Tamino: Cheaper by the Decade offers a good post about recent global temperature trends.

The post states that “The cause of the swings in decadal rate is random events like el Nino… They can change the rate of temperature increase dramatically, and they are (as far as we know) random”. I would disagree. El Nino is not random. It is certainly pseudorandom, meaning that it appears to be random, but is an entirely deterministic causal process which is not fully understood yet. We can look at the Fourier transform of the Southern Oscillation Index (SOI; a measure of El Nino) to see on what temporal scales that El Nino repeats itself.

To get the plot above, I applied a 13-month moving average to the SOI, which acts as a lowpass filter. This means that the only frequencies we’ll see are those corresponding to time periods of over one year. I also filtered the extreme low frequencies as well. Anything over 20 years will be dominated by the Pacific Decadal Oscillation (PDO) [see e.g. Chan and Zhao, 2005]. In the figure above, two “peaks” in the frequency spectrum are noticable. One occurs at about 0.015 cycles/month, and the other at 0.006 cycles/month. These two frequencies correspond to periods of 5.6 and 13.9 years respectively. I would argue that the 13.9 year period is too long to be ENSO, and must be something else, perhaps a harmonic of the PDO. The other period is 5.6 years, which is most likely the true ENSO signal in the SOI data. ENSO is not truely stochastic; it is a quasi-periodic time-series that occurs roughly every 5-6 years. Jolliffe (1983) has shown that some quasi-periodic series can be modeled as second-order autoregressive processes. It would be interesting to see if this applies to ENSO as well.

Tamino then says “…in the past given the impression that global warming has recently accelerated. Under certain circumstances it has, but those are limited to consideration of special time intervals.” To investigate this, I used the CRU Global Temperature dataset [Tamino used GISTEMP]. I also did not limit my analysis to the last 30 years. Below is the 21-year averaged temperature trends as a function of the central year. So for example, the data point for the year 1900 would be the linear temperature trend over the years 1890 through 1910.

The average trend in the temperature trend (the temperature acceleration?) is 0.019C/decade/decade. That is shown as the blue dashed line above. The actual temperature trends (white line) are quite variable, even though a 20-year average was done. If the averaging length was increased to 100 years, the following plot is obtained.

And if you’re wondering how the temperature acceleration changes with averaging length, have no fear - underdog is here. Actually not, just look below.

The temperature acceleration decreases around an averaging length of 70 years because of the two period of level temperatures, as shows at Tamino, which each last about 30 years. Because the average temperature accelerations at all timescales above 6 years are positive, this suggests that the rate of increase in the temperatures has been increasing over the entire time series (since the 1880s).

References:
Chan, J. C. L., and W. Zhou (2005), PDO, ENSO and the early summer monsoon rainfall over south China, Geophys. Res. Lett., 32, L08810, doi:10.1029/2004GL022015.

Jolliffe, I.T. (1983), Quasi-periodic meteorological series and second-order autoregressive processes, International Journal of Climatology, 3, 413-417, DOI: 10.1002/joc.3370030409.

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