416 EARTH/Orbital Variation (Including Milankovitch Cycles) interpretation of Milankovitch’s theory, which would imply that the ice-ages are best explained by the summer insolation curve computed at 65 N Instead, a better understanding of the complex mechanisms of the climate system will have to be achieved through the use of geological data providing boundary conditions for climate models they display modulations in amplitude and frequency These modulations provide a ‘fingerprint’ of a particular astronomical calculation at a given time The modulation terms arise through the interference of individual cycles to produce ‘beats’, with periods ranging from hundreds of thousands to millions of years The most prominent amplitude modulation cycles are listed in Table An excellent visual representation of amplitude modulation cycles in astronomical calculations can be obtained by computing evolutionary or wavelet spectra, which show the variation in amplitude at different frequencies over time This is shown in Figure for the past 10 million years Amplitude Modulation Patterns: The ‘Fingerprint’ of Orbital Cycles A very important feature of Earth’s eccentricity, obliquity, and climatic precession variations is that Figure Earth’s insolation over time (1.2 million years) at various latitudes and frequency analysis for a 10 My time span (on a logarithmic amplitude scale); the numbers over the peaks represent the periods (in thousands of years) The precession component is out of phase between the northern hemisphere summer and the southern hemisphere summer Note that the eccentricity component in insolation computations is always very weak compared to the obliquity and precession components Also note the latitudinal dependence of the relative strength of the obliquity cycle in the insolation curves Table Modulation termsa Type Interfering terms Short eccentricity amplitude modulation terms (g4 (g3 g5) g5) (g4 (g3 Short and long eccentricity amplitude modulation terms (g4 (g4 g5) g2) (g3 (g3 Climatic precession amplitude modulation terms Identical to eccentricity frequencies and amplitude modulation terms Obliquity amplitude modulation terms ‘Beat’ term g2) g2) g5) g2) (p ỵ s3) (p ỵ s4) ỵ g3 ) (p ỵ s3 þ g4 g3) (p þ s3 g4 (p þ s3) (p ỵ s3 ỵ g4 g3) (p ỵ s3) (p þ s3 þ g4 g3) (p þ s3) (p þ s6) g5 Þ (g2 Period % g3 Þ ðg4 400 ky % 2.4 My (s3 s4) (2g4 2g3) % % 1.2 My 1.2 My g3 Þ % 2.4 My % 173 ky ðg4 (s3 s6) a Origin of amplitude modulation terms that affect Earth’s eccentricity, obliquity, and climatic precession Individual gi and si terms refer to those given in Table The $100 ky (short) eccentricity cycles are modulated with a period of $400 ky by the long eccentricity cycle Both short and long eccentricity cycles are modulated with a period of 2.4 My, but with a phase difference of 180 (i.e., an amplitude maximum of the $100 ky eccentricity coincides with an amplitude minimum of the $400 ky eccentricity) Because eccentricity directly modulates the climatic precession, all eccentricity amplitude modulation terms are also present in the climatic precession signal The obliquity signal is weakly amplitude modulated with a period of $170 ky, and more strongly with a period of 1.2 My This amplitude modulation cycle is dynamically linked with the 2.4 My cycle present in the eccentricity modulation All period cycles listed here are shown in Figure