Phenomenology of Ice Ages

The exact cause and evolution of ice ages still remain a mystery [1]. Why did the Earth shift into an unstable climate with global oscillations of 4-5 degreesC every 100,000 years? What is the cause of the large scale glaciations with shorter warm inter-glacials? Proposed Milankowitz cycles cannot properly explain why their relatively small radiative effects apparently have been amplified during the last million years or why long term temperatures have been falling for over 20 million years. The work presented here does not attempt to explain the origin of  the ice ages, but instead it tries to  parameterise the observed temperature dependencies to derive as much quantitative information as possible. This approach applied in other branches of physics is called phenomenology[2]. The amplitudes of Milankowitz harmonic cycles are derived from making fits to data.  These fits are then used to predict the occurence of the next Ice Age with some confidence.

The “LRO4” data [3] is a remarkable set of global proxy temperature data spanning a 5.3 million year period throughout the pleistocene Ice Ages.  It consists of a  stack of 57 globally distributed benthic d18O records. Unlike the Vostok Ice core samples which measure temperature at a single site in Antarctica, LRO4 represent the global temperature  and should therefore be more representative of climate changes. The data are based on samples of deep sea sediments consisting of calcium carbonate from plankton. The oxygen content (CaCO3) consists of a small amount of O18 mixed with O16. The ratio of O18 to O16 increases slightly with cooler surface temperatures. This is because O18 is slightly heavier and evaporates less readily than O16. Delta O18 is the ratio of  O18/O16 compared to a standard Calcite value. LRO4 represents a global measure of this ratio from ocean sediments and can be directly related to prevailing temperatures at the time. It provides a unique overview of the onset of Ice Ages (Pleistocene Era) starting 5.3 million years ago.

The objective of this post is to try and quantify the size of Milankowitz components in the LR04 data by fitting the data to a linear sum of Milankowitz harmonics plus any overall linear trends. The data as presented fall into 5 natural time periods based both on sampling rate and clear differences in signals. These are 1) 0-600 thousand ya 2)600-900 thousand ya 3)900-1500 thousand ya 4) 1500-3000 thousand ya and 5)3000-5300 thousand ya. For each period  a fourier transform was used to identify any harmonics present and then the data was fitted to a general  form with up to 3 harmonics and a linear offset with optional slope

deltaO18 = const + ax + b*sin(2pi/wavelength*x – c) + d*sin(2pi/wavelength2 – e)+ f*sin(2pi/wavelength3 – g)


1) For the last 600,000 year data there are clear oscillations present at 100,000 years and 41,000 years corresponding to the eccentricity changes of the Earth’s orbit and the change in obliquity. A very small signal for 23,000 years was seen but including it in the fit made little difference to Chi-squared. It seems to have a negligible effect on Ice Ages. The best fit result was:

delO18 = 4.0 +0.407*sin(0.0628*x-39.5) + 0.259*sin(0.153*x-45.3)

2) 600 – 900 kya

Already at 600 kya there is a change evident in the cycle of Ice Ages. The 41,000 year cycle is clear but the time delay between successive Ice Ages has begun to shorten from 100,000 years. In fact a fit using 100,000 years is not good.  A much better fit is found with a time period of 84,000 years. The reason for this change in the data is not clear. No 23,000 year signal is present. The best fit found was

delO18 = 4.2 +-0.36*sin(0.075*x-31.1) + 0.29*sin(0.153*x+5.27)

The combined fits compared to the data from both eras combined is shown below.

Combined fit back to 900,000 ya

Combined fit back to 900,000 ya

3) 900 – 1500 ya

Big changes begin to be evident in the data further back than 900,000 years. The data set from 900-1500 shows that the 100,000 year cycle has almost disappeared leaving just the 41,000 year signal. The best fit found was del18 = 3.8 + 0.1*sin(0.0628*x+19.7) + 0.248*sin(0.153*x+11.0). There is then a clear linear warming trend from 1500 ya until 3000ya where the only evident signal is that from the obliquity (41,000 year cycle). The best fit was a) from 900-1500

3.8+0.1*sin(0.0628*x+19.7)+0.25*sin(0.153*x+11)  – (small 100,000y cycle)

and b)

del18 = 4.0 – 0.00049*(x-1500) -0.17*sin(0.153*x-4.5) – 0.006*sin(0.273*x-29.7)

The third term is the 23,000 year precession term and the tiny amplitude demonstrates that it has a negligible effect. The combined fits from

Combined fits compared to data 900-1500 ya

Combined fits compared to data 900-3000 ya

Finally the fit to data from 3000 to 5300 kya begins to show a longer 400,000 year eccentricity oscillation as well as t 41,000 year oblicity. The best fit found was

delO18 = 3.25 -0.0002*(x-3000) -0.03*sin(0.015*(x-3000)-49.6) +0.07*sin(0.153*(x-3000)-31.3)) and is shown below.

Evidence of a 400,000 year elipticity oscillation 3000-53000 ya

Evidence of a 400,000 year elipticity oscillation 3000-53000 ya

The full 5.3 million years of global temperature change as reflected in the LR04 data with the fits described above is shown in figure 5.  This clearly shows a long term cooling of the climate leading  to the severe Ice Ages of the recent past. Three proposals have been given for this long term cooling trend. The first is that Antarctica has moved to fully cover the  South  Pole, isolating any heat flow from the oceans and lowering the Earth’s albedo [4]. The second proposal is that the Tibetan plateau has been slowly rising as India continues to crash into Asia[5]. The increasing ice cover over a large tropical region then changed the Earth’s energy balance by  decreasing albedo.  The third proposal is that the closing of the Panama Isthmus 3 million years ago altered the flow of heat in the oceans leading to the Gulf stream[6]. This brought more moist air to the polar regions resulting in more snow and ice.  The Earth’s climate appears currently to be in a highly unstable state, with sawtooth-like oscillations every 100,000 years flipping between long glaciations and shorter warm inter-glacial periods. The onset of a new Ice Age is a gradual process ending when temperatures reach a lower limit flipping  back rapidly to a warmer phase for 10-20,000 years. The fits demonstrate that the driver for this instability are the two cycles – eccentricity and obliquity. However the details of the correlation are surprising.

For the last 600,000 years Ice Ages have followed a 100,000 year cycle coinciding with the Milankowitz cycle. Every inter-glacial period has been in phase with a maximum in the eccentricity. This corresponds to increases in elipticity of the orbit, which seems counter-intuitive since it accentuates the variation in solar energy throughout the year. One fact though is that a smaller perihelion increases the maximum solar insolation. Unlike Ice core data the LR04 data are global and therefore must represent changes in total energy balance.  From 600-900 thousand years ago the duration of Ice Ages shorten slightly to 84,000 years and further back disappear completely. It is as if the long term cooling trend needed to reach a threshold for the orbital eccentricity oscillation to kick in.

The second clear observation is  that the 41,000 change in the angle of rotation of the Earth to the orbital plain (oblicity) has had a major effect on climate for at least the last 5 million years.  Surprisingly, the larger the tilt the warmer the climate, as demonstrated in figure 4. A larger obliquity means there are larger extremes in summer and winter temperatures. Both the Arctic Circle and the tropics increase in extent.  I suspect it must be the second effect which wins out, and when this is coincident with  large eccentricity with an annual closer distance to the sun – Ice Ages end !

Correlation of larger obliquity and warmer temperatures

Correlation of larger obliquity and warmer temperatures. Note that lower deltaO18 mean warmer global temperatures. The fit to data allowed a free phase component.

Correlation of inter-glacials with maximum eccentricity of Earth's orbit

Correlation of inter-glacials with maximum eccentricity of Earth

The overall fit to 5.3 million years of proxy temperature data is not perfect but does reproduce the main features of the observed data. The rapid end to recent  Ice Ages resembles better a saw-tooth oscillation rather than a simple harmonic. However the recurrence of Ice Ages over the last 600,000 years is very  well represented by the fit. Therefore this fit can be used with some confidence to extrapolate into the future and thereby predict the onset of the next Ice Age. This is shown below.

Next Ice Age due to start in 5000 years time.

Next Ice Age due to start in 5000 years time.

Detail of near term climate

Detail of near term climate

Within 10,000 years the Earth will be well on the way into a new deep glaciation which should peak 30,000 years into the future. By this time much of North America and Northern Europe will be under a huge ice sheet. Looking in detail at the data it can be seen that already within 2 thousand years from now, the climate will be noticeably cooler than the current climate. It appears to be the case that the climate is at its warmest period and will naturally begin to cool in the future.


The earth’s climate has cooled over the last 5 million years leading to a series of major glaciations over the last 900,000 years. Various origins of this cooling have  been proposed such as  the movement of Antarctica over the South Pole and the uplifting of the Tibetan plateau. Detailed analysis of recent  oscillations in temperature show a clear 100,000 year correlation with interglacials coincident with maxima of the elipticity of the Earth’s  orbit. The oscillation is not present more than 1 million years ago, however a 400,000 year super-oscillation of elipticity is evident from 3 – 5.3million years ago. The  41,000 year Milakowitz oscillation is observed throughout the full 5.3 million years with warmer interglacials coincident with a maximum tilt of the the Earth’s axis. No evidence of a significant 23,000 year  oscillation due to  the precession of the axis of rotation is observed.

The parameterized fit to the LR04 data for the last 600,000 years reproduces all previous glaciations and therefore can be used to predict the next Ice Age. It is found that the Earth is currently at its maximum interglacial global temperature and will start cooling within the next 2-5000  years. 20,000 years from now the Earth will likely be in the depths of another major Ice Age.


1) Maureen Raymo & Peter Huybers, Unlocking the mysteries of the ice ages, Nature Vol 451/17 P. 284, 2008

2) Concise Dictionary of Physics: Phenomenological Theory. A theory that expresses mathematically the results of observed phenomena without paying detailed attention to their fundamental significance.

3) Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography, 20, PA1003

4) Antarctic drift animation

5) Raymo, M.E., W.F. Ruddiman, and P.N. Froelich (1988) Influence of late Cenozoic mountain building on ocean geochemical cycles. Geology, v. 16, p. 649-653.

6) Gerald H. Haug2 & Ralf Tiedemann, Effect of the formation of the Isthmus of Panama on Atlantic Ocean thermohaline circulation,  Nature 393, 673-676 (18 June 1998)

About Clive Best

PhD High Energy Physics Worked at CERN, Rutherford Lab, JET, JRC, OSVision
This entry was posted in Climate Change, Physics and tagged , . Bookmark the permalink.

20 Responses to Phenomenology of Ice Ages

  1. Tom Loeber says:

    Yes, Milankovitch cycles are questionable as to their explanation of the total picture. Hamaker’s hypothesis in light of the growing incidence of noctilucents may better fit the saw-tooth sine wave. Unlike the Milankovitch cycles theory, Hamaker’s idea does not let carbon dioxide pollution off the hook as to complicity with climate change but, conversely, blames it. Devil’s Hole study sought to be more accurate at dating than ocean sediments and shifts the start of ice age conditions to peak carbon dioxide content of atmosphere. 2008 coral deposit samples analysis found ice caps melted before major ice ages started twice for the last two major swings. Global warming triggers collapse of interglacials.

  2. Pingback: Clive Best » Blog Archive » Part 2: What really causes Ice Ages ? - Is it Resonant Dust Clouds ?

  3. Pingback: Clive best: The real cause of Ice Ages – Resonant dust clouds? « Tallbloke's Talkshop

  4. Joachim Seifert says:

    Interesting and readable…. please add another ice age
    mechanism given with
    detailed tranparent calculations in ISBN 978-3-86805-604-4
    on the German “”

    Question: The most influencial Milankovitch cycle is the shortest
    cycle of the apoapsis precession (perihelion shift) [shifting a spot with
    7% more solar irradiation from the NH to the SH to the NH etc…
    continously around the globe…
    plus the second cycle, in the AGW literature always highly pointed
    at: The Axial
    precession cycle (wobbling of the Earth axis by 2-3 degrees),
    …… both cycles being 20,000 + years long (both the shortest cycles)…..
    and both described
    as super important and responsable for almost all paleo-everything….
    . why dont the 2 cycles show up in your curves…?

    • Clive Best says:

      Yes I agree that this should be the largest swing of solar heating between northern and southern hemispheres. However, all this is 100% dependent on the orbital eccentricity. If the Earth had a circular orbit the precession of the equinoxes would have no effect at all.

      My gut feeling is that changes in solar insolation at the poles due to orbital tilt (obliquity) have driven glaciations for the last 5 million years. The Earth cooled for independent reasons triggering ice ages. 1 million years ago eccentricity for some reason dominated the cycle. This must be astronomical, unless I can be convinced otherwise.

      The next ice age will begin within 2000 years. It is a far greater threat to humanity and nature than the hype over AGW. It is impossible for humanity to stop another glaciation, but AGW could perhaps offset some of its effects in the short term.

      Why do we torment ourselves worrying about how to dispose “safely” of nuclear waste over 100,000 years when much of the northern hemisphere will be uninhabitable in 20,000 years ?

  5. Jackie Pratt says:

    Why doesn’t this explanation, most especially the conclusion, get any real acknowledgement from the scientific community? Or has it happened, and just been buried under a mountain of AGW hubbub and screeching? What is the most legitimate refutation that has been offered to counter what you’ve done here? What this shows is a prime example of ‘simple solutions often work best’. Does the movement of our solar system in and out of the galactic plane present any significant basis for effects on our climate. Even though it is only every 26 million years or so. Thanks. JBP

    • R Graf says:

      Cosmic rays were found by CERN in 2012 to aid cloud seeding. Clouds are figured as a net cooling influence on Earth. Also, most cosmic rays are deflected by ours and the suns magnetic shield (Van Allen Belt) except when the polarity is changing. The sun flips every 11 years and the Earth about 100,000 to a million years. The Earth’s shield can also be temporarily be compromised by a coronal mass ejection from the Sun. Personally I think the ocean currents are paramount in Earth surface temp.

  6. Bob Peckham says:

    Jackie asks: “Does the movement of our solar system in and out of the galactic plane present any significant basis for effects on our climate. Even though it is only every 26 million years or so”.

    In this context H. Svensmark, in a paper entitled “Evidence of nearby supernovae affecting life on Earth” has shown fairly convincingly that the movement of the solar system through the spiral arms of the galaxy has influenced the earth’s climate over the past 500 Million years. According to his theory (if I’ve understood it) as the solar system passes through the spiral arms the earth is exposed to a greater flux of Galactic Cosmic Rays (GCR) coming from supernovae. More GCRs provoke more cloud formation, raising the albedo, and thereby causing cooling leading to ice ages and lowering of sea levels. The results tie in very neatly with variations in marine biodiversity seen in the geological record.
    See the full paper in:

    So if this theory is correct the effects of the movement of the solar system through the spiral arms, and in and out of the galactic plane would have an effect on earth’s climate – and this effect would have to be superimposed on the effects of the Milankovitch cycles to get the full story. Wouldn’t it Clive?

    Bob P.

  7. Clive Best says:

    Bob, Jackie,

    According to Wikipedia the Sun takes 230 million years to orbit the centre of the Milky Way. During that time it traverses through about 6 or so spiral arms. This must effect the climate on Earth in some way. The time scales are too long to play a role in the recent regular glaciations every 100,000 years. However they must effect long term temperature trends including cloudiness through cosmic ray flux.

    Perhaps ice ages can be better understood by comparing the rate of change in temperature with Milankovitz cycles. There is a paper by Gerard Roe (GRL) which shows much better agreement between rate of change or ice volume(T) and insolation. see -below.

    However it is still not obvious what triggers the end of an Ice Age.

  8. Clive:
    I don’t know where it best to bring up what I consider to be related. But the book listed below has a chapter on Glaciogenesis: The Cause of the Ice Epoch,” Chapter VI which may be of interest.

    Patten, Donald W. (1966) The Biblical Flood and the Ice Epoch: A Study in Scientific History, (Pacific Meridian Publishing Co. 13540 39th Av. NE, Seattle, WA 98125), [Online: html – and a pdf version at –]

    One major fact that the theory covers is how rapidly the mammoths etc. were fast-frozen in Siberia and Alaska. In some cases the animal’s last meal had not even been digested before being frozen.

    This catastrophe may have been the last Ice Age but it surely came on quickly.

  9. JBP says:

    Hey its almost been 100,000 years since my last post. Are we gonna heat up some more or cool off now. Seriously, why doesn’t your work here get more recognition?

  10. Stu L says:

    I have read a theory, that ice ages end suddenly, because of seal levels, when the sea level lowers to a certain amount the huge stores of methane hydrates do not have sufficient pressure to keep them locked up as hydrates and they bubble up to atmosphere, causing warming

  11. Good job Clive. Best theory I’ve seen so far.

  12. Jackie Pratt says:

    Clive, just reread this (for the x-teenth time, it is intriguing) and noticed one of your sentences states:

    “From 600-900 million years ago the duration of Ice Ages shorten slightly to 84,000 years and further back disappear completely”

    Was that supposed to be:
    “From 600-900 thousand years ago the duration of Ice Ages shorten slightly to 84,000 years and further back disappear completely”

    Great stuff. Congrats on the posting with the UK ECC IPCC submission. Thanks


  13. John Reid says:

    Clive, your combined fit back to 900,000 ya is pretty good I must admit, but there is no physical basis for choosing the amplitudes and phases of the sub-harmonics of the 41 ka obliquity cycle. Physically all we can say is that sometimes obliquity triggers a termination and sometimes it does not at random. Hence interglacials tend to be 40, 80 and 120 ka apart. In such a situation would it always be possible to get an apparent fit by suitable selection of amplitudes and phases of the subharmonics? Perhaps a Monte Carlo experiment could settle this.

    • Clive Best says:

      I think there is a physical basis for the 41ka obliquity cycle because one or other of the poles is receiving higher summer insolation with higher obliquity. The summed polar insolation shows a regular increase. For the first 4 million years the glaciation cycle was ended regularly with maximum obliquity. As general cooling continued the ice sheets becam too large for a single cycle to melt them back and something else was needed. There was a small period when 2 cycles were sufficient before the current phase set in with 3 obliquity cycles coincident with maximum eccentricity. The possible reason for that is another story


  14. John Reid says:

    What I meant was: what is your justification for including a component of 83.77 ky period (angular frequency = .075) and what is the physical significance of its phase and amplitude?
    See Huybers, P., Wunsch, C., 2005. Obliquity pacing of the late Pleistocene glacial terminations. Nature 434, 491-494: “… According to our analysis, the null hypothesis that glacial terminations are independent of obliquity can be rejected at the 5% significance level, whereas the corresponding null hypotheses for eccentricity and precession cannot be rejected. The simplest inference consistent with the test results is that the ice sheets terminated every second or third obliquity cycle at times of high obliquity, similar to the original proposal by Milankovitch.”
    The existence of a 100ky eccentricity cycle is questionable – terminations are separated by 40, 80 or 120 ky. There is no 100 ky period evident to the naked eye.
    Try plotting the variance spectrum on logarithmic scales. It has an f^-2 spectrum at periods less than 100 ky and it is approximately flat at longer periods. The -2 index implies a random walk and, in my view, the flattening at long periods is due to a bounding process (see ). Conclusion: “Thus the climate of the late Pleistocene can be conceived as a random walk between two temperature boundaries. The upper temperature boundary is characterized by small ice-caps, saturated CO2 and H2O absorption bands with a convection transport atmosphere while the lower temperature boundary is characterized by large ice-caps, low atmospheric CO2 and H2O and a radiation transport atmosphere. Climate oscillates between these two metastable states in a random manner which includes some phase-locking to the obliquity cycle of the earth’s orbit.”
    The bottom line is that climate is primarily a stochastic process not a deterministic one.

  15. brianrlcatt says:

    Please Sir! I know sir! I believe I have quantified a capable physical cause for the interglacial perturbation from the stable glacial state, based on published and validateable observations of quantity and variability. It seems unreasonably hard to get a truly scientific response to this proposition, although I am collecting some eminet geologists who believed the consensual BS until I showed them the numbers, which clearly support the proposition from observations of the emissions through the time period involved. The deterministic, not statistical, model, like me, is simple, so easy to check without anything more than the paper itself. Also being re written, but most numbers are the same. The key to the whole thing is the current 1×10^22 Joules pa of submarine heat de[ositied in the oceans, roughly, from 2,800km^3 of magma pa delivering 1.4×10^9 Joules per tonne currently, also shown to increase by 100’s of percent at Milankovitch maximums., 41Ka and 100Ka.


    Sadly, most deniers appear more interested in arguing about the atmosphere to disprove the activists and seem more obsessed with unreal effects than considering real effects under the oceans – where all the heat is, that control atmospheric temperatures based primarily on SST levels in the tropics, using evaporation and consequential cloud albedo, currently running at 150W/m^2 or so with plenty of range in reserve (most of the rime this control kepan ice free planet stable. Its the cold end when evaporation falls off exponentially we should be worrying about. Warming is taken care of by oceans, has been for 500 Million years at least, through asteroids and Super Volcanoes, etc. No trubs, easy.

    Most responses are that we know internal heat isn’t enough, and volcanoes don’t have a large effect (based on the land based emissive effect of particulate emissions, not the dominant submarine effects) . Which also shows they don’t even read abstracts before rejecting based on prejudice alone, so are no more scientists in their denial of new ideas than are the activists..

    The DWK response.

    Yes it is (Enough and variable enough) , its just geologists were wrong about how much magma emission there is under the oceans. Volcanoes exceed divergent ridges by a factor of c.100. The total amounts of magma were massively underestimated by the geologist consensus. Their assumptions, and hence those of University climate modellers focussed on attributing climate change to CO2, were based on wholly inadequate information that recent work exposes as massively wrong, while also not wanting to rock the CO2 PC grant funding boat. No body publicly joined the dots between the disciplines. So I did :-).

    PS What I was looking for when I came to this blog……. was any Fourier signal from the 2 degree range 1,000 year periodicity change, apparent as superimposed on the the entire ice age temperature record. Is there such a signal. I couldn’t see Fourier power spectrum above, or a table of peak frequencies and % power. Hope I didn’t gloss over it?

    You may also not know of the Madison model that convolves Milankovitch cycles for you and overlays the result on the Vostock ice core record. It also predicts, cooling as you suggest, because that’s happened so many times before at this point in the orbital forcing cycle, and the forces involved are more powerful than a bit of CO2 can change much, or activists can possibly imagine. Enjoy!

  16. Christopher Stearns says:

    Thank-you for this long multi-year discussion on the ice ages! There are some wonderful snippets that show much remains to be properly explained: The Mammoths freezing rapidly while still chewing their food; apparently the onset of temp changes can be quite rapid! The surface erosion features found along continental slopes (underwater in the ocean) well below the lowest full ice age sea levels. No one in the geological community has yet to explain these erosion features. Also found off shore in the northeastern Pacific are former coral reefs from Oregon to Alaska that thrived during the lower sea levels of the past ice ages that are still present and now due to ocean acidity changes are breaking up and getting washed up at Cape Blanco on the Oregon coast.
    One explanation for the onset of continental glaciation could be explained not so much by the temperature changes which do provide the means for it to occur and remain stable. Rather, we should be examining what is the trigger? What provides the mechanism to transfer so much moisture over land that the feedback loops only accelerate the process while it is underway? What is the heat engine that will continue to deliver large quantities of water over ice sheets that will allow them to continue to grow? One idea for this global “heat engine” is to have the planet go through differential heating (in the tropics) and cooling (in the higher latitudes) which would allow a greater temperature differential (or gradient than now exists) possibly creating certain locks in the jet stream (or the circumpolar vortex) that with the increased temperature gradient would produce larger weather systems arriving over land to keep these continental glaciers growing. The reverse could also help explain the eventual end to the ice age as well! Ocean currents could also reinforce this function as well!
    A former grad student of Easterbrook at Western Washington University’s Geology Program many years ago, now a local water commissioner fighting to create more public utilities!

Leave a Reply