Tropical timings: more origins of Earth’s 2.4 million year eccentricity ‘grand cycle’ 

In the previous post on this topic, we said: ‘In a follow-up post we’ll look in more detail at the José Rial (1999) research article’: Pacemaking the Ice Ages by Frequency Modulation of Earth’s Orbital Eccentricity.’

So here we are. The numbered ‘References and Notes’ at the end of Rial’s article also contain useful commentary, but these are the author’s opening remarks, in effect an ‘abstract’ in science paper terms.

‘Evidence from power spectra of deep-sea oxygen isotope time series suggests that the climate system of Earth responds nonlinearly to astronomical forcing by frequency modulating eccentricity-related variations in insolation. With the help of a simple model, it is shown that frequency modulation of the approximate 100,000-year eccentricity cycles by the 413,000-year component accounts for the variable duration of the ice ages, the multiple-peak character of the time series spectra, and the notorious absence of significant spectral amplitude at the 413,000-year period. The observed spectra are consistent with the classic Milankovitch theories of insolation, so that climate forcing by 100,000-year variations in orbital inclination that cause periodic dust accretion appear unnecessary.’ [bold added]

He goes on to say: ‘One of the well-known features of the [oxygen-18] time series from deep-sea sediments is the
slight but evident change in the duration of consecutive glacial periods (7), which oscillates from about 120 to 80 ky.’

This seems to mean between the periods of 3 and 2 obliquities of 41~kyr each.

Caption: Fig. 4. (A) High resolution spectra (signal bandwidth 0.00093 cycles/ky) of the tuned Site 849 record (see Fig. 3) is shown compared to the Fourier transform of the model FM signal given by Eq. 3. As predicted by FM theory, the modulating power does not appear as a spectral peak, but as separation between each carrier and its sidebands. [bold added]

We can translate some of the periods in Figure 4(A) into a numerical chart, based on data from some of our earlier tropical timing posts.
Analysis of Rial (1999) figure 4A

” data-image-caption=”" data-large-file=”https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=614″ src=”https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=614″ alt=”" width=”614″ height=”270″ class=”aligncenter size-large wp-image-87387″ srcset=”https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=614 614w, https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=150 150w, https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=300 300w, https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png?w=768 768w, https://talkshop.blog/wp-content/uploads/2026/08/rial99_ts.png 876w” sizes=”(max-width: 614px) 100vw, 614px” />
This covers the periods shown from ’77 kyr’ to ‘123 kyr’, excluding ‘100 kyr’ which we discussed in the previous post on this topic. The 2 long eccentricities (LE) are the subharmonic of 1 LE, as used in the Rial paper.

The caption to Fig.4(A) refers to ‘each carrier and its sidebands’. In our chart the carriers are at 3/20 (3*obliquity each), 3/26 (short eccentricity) and 3/32 (3*axial precession each). The sidebands are 3/23 and 3/29. The periods from Fig.4(A) are shown in quote marks.

To remove the fraction we multiply the 2 long eccentricities (LE) by 3, giving 6 LE = the ‘2.4 million year’ grand cycle (in fact 2.47~ myr), which consists of:
60 obliquities (3*20)
26 short eccentricities
96 axial precessions (3*32)

The sidebands at 3/23 and 3/29 have their own pattern.
From Note 18 of Rial’s paper:
‘Eq. [equation] 3 predicts that the spectral peak at 107 ky is strong because it is both a sideband of the 95-ky carrier modulated by the 826-ky subharmonic and a nonlinearly produced combination tone, which probably explains why it appears to have its own sidebands (Fig. 4).’ [bold added]

We find the ‘107 ky’ period to be 107568 = 108*996 tropical years (TY). In the Talkshop post on the orbit of Neptune (here) it was found:
73 Neptune = 1008 Jupiter (144*7) = 11952 Earth (144*83 or 72*166 TY). Here we’ll call this the JNE cycle.

Since 11952 = 12*996 TY, the ‘107 ky’ period is 9 JNE cycles. The periods of ’71 ky’ and 143 kyr’ in Fig.4(A) are its sidebands. Then we can propose a combination tone:
2/23 * 2 LE = ’71 ky’ (72*996 TY) = 6 JNE cycles (72/12)
3/23 * 2 LE = ‘107 ky’ (108*996 TY) = 9 JNE (108/12)
4/23 * 2 LE = ‘143 ky’ (144*996 TY) = 12 JNE (144/12)

The periods at each end of Fig. 4(A) look likely to be:
5/23 * 2 LE = ‘179 ky’ (180*996 TY) = 15 JNE (180/12)
3/38 * LE = ’65 ky’ (65206.9 TY), a +6 extension of the 3/20, 3/26 and 3/32 series.

In summary, the chart supports the idea of a 2.4 million year grand eccentricity cycle, being 6* the long eccentricity period (‘the 413,000-year component’ – J.Rial) which we believe is 414*996 = 412344 TY.