The exact cause and evolution of ice ages still remain a mystery . 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. 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  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.
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)
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
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.
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 . The second proposal is that the Tibetan plateau has been slowly rising as India continues to crash into Asia. 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. 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 !
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.
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 http://www.exploratorium.edu/
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)