Milankovitch back to 1974

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Milankovitch and the ice ages – welcome back to 1974

Why am I chuckling? After he’d had misgivings about the Milankovitch theory of the comings and goings of the ice sheets, Luboš Motl now says in The Reference Frame:

… the Milankovitch orbital cycles do describe the glaciation cycles in the recent 1 million years very well and nothing else – CO2 or random internal variations – is needed to account for the bulk of the data.”

You can read Motl’s story in full at

— and download from there a 2006 paper that wins Motl over, by Gerard Roe of the University of Washington in Seattle.

The abstract of that paper reads (with my emphasis added):

The Milankovitch hypothesis is widely held to be one of the cornerstones of climate science. Surprisingly, the hypothesis remains not clearly defined despite an extensive body of research on the link between global ice volume and insolation changes arising from variations in the Earth’s orbit. In this paper, a specific hypothesis is formulated. Basic physical arguments are used to show that, rather than focusing on the absolute global ice volume, it is much more informative to consider the time rate of change of global ice volume. This simple and dynamically-logical change in perspective is used to show that the available records support a direct, zero-lag, antiphased relationship between the rate of change of global ice volume and summertime insolation in the northern high latitudes. Furthermore, variations in atmospheric CO2 appear to lag the rate of change of global ice volume. This implies only a secondary role for CO2 – variations in which produce a weaker radiative forcing than the orbitally-induced changes in summertime insolation – in driving changes in global ice volume.

Roe, G. (2006), In defense of Milankovitch, Geophys. Res. Lett., 33, L24703, doi:10.1029/2006GL027

The reason for my chuckles is that the “change in perspective” that Roe adopts was available more than 30 years earlier in the first formal verification of Milankovitch, which I published in Nature in 1974. Using a pocket calculator, I simply assumed that the rate of change in global ice volume per thousand years was proportional to the difference between the summer sunshine at a high-ish northerly latitude and a level of sunshine at which the ice neither advances or retreats.

I’ve formatted my paper to go on this blog. Some comments in passing. The paper was cited for a few years, but then forgotten because I wasn’t in the climate physicists’ club. I don’t regret choosing 50 North for the critical latitude, even though everyone else wants to go to the Arctic Circle. In Table 1 the match of dates for core stages 16 and 18 was much improved when the date of magnetic reversal was pushed back from 700,000 to more than 720,000 and perhaps even 780,000 years ago. (I kick myself now – I could have predicted that correction.) My working address has changed — the current one is in “About”. And there’s an earlier story on this blog about Milankovitch at

Reprinted from Nature, Vol. 252, No. 5480, pp. 216218, Nov. 15, 1974. Reformatted from OCR scan

Arithmetic of ice ages

Fig. 1 Upper: measured oxygen-isotope changes in marine organisms from Fig. 9 of ref. 1; low points indicate a large volume of ice. They are plotted against depth in core and so the dating is uncertain except at the magnetic reversal 700,000 yr BP. Lower: ice volume derived by arithmetic as described in the text, from 50 oN insolation data given in ref. 3 (inverted, arbitrary units).

THE Milankovitch hypothesis is that glaciations occur when the Northern Hemisphere receives relatively little summer heat from the Sun, because of astronomical factors that alter the orientation of the Earths axis and the eccentricity of its orbit. A new time scale for the oceanbed record of the past eight glaciations is provided1,2 by the magnetic reversal at the start of the Brunhes epoch, 700,000 yr ago. In addition, Vernekars recalculated insolation tables3 are now available. For a popular account of climatic change4, I wanted to illustrate the opportunity thus provided, for a re-evaluation of the Milankovitch hypothesis.

An inspection of Vernekars tables suggested that the crucial zone for summer sunshine was not at the Arctic Circle, as has often been supposed, but at 50 oN. The theory of ice sheets growing from the bottom up5,6 and the discovery of the English Channel glacier7,8 fed from the sea bed south of Ireland make this choice of latitude glaciologically plausible.

Suppose, now, that a decline in summer sunshine at 50 oN below a certain level allows the volume of glaciers and ice sheets to grow in simple proportion to the deficit, while summer sunshine above that level melts ice with a different proportionality. For the point of equilibrium I take 17 langley per day (1 langley = 1 calorie/cm-2) above the 1950 value of 847 langley per day. Glacial maxima or minima are then predicted at the dates when the summer insolation at 50 oN crosses the +17 level.

Simple summing, by 1,000-yr steps, of the surpluses or deficits above or below +17 indicates in arbitrary units the extent of freezing or melting between the maxima and minima. With a melting rate of unity, a freezing rate of 0.22 gives a realistic curve for the most recent glaciation (the past 78,000 yr); melting the ice is easier than making it. The same proportionalities are then applied over the past 860,000 yr. Finally, as surplus sunshine cannot melt ice that is not present, a limiting value for the reduction in ice volume can be assumed. The running totals then predict the amount of ice in the world. Figure 1 compares the resulting arithmetical curve with measurements of the oxygen-isotope ratios in marine fossils1, which are also thought to be proportional to the amount of ice in the world. Table 1 compares the dates of maximum glaciations arrived at arithmetically, with the corrected dates deduced by Emiliani and Shackleton2 who take account, as best they can, of variations in ocean-bed sedimentation rates.

Table 1 Comparison of corrected ocean-core dates of maximum glaciation, taken from Fig. 4 of ref. 2, and the dates deduced arithmetically.

Meteorological processes are so notoriously nonlinear that my assumptions are almost frivolous. The matches between the curves of Fig. 1 and the dates of Table I are very much better than they deserve to be unless the Milankovitch effect is indeed dominant. The arithmetical curve captures all the major variations and the core stages can be identified with little ambiguity. The defects include an excessive warm peak 170,000 yr ago, and excessive freezing in the more recent parts of core stages 11 and 21. On the other hand, the arithmetical curve registers two known events not conspicuous in Shackleton’s oxygen-isotope curve, namely the cooling at 90,000 yr ago9,10 and the warming at 100,000 yr BP required by the speleothem data2.

Other processes are at work, including the 2,500-yr oscillation11 that correlates with 14C production in the atmosphere, and hence with solar events rather than with the Milankovitch effect. Nevertheless the variations in summer sunshine available for melting the snow of the Northern Hemisphere plainly determine the first-order pattern of past glaciations. One can even put an order of magnitude to the process. A surplus of one langley per day above the +17 level, at 50 oN in summer, will melt sufficient ice to change the oxygen-isotope ratio of ocean water at a rate of 0.01 0/00 per thousand years.

Fig. 2 Enlargement of the arithmetical curve for the most recent (Würm/Wisconsin) glaciation and an extrapolation for 120,000 yr into the future by the same arithmetical rules.

Extrapolation of the curve gives a first-order forecast (Fig. 2) for the ‘next’ ice age, which began 5,000 yr ago and will end 119,000 yr from now. Broecker and van Donk12 arrived at a broadly similar forecast by more general reasoning from the insolation predictions. This ice age looks like a relatively slow starter. The theory, though, is of widespread snow that fails to melt in the vicinity of 50 oN in summer, so that large areas of North America, northern Europe and the USSR will have to be encrusted with ice sheets during the next few thousand years, to fulfil the expectations of Fig. 2.

I thank Dr N. J. Shackleton for suggestions and advice, and Professor H. H. Lamb for encouragement.


8 The Chase, Furnace Green, Crawley, Sussex RHIO 6HW, UK

Received July 22; revised September 5, 1974.

1 Shackleton, N. J., and Opdyke, N. D., Quat. Res., 3, 39 (1973).

2 Emiliani, C, and Shackleton, N. J., Science, 183,511 (1974).

3 Vernekar, A. D., Met. Monogr., 12, No. 34 (1972).

4 Calder, N., The Weather Machine (BBC London, 1974).

5 Lamb, H. H., and Woodroffe, A., Quat. Res., 1, 29 ([970).

6 Matthews, R. K., Quat. Res., 2, 368 (1972).

7 Nature, 248, 103 (1974).

8 Kellaway, G. A., Proc. R. Soc. (in the press).

9 Dansgaard, W., et al., Quat. Res., 2, 396 (1972).

10 Kennett, J. P., and Huddlestun, P., Quat. Res., 2, 384 (1972).

11 Denton, G. H., and Karlen, W., Quat. Res., 3, 155 (1973).

12 Broecker, W. S., and van Donk, J., Rev. Geophys. Space Phys., 8, 169 (1970).


3 Responses to Milankovitch back to 1974

  1. Luboš Motl says:

    Dear Nigel,

    thanks for sharing this interest with many of us and congratulations to having known about the right comparison of the functions decades before others! I completely trust you – and I probably had the same idea 30 years later but didn’t push it much… 😉

    Best regards

  2. […] – can be made tolerable by adaptation and technological innovation. Nigel Calder this week revisited the study of Milankovitch cycles he published in […]

  3. […] Roe, an ex-student of Richard Lindzen, 30 years after some visions by Nigel Calder published in Nature, realized a serious technical mistake many people before him were making. They […]

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