternate title “Standing on the shoulders of Giant Bob” Perhaps my alternate title should be the same. I have read and re-read Phil’s definitive article, and as Isaac Newton was believed to have complained of the three-body problem:-“his head never ached but with his study on the moon”. So in my own way, I want to raise issues associated with what I see as true chaos, and whilst following (albeit very slowly) Phil’s work, that was nonetheless focused towards ENSO and away from the general Climate Models that I want to investigate.
Why a butterfly? Most students of chaos theory will know the “butterfly effect”, whereby it is asserted that in a chaotic non-linear system, a butterfly beating its wings in say Brazil could inject such feedback as to disrupt the airflow sufficiently that many years later a tornado would form over Texas.
Similarly, travelling back in time and moving the butterfly a few centimetres would cause the tornado not to form, or form elsewhere.
Ascribed to Edward Lorenz, the US mathematician and meteorologist who sadly passed away a few years ago. Initially Lorenz referred to a Seagull flapping its wings forever changing the weather, but later in a 1972 speech entitled “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas”, the butterfly analogy was born.
It is Lorenz’s work on meteorological chaos that I want to look at specifically.
In or around 1961, vacuum-tube computers arrived at Lorenz’ disposal, and not surprisingly the first weather model was born as a set of a dozen or so differential equations involving such things as temperature, pressure, wind velocity etc.
During a re-run of this early model, Lorenz is believed to have restarted the program in the middle of its run by entering a variable to 3 decimal places – to his surprise the results were completely at odds with what was achieved earlier.
Restarting and re-entering the variable to its full 6 decimal places produced a repeat of the initial results – from this Lorenzo drew the inevitable conclusion that with his dozen or so equations, even a miniscule variation on input is capable of creating massive change in output.
But why such a radically different outcome for such a miniscule difference in input?
It transpires that the equations were non-linear, with a so-called “great dependence on initial conditions” – change the initial conditions even slightly and a large change in output is observed in a later state.
The conclusion that Lorenz drew, was that given that such small variations can create such massive variation in output, it was impossible to “model” a weather system.
This “sensitive dependence on initial conditions” was destined for higher things however.
I’m not sure if there is any relationship here to Peter, but James Gleick’s bestseller, ‘Chaos: Making a New Science’ built on Lorenz’ musings, became the mantra for many to follow in all walks of life:- finance, science and even time-travel effects in science-fiction. It is now bandied around in insurance, marketing and business boardrooms throughout the world.
Being quite a reserved individual, Lorenz was taken aback by the devotees to his speech. ‘I was just trying to determine why we didn’t have better luck with our weather forecasts, I never reached a point where I believed the butterfly was a scientific fact. At most, it’s a hypothesis. I never expected it to become so huge outside meteorology.”
So my question now is, given that we cannot even begin to measure things such as SST to anywhere near 3 decimal places, how can we expect low-accuracy and highly volatile data, entered into chaotic models of even more chaotic systems to produce anything of significance?
If Lorenz gave up when he discovered weather to be totally chaotic and unpredictable beyond a few days, what makes the Climate Modellers believe they can do better forecasting years or even decades ahead?