FFT of TSI and Global Temperature

This is the application of the work-in-progress Fast Fourier Transform algorithm by Bart coded in R on the total solar irradiance (TSI via Lean 2000) and global temperature (HadCRU). The results show (PDF) that the atmosphere is sufficiently sensitive to variations in solar insolation for these to cause recent (post 1950) warming and paleowarming.

The mechanism, suggested by the basic energy balance model, but confirmed by the plots below, is accumulation. That is, global temperature is not only a function of the magnitude of solar anomaly, but also its duration. Small but persistent insolation above the solar constant can change global temperature over extended periods. Changes in temperature are proportional to the integral of insolation anomaly, not to insolation itself.

The figure below is the smoothed impulse response resulting from the Fourier analysis using TSI and GT. This is the simulated result of a single spike increase in insolation. The result is a constant change, or step in the GT. This is indicative of a system that ‘remembers shocks’, such as a ‘random walk’. Because of this memory, changes in TSI are accumulated. (Not sure why its negative.)

Below is the Bode plot of the TSP and GT data (still working on this). The magnitude response shows a negative, straight trend, indicative of an accumulation amplifier. This is also consistent with the spectral plots of temperature that cover paleo timescales in Figure 3 here.

Bart’s analysis is going to be very useful doing this sort of dynamic systems analysis in a very general way. Up to now I have been using spectral plots and ARMA models.

This analysis above is an indication of the robustness of the method, as it gives a different but appropriate result on a different data set. Its going to be a very useful tool in arguing that the climate system is not at all like its made out to be.

I will post the code when its further along.


0 thoughts on “FFT of TSI and Global Temperature

  1. Are you assuming a leaky capacitor with a nominated decay constant, or some other assumption? Given the narrow global T range as much as can be deduced from geology, the accumulation must de-accumulate sometime. Any ideas on mechanism and rate? (Apologies in advance if you have covered this and I missed it).
    I’m looking at the whole cycle now as the combination of the numerous paths that an incoming photon or its energy can take between entering the global scene and leaving it. This is not restricted to radiative physics.

  2. David, it’s great to see someone with real expertise getting into accumulation models of solar input to the climate system. I did a very crude analysis by working out the sunspot number at which the ocean neither gains nor loses heat. Coincidentally(?) it comes out at the same number as the longterm average SSN of around 40 using SIDC’s time series.

    I then made a cumulative total departing from this number to see how much solar energy accumulated and was lost over the time period of the HADsst2gl temperature series.

    I found that once the big oceanic oscillations corresponding to the El Nino and La Nina dominant periods were accounted for, the accumulation of solar energy as ocean heat content pretty much explains the temperature history, if an amplifying mechanism such as reduction in tropical cloud cover is included.


  3. This is actually just what you would expect in a steady state system which his a moderate degree of elasticity.
    You would get exactly the same type of data of you heated one face of a slow rotating ball; er sort of like the Earth really.
    The oceans provide a large heat sink and so even things out, but slight increase in light flux, maintained over a long period will change the temperature.
    I have always wondered what happens to all the energy in the, variable, uv part of the solar spectrum. This is pretty much ignored as it only heats up the thermosphere and so doesn’t get counted in the total energy budget.

  4. The primary mover of energy from ocean to space is water evaporation and high altitude condensation or freezing and not radiation / conduction through temperature difference.  pg

      • David ,thanks – I am curious to know why a longer period wasnt looked at – is the nino information unreliable?
        I have been playing around and find that from 1871 to 2010 a simple straight line explains 65% of HadCrut and cumulative Nino 75% .  Bob Tisdale suggests that Elnino heats more than la nina cools so I had a look at a ‘broken stick’;   LibreOffice solver came up with the kink at 1.2 and a factor of 1.7x above and 0.6x below explaining about 82% but maybe this is a case of overfitting?

      • Chas, the study above was done on all the data 1880-on.  In the papers the period has been back to 1950, or back to 1900.  I think the global temperature becomes unreliable around the bucket-adjustment period, and very poor thereafter, at least for recovering solar cycle variations.

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