420 EARTH/Orbital Variation (Including Milankovitch Cycles) Together with improved and more detailed astronomical models, the limits of accuracy of astronomical calculations are also likely to extend further back in time A clearer representation of chaos in the Solar System is provided by amplitude modulation terms The $2.4- and 1.2-My-long amplitude modulation terms that occur in the calculations of eccentricity and obliquity, respectively, are in resonance, and the expression (s4 À s3) À 2(g4 À g3) ¼ can evolve into a new state, where (s4 À s3) À (g4 À g3) ¼ This implies a change from a 1:2 resonance to a 1:1 resonance Laskar found this behaviour to be the main source and representation of chaos in the Solar System As shown in Table 5, these terms are present in several astronomical frequencies, and should be possible to detect in the geological record stronger than expected It is now becoming clear that geological data show a wide variety of responses to individual orbital frequencies, depending on factors such as palaeolatitude, the prevailing oceanographic system at the study site, global ice volume, etc., with records showing much more variation than would be expected from a simple insolation calculation A better understanding of the interaction between Earth’s orbital variations and their imprint on the climate system and geological records is likely going to be gained from integrated Earth system modelling studies, making use of the growing body of observations that has been provided recently by ocean drilling As a final note, orbital variations also affect the other planets of the Solar System, and recent attempts have been made to link these to climatic variations on Venus and Mars Earth’s Orbital Variation Encoded in Geological Data See Also The imprint of Earth’s orbital variation in geological records, first statistically demonstrated in 1976 for the recent geological past, in the seminal paper by Hays and colleagues, has now been found throughout parts of the Cenozoic and beyond, through variations of stable isotope measurements that act as a proxy for Earth’s climate system, as well as in a large number of lithological parameters A review of this body of data is beyond the scope of the present discussion, but it is illustrative to show at least one example of very highquality data that demonstrate the imprint of Earth’s orbital variations in the rock record Figure 10 shows part of a record used to correlate geological data for the past $30 My with astronomical calculations The record shows exceptionally well-encoded obliquity and climatic precession cycles Most importantly, this record also demonstrates the consistent variation in amplitude of the obliquity cycles This can be illustrated with the help of evolutionary spectral analysis, whereby the relative amplitude at individual frequencies is evaluated at different times This is shown in Figure 11 Linking Earth’s orbital variations (Milankovitch cycles) with geological records has caused controversies as to whether the theory that orbital variations driving Earth’s climate conditions can be correct The controversies stem from observations of palaeoclimatic proxies from the recent past that reveal an imprint that does not correspond to the expected strength of orbital variations in insolation calculations, and instead suggest a nonlinear response of the climate system at different orbital frequencies In particular, during the past 800 ky, the imprint of eccentricity in stable isotope records has been much Analytical Methods: Geochronological Techniques Carbon Cycle Earth Structure and Origins Famous Geologists: Agassiz Gaia Magnetostratigraphy Microfossils: Foraminifera Palaeoclimates Solar System: The Sun; Asteroids, Comets and Space Dust; Meteorites; Mercury; Venus; Moon; Mars; Jupiter, Saturn and Their Moons; Neptune, Pluto and Uranus Tektites Tertiary To Present: Pleistocene and The Ice Age Time Scale Further Reading Berger A, Imbrie J, Hays J, Kukla G, and Saltzman B (eds.) (1984) Milankovitch and Climate: Understanding the Response to Astronomical Forcing Dordrecht and Boston: D Reidel Publishing Company Berger A and Loutre MF (1994) Astronomical forcing through geological time In: de Boer PL and Smith DG (eds.) Orbital Forcing and Cyclic Sequences (IAS Special Publication), vol 19, pp 15 24 Oxford: Blackwell Scientific Berger A, Loutre MF, and Tricot C (1993) Insolation and Earth’s orbital periods Journal of Geophysical Research 98(D6): 10341 10362 de Boer PL and Smith DG (eds.) (1994) Orbital Forcing and Cyclic Sequences (IAS Special Publication), vol 19 Oxford: Blackwell Scientific Publications Croll J (1875) Climate and Time in their Geological Rela tions: A Theory of Secular Changes of the Earth’s Climate London: Daldy, Tsbister and Co Einsele G, Ricken W, and Seilacher A (eds.) (1991) Cycles and Events in Stratigraphy Berlin: Springer Verlag Gilbert GK (1895) Sedimentary measurement of Cret aceous time Journal of Geology III: 121 127 Hays JD, Imbrie J, and Shackleton NJ (1976) Variations in the Earth’s orbit: pacemaker of the Ice Ages Science 194(4270): 1121 1131