Is best fit for Milankovitch cycles at 65N?

“Classical” Milankovitch theory is about 41ky and shorter periods, without the significant long terms of 100ky and above which are the subject of a great deal of postulation today. As an exercise a special version of temperature proxy Vostok ice core data was prepared and correlated with four different computations of Berger 1991 solar insolence at lags of between zero and 18ky. The best correlation was for the sum of 65NJul and 65SJan, r-squared=0.31 and at a lag of 7ky.

Figure 1

This result was unexpected because of the popular view that 65N is best fit. Further it suggests a rolling effect starting in the north and ending in the south.

Two problems were noted in private discussion:

• Is summing 65NJul and 65SJan a valid process?
• Few if any datasets exist where Arctic and Antarctic can be examined for a phase difference because of the unreliable dating of proxies, some of which have been adjusted for time coherence.

The primary period of the mean is about 41ky which makes sense. No investigation of phase skew has been done where I would expect the lag to vary with frequency.

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A description of the data preparation follows

Vostok data

The published data is irregularly sampled but regularly sampled data is far preferable mathematically, and so the dataset was resampled to 1ky. This is standard signal processing, in this case oversample at 1 year, filling missing datapoints with null and low pass filter at 2ky, which turns nulls into valid. The result was decimated from 1 year to 1ky. A 766 year skew was introduced so that the sample points are concurrent with the insolation data.

Figure 2

Figure 2 , plotted overlay and irregular data.

Figure 3

Finally the data was high pass filtered at about 55ky (figure 3), removing the 100ky and above content.

Figure 4

Figure 4 illustrates what is going on, is not actually complicated, just difficult to explain in words.

Figure 5

Figure 5 shows the whole thing as straight plots. The “<50ky periodicy” data in blue is the data which is going to be used for correlation.

Insolation data

Figure 6

The data is actually output from solar system modeling. this has to be taken as fact because no accurate historic reference exists. The sun or planet orbits might have changed. This model is used as published, with the addition of sum and difference of 65NJul and 65SJan. (this was not expected to be part of a result) An extra 20,000 years of insolation data is necessary so that the full length of the Vostok data can be used at all time lags.

Figure 6 shows a plot of 65N, 65S and mean (sum). This data is used for correlation and the dataset is 20ky longer than the Vostok data to allow for a sliding correlation window on the whole Vostok data.

General

• Dates are adjusted from the dataset BP (reference AD1950) to AD.
• All plots run conventionally left to right which is old to the left and new to the right.
• Filtering uses dataset end compensation

The four insolation parameters were correlated with the Vostok data lagged from zero to 19 ky.

Results

In table format:

lag	65NJul	65SJan	difference	mean	r-squared
18	-0.05	-0.01	-0.02	-0.07
17	-0.06	0.07	-0.07	0.01
16	-0.06	0.15	-0.11	0.1
15	-0.06	0.21	-0.15	0.19
14	-0.05	0.27	-0.17	0.27
13	-0.02	0.31	-0.18	0.34
12	0.01	0.33	-0.18	0.41
11	0.05	0.34	-0.16	0.47
10	0.1	0.32	-0.12	0.51
9	0.15	0.3	-0.08	0.54
8	0.2	0.26	-0.03	0.56
7	0.25	0.21	0.02	0.56	0.31251
6	0.29	0.16	0.07	0.55
5	0.32	0.11	0.11	0.52
4	0.33	0.07	0.15	0.48	0.11138
3	0.33	0.03	0.17	0.43
2	0.31	-0.01	0.18	0.37
1	0.28	-0.03	0.17	0.3
0	0.23	-0.04	0.15	0.22

For a plot of the table, see figure1.

Figure 7

Figure 7 show the Vostok derived data and leading insolation data.

Appendix

NAME OF DATA SET: Vostok Ice Core Data for 420,000 Years

LAST UPDATE: 11/2001 (Original Receipt by WDC Paleo).

CONTRIBUTOR: Jean Robert Petit, LGGE-CNRS.

SUGGESTED DATA CITATION: Petit, J.R., et al., 2001, Vostok Ice Core Data for 420,000 Years, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2001-076. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA.

Dataset web page

Dataset

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Berger A. and Loutre M.F., 1991, Insolation values for the climate of the last 10 million of years. Quaternary Sciences Review, Vol. 10 No. 4 pp. 297-317, 1991.

Insolation data, directory

Insolation text data file

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