Sinusoidal Wave in Global Temperature

A dynamic way of looking at global temperature is to plot it in phase space, which is usually with the position on the x axis and velocity on the y axis. Below is the phase space graph of global temperature since 1996 with temperature on the x axis and change in temperature on the y axis.

The graph of position versus velocity displays an inward spiral. In classical mechanics, this is described as an “attractor” and shows that the system is trapped in a potential well from which it cannot escape, as in this animation of a damped harmonic oscillator.

Graphs of temperature versus time show that the temperature since 1996 should be seen as a sinusoidal wave that decreases exponentially since the sudden impulse from the “El Nino of the Century” in 1997-8.

The phase diagram provides another way of showing that the global temperature has stopped warming. With average temperature acting as an “attractor”, the system has been trapped in a potential well for 15 years, that’s as good a description of “stopped” as you find in dynamics.


0 thoughts on “Sinusoidal Wave in Global Temperature

  1. Why am I reminded of the Uni days, stories of that great Bird that flew aound in ever-decreasing circles until, with a puff of smoke, it disappeared up its fundamental orifice?
    OK, so you say that the El Nino of the century started the space for the spiral to inhabit. Then, as the spiral tightens, it must approximate to a point awaiting the next shock. I can’t recall any temperature graphs that show this reduction to a point. Is this because
    (a) I observe badly
    (b) the data are faulty
    (c) the time interval is unrepresentative
    (d) shocks happen frequently
    (e) some reason I have not thought of yet?
    Over at Real Climate there is a thread on the use of cycles, leading to Fourier transforms and relations to orbital geometry, thence to climate. They might have some arguments, for a change, that would cause you to pause before developing this too far.
    Also, there is at least one simple mechanical device that can produce similar attraction, e.g. a damped pendulum whose axis is rotating. Not sure of the relevance to global temps.
    Finally, in case you are wondering, no, I have not gone over to the dark side. I’m just stimulating discussion.

    • Geoff, If you look back there are similar periods, but also there are shocks.  If the spiral is a real representation of the physics, then it suggests the temperature record is OK (at least back 16 years).  This is not the same as the Fourier transform, which has no physics behind it (by physics I mean the conservation of energy) only a mathematical transform.  The pendulum is an example of an harmonic oscillator too.    

  2. Hi David,
    I’ve thought about these kinds of ‘decay curves’ as well. The entire climate history of the Holocene can be interpreted this way. From the initial peak of the uplift out of the last glacial, through the holocene optimum, the mycean, Roman and medieval warm periods. a decreasing undulation.

    You can generate an similar decay curve by taking the difference  from the golden section of successive fractions representing the fibonacci series too.

  3. This brings to mind the superimposed (roughly) sinusoidal trends with 934 year and 59.6 year periodicity – plotted entirely from astronomical data for the sun and nine planets.

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