Home > GIStemp, LSCF, Statistics > Lines, Sines, and Curve Fittings 14 – Two Halves

Lines, Sines, and Curve Fittings 14 – Two Halves

2011 February 14

Assume a spherical cow. Slice in two. Broil one half. Bake the other. Bones go into the stew.

Here is GISTEMP for both hemispheres (north and south). The hemispheric data is taken from the GISTEMP zonal annual means.

The linear trend residuals for the Northern Hemisphere:

We use the same fourier technique we used in the previous post, namely the R spec.pgram as wrapped in spectrum

The fourier spectral peak for the Northern Hemisphere remains the same as in the global analysis as seen in the previous post (67.5 years).

For comparison, here are the residuals of the linear trend for the Southern Hemisphere:

The 67.5 year peak is entirely absent in the Southern Hemispheric data. Instead, we have peaks at 135, 45, 22.5, 15, and 3.6 years. The 135 is just slightly longer than our data range and is suspicious – but it is a multiple of 45 which is a multiple of 22.5. (see update below)

1/sp$freq[sp$spec==max(sp$spec)] # [1] 135
1/sp$freq[3]  # [1] 45
1/sp$freq[6]  # [1] 22.5
1/sp$freq[9]  # [1] 15
1/sp$freq[37] # [1] 3.648649

The 135 / 45 / 22.5 series is interesting in that they are all multiples of 11.25. The sunspot cycle is described as approximately 11 years – although the average period seems to be slightly below 11 years rather than slighlty above it.

We can fit an exponential + sine wave to both hemispheric series using nls. Over this period, the global best fit is very similar to the NH best fit + SH best fit.

However, the best fit for the global series is not the same as the NH best fit + SH best fit as seen in the extension to 2100. The best fit for the NH gives a sine periord of 67.6 years – a much better match for the spectral analysis than the sine period using global data. The best fit for the SH is 46.1 years.

The script is here

Coral records are now being used to reconstruct the amplitudes and frequencies of El Niño events in the Pacific (see Figure 8.6.4). A search for coral growth cycles yielded the following periods: 37.5, 30.8, 27.0, 21.7, 7.5 and 6.0 years. Note that here is no peak near 11 years, the cycle of sunspots. Four of these peaks resemble a series of multiples of 7.5 years (7.5, 15, 22.5, 30, 37.5) but with the 15 and 30-year cycles missing. This suggests a dominant influence of something called the “North Atlantic Oscillation” with a period near 7.5 years. The period near 22 years is twice the major solar cycle. Thus, if solar cycles are important in stimulating the system, their energy is subsumed into internal oscillations, possibly locked in near 22 years. The coral record also may reflect volcanic eruptions. The elevated growth rate after the 1601 A.D. Peruvian eruption suggests favorable effects occurred from increased ocean mixing during harsh winter storms, leading to higher nutrient content in this nutrient-starved region.


Although it would be curious if the NAO is the dominant signal in the Southern Hemisphere.